lcd screen size calculator free sample

The screen size calculator can help you in determining the screen dimensions. Have you ever wondered what the statement, the diagonal of the screen is equal to 40", means? How much space does it take up on the wall? What are its height and width? Here you can determine the monitor size or phone screen dimensions. If you"re curious enough, you can even determine how to measure a curved TV screen size!

If you want to find the ideal size of your TV or its distance from your eyes, check out this TV size calculator. Another useful tool is this great projector calculator, which can help in fulfilling your dreams about a home cinema.

Aspect ratio is the relationship between the height and width of a rectangular display. Every device with a screen uses that value - your laptop, smartphone, tablet, monitor, or projector. However, it doesn"t tell you how big a screen is. It only explains the proportion between the height and the width.

The value 5.8-inch stands for the diagonal of the screen. To check whether that smartphone will fit in your pocket, you will need to know one more parameter - the aspect ratio, the width, or the screen"s height. In our example, let"s assume we know the aspect ratio, and it is equal to 16:9:

Let"s say we want to compare two smartphones: The Apple iPhone X with a 5.85-inch display and the iPhone 8 Plus, which has a 5.5-inch screen. We could expect that the former would have a bigger screen, but we can"t forget about aspect ratios! iPhone X has a narrower screen with a 2.17:1 ratio, and iPhone 8 Plus has a standard 16:9.

Repeat the steps for iPhone 8 Plus, choosing a 16:9 aspect ratio and 5.5-inch diagonal. And what do you get? 4.8" for screen width, 2.7" height, and 12.93 in² screen size. So even though the first iPhone has a longer diagonal, the screen size is smaller than in iPhone 8 plus. (iPhone X also has the big cutout and the curved edges, but we are not taking them into account - even with that simplification, the screen area is smaller).

Our screen size calculator offers the possibility to estimate both a flat and curved screen size. As we"ve already learned how to proceed with a flat monitor, let"s see the differences for a curved one.

How do I measure a curved TV screen size, then? - you may ask. To evaluate the screen"s length, height, and area, we can follow the same equations as for a flat one:

The crucial geometric difference between the curved and flat monitor is that the curved one occupies more space perpendicular to the screen from a user"s point of view while being a little narrower. We call these dimensions depth and width, respectively. To avoid confusion, we can depict all essential measures in a single picture.

Assuming the screen"s length is the arc length of a circle, we can find the base depth and width by using the following formulas which we use in the screen size calculator:

If you"re after the size of the screen"s diagonal, you can either measure it or use Pythagoras" theorem where a & b are the screen"s length and width.

The size of a 16:9 screen depends on how long the screen"s diagonal is, as 16:9 is merely the ratio of the screen"s width to its height. If you have the screens diagonal, you can multiply that measurement by 0.872 to get the screen"s width. You can also multiply the diagonal by 0.49 to get the screen"s height. Then, if you wish to find the screen area, multiply the width by the height.

and a screen the image will also increase. If your projector has a zoom lens, the lens can be adjusted to change the size of the screen image without changing

the distance of the projector. Since each projector lens is different, an online projection calculator tool will help you calculate the size of an image

A short throw projector is a projector with a lens that has a throw ratio of 0.4 (distance/width) or less. These projectors are ideal for rear screen applications

where the area behind the screen is limited, or for a wall mounted application where the projector will be mounted within 1 or 2 feet from the screen. The

A lot goes into determining the best viewing distance, and there are several different criteria you can use. Aside from size, things like resolution and even how strong your eyesight is can affect how you see the screen. Because everyone"s eyesight is different, this is less an exact science and more of a general guide based on scientific principles of vision and resolution.

That doesn"t mean you should be sitting a foot away from your TV. Having the largest screen possible isn"t always ideal. The human visual system has a total horizontal field of view of about 200 degrees, although a portion of that is peripheral vision. While it makes some sense to get as large a TV as you can for movies, not all content is made to fill the entire field of view. This becomes very apparent if you try to watch sports from up close while fixating on a single part of the screen, which quickly starts to feel nauseating.

The Society of Motion Picture and Television Engineers recommends sitting at a distance where the screen fills up a minimum of 30° of your field of vision for a good experience.

This is generally good guidance, but people who use their TVs mostly for watching movies might benefit from sitting a bit closer to get a more theater-like experience. The SMPTE "reference" position for movie theaters and the THX recommendation is about 40°. The minimum angle of vision works well for most usages, though, and sitting at a distance where the screen fills 30° of your horizontal field of view should be comfortable for most people.

Our size and distance tool above is based on the 30° guideline that is suitable for mixed usage, but you can find distances for a variety of sizes at 40° here.Learn more about the human visual field.

For instance, sitting close to a 1080p TV can look almost like watching through a screen door because you can see the individual pixels, even if it"s playing a high-quality 1080p HD movie. Increasing your distance to the TV also increases the density of details, producing a better image. Since 4k TVs have such a large density of pixels, it"s much more difficult for this issue to arise. You need to be quite close to a fairly large TV for the pixels to be noticeably distracting.

With 8k TVs, that density increases further, making it even harder to notice flaws with the resolution unless you"re sitting extremely close. However, this also decreases the point at which the perceived difference in picture quality becomes noticeable. Because the pixels are more densely packed with an 8k resolution, you need to sit closer to actually resolve those details. For that reason—content aside—8k only really makes sense if you want a really big screen and plan on sitting close to it. Learn more about the difference between 4k and 8k.

This chart shows the point at which an upgrade in resolution becomes worth it depending on size and distance to the TV. Each line represents the optimal viewing distance for each resolution, but any TV that falls within the range of that color will be suitable to notice a difference in picture quality. So, for example, if you have a 65 inch TV, the viewing distance at which the eye can actually process the details of 4k content is about 4 feet. However, any distance between 4 and about 8.5 feet will be enough to appreciate the difference between 4k and 1080p on a 65 inch TV. Go too far, and the image will look identical to 1080p HD.

The chart suggests that at a certain point, 4k UHD may not be worth the upgrade—if you"re sitting more than 7 feet away and have a 55" TV, for instance. Really, though, this chart is just a guide, and as 4k TVs have become the standard, the question of whether it"s worth it or not is a moot point. While your eyes may not be able to tell the difference at a certain point, your next TV will more than likely be a 4k TV anyway. Knowing the optimal viewing distance for the resolution can help you determine a living room setup that takes full advantage of your TV"s resolution, but since angular resolution is almost a non-issue with UHD content, we recommend using our calculator tool at the top of the page, which is based on the optimal field of vision.

You"re probably thinking something along the lines of "My couch is 10" away from my TV, which according to the chart means I need a 75 inch TV. This is insane!" It"s true that if you want to take full advantage of higher resolutions, that"s the ideal size you should get. That said, this may not be possible for everyone, which brings us to budget.

The price of a TV is usually exponential to its size. Size isn"t the only factor though, as resolution, panel type, and features all play into it as well. Looking at 65 inch TVs, for instance, an OLED like the LG CX OLED is inevitably going to cost more than a budget LED TV like the Hisense H8G, and both of these will seem downright cheap compared to an 8k TV like the Samsung Q900TS 8k QLED. Fortunately, though, as technology improves and the availability of higher resolution TVs expands, larger TVs have become more common and therefore more affordable. Feel free to compare the prices of our picks for the best 65 inch TVs, the best 70 to 75 inch TVs, and the best 80 to 85 inch TVs to really see the difference that size makes.

We recommend a field of vision of about 30 degrees for mixed usage. In general, we also recommend getting a 4k TV since lower resolution TVs are becoming harder to find. To easily find out what size you should buy, you can divide your TV viewing distance (in inches) by 1.6 (or use our TV size calculator above) which roughly equals a 30-degree angle. If the best size is outside your budget, just get the biggest TV you can afford. These are guidelines, after all, and since most TVs nowadays are 4k, you can"t really go wrong with the size that works for you, especially since picture quality also depends a lot on the content and viewing conditions. Ideally, you would optimize the capacity of your TV by getting one that"s large enough for you to notice all the visual detail that 4k has to offer, but ultimately, you should watch however feels most comfortable to you, whatever the size and distance may be.

If you already have a TV, then enter the TV size to find out how far you should place your seating. If you are looking for a TV, then enter the distance from your seating position to the TV to determine which size TV you should purchase.

Believe it or not, there is actually a science to choosing how big of a TV you should get for the optimal viewing experience. There are several factors to consider when selecting a TV size, notably distance and viewing angle, resolution, and the type of content you’ll be viewing.

There are a number of ratios that get roughly close. Multiplying the seating distance by 0.6 will yield a TV size that will be close to a 30° viewing angle, while multiplying the seating distance by 0.84 will get you a TV size close to the 40° viewing angle.

Since these viewing angles are the horizontal viewing angles, the result will be the ideal TV width. Then, using an aspect ratio calculator you can find the screen height to get the ideal TV size.

What you watch on your TV will determine the optimal size and viewing distance. If you intend to watch 4k Bluray movies, you’ll want to choose a TV size with a viewing angle closer to the 40° mark for the most immersive experience.

Part of selecting the right TV for you also involves figuring out what the best viewing distance is for the TV. And that might depend on a few factors such as the size of the room, the type of the room, the use of the TV, and its resolution.

The room’s size will certainly determine the maximum viewing distance, which will undoubtedly have an impact on just how big of a TV can fit in the space.

As discussed above, the screen viewing angle is a significant factor in determining the optimal viewing distance. The chart below shows the optimal viewing distances for various TV sizes in the suggested 26° – 40° range.

The TV’s resolution will also play a role in how far you can sit from the TV. There is a point at which your eyes can make out the individual pixels of the TV screen, and the picture begins to degrade based on your visual acuity.

The number of pixels on a display in relation to the size is known as pixel density, and it’s measured in pixels per inch, or PPI. Use our PPI calculator to measure the pixel density of your screen.

If you can’t see the pixels on the screen at 1080p resolution, then an upgrade to 4K might not be noticeable. If your seating distance is closer than the minimum viewing distance for the 1080p resolution, then an upgrade to 4k will be a noticeable improvement.

Safety should also be considered. When placing the TV on a piece of furniture, be sure to consider the TV’s size and weight and the furniture’s weight limit.

Consider the best height to mount your TV, which could determine how large the screen can be. The height of the TV may change the room’s aesthetics and may be a determining factor.

Finally, the budget should factor into your decision when selecting a TV size or resolution. Larger screens and higher resolution displays cost more, and it would be wise to evaluate the cost of the display into the decision when selecting the ideal TV for your application.

The PPI Calculator finds pixels per inch (PPI) and pixels per centimeter (PPcm). It will calculate PPI when inches are entered and calculate both PPI and PPcm when centimeters are entered.

PPI is a measure of pixel density or resolution of a computer screen, television screen or other display device. Pixels per inch or PPcm indicates how many pixels are in a 1 inch line or 1 cm line on a display. Also calculated are dot pitch, diagonal in pixels and total number in megapixels.

The number of pixels per inch or PPI tells you how many pixels are in a 1 inch line on a display screen. The PPI will be the same whether it"s a horizontal or vertical or diagonal inch because pixels are square and therefore symmetric. If a display does not have square pixels then this calculator does not apply.

You have a computer screen that is 1920 pixels wide by 1080 pixels high. The diagonal is 10 inches. You want to find the pixel density in one linear inch of display.

For example, let"s say you have a screen width equal to 1920 pixels and height equal to 1080 pixels. The ratio of width to height is 1920:1080. To reduce this to lowest terms we find the

To determine what projection screen dimensions you will need based on a diagonal screen size use the projection screen size calculator below, this should be used for a general guideline for Projection Screens sizes, Plasma, LCD and LED Flat Panel

Displays diagonal screen sizes. Use this for both 4:3 and 16:9 aspect ratios; this is great for front and rear rigid projection screens and adhesive rear projection film screens sizes calculation.

To determine what projection screen dimensions you will need based on a diagonal screen size use the projection screen size calculator below, this should be used for a general guideline for Projection Screens sizes, Plasma, LCD and LED Flat Panel

Displays diagonal screen sizes. Use this for both 4:3 and 16:9 aspect ratios; this is great for front and rear rigid projection screens and adhesive rear projection film screens sizes calculation.

Currently, there are two main types of TV – an LED and an OLED TV. You might be surprised to know that these TV types are available in very different screen sizes.

Some of the numbers presented here are based on the excellent work by Carlton Bale. If you like working with spreadsheets, you might want to download his home theater spreadsheet calculator.

Therefore, a 26° FOV is the furthest distance from the screen they recommend – but, ideally, the best distance would be a field of view of 36° or closer.

Here is a calculator for working out the recommended viewing distance for a 16:9 screen based on the field of view. Just select your screen size to see the results.

As stated previously, there is no absolute right or wrong here. It will often come down to personal taste, your eyesight or how you use the screen in your room.

One popular rule-of-thumb is to simply use one foot of viewing distance for each 10-inches of diagonal screen size. This might sound more complicated than it is:

So, for example, if you know the viewing distance in your room will be about 10 feet (or 120-inches), you can work out that a good TV size will be in the range of:

Now, that still gives you quite a bit of choice, but at least you can rule out screens below 48-inches, and you have a better idea of where to start looking.

The simple answer is that the brand of your TV doesn’t matter. Regardless of who makes it, they all have the same essential specifications – screen size and resolution.

If you mainly watch high-definition or 4K Ultra HD images, a larger screen will allow you to appreciate the extra detail – and it will also look great if you sit very close.

If you mostly watch movies, sports and documentaries – anything where you sit down for an extended period and concentrate – then a larger screen is perfect for appreciating the action and detail.

On the other hand, if much of your TV viewing is for shorter programs that require less attention – or your TV is on ‘in the background’ much of the time – a bigger screen may be too overwhelming in the room.

Due to the size of the wall – and because the screen appears more ‘removed’ from the room – it can often make a bigger TV appear smaller and less noticeable.

A large shop floor with many other TVs around can make it difficult to judge the size of a screen. If possible, try and see a similar-sized screen in someone’s home where you will get a better perspective on the size.

Get a feel for a good viewing distance by working it out from your screen size – then consider how you will be using the TV and the type of things you will watch.

After that, you need to consider things like the type of images you will be watching on the TV, how you will be using the screen and the location in the room you will be installing it.

One way to work out what size TV to buy for a specific viewing distance is to use the field of view. If you multiply your viewing distance (in feet) by 6.5, you will get a diagonal screen size (in inches). This will be the minimum screen size you should look for, according to the THX maximum viewing distance of a 26° field of view. Alternatively, use a calculator to get the best TV size for the room.

The best way to calculate the optimal viewing distance for a TV is to use the field of view (FOV). THX recommends a viewing distance that gives a FOV of 36°. The ideal distance will vary depending on the size of your TV. The easiest way to calculate this is to use a TV distance calculator.

It is usually best to calculate the viewing distance from the field of view to the screen. Using the typical field of view numbers of 26° and 36°, the ideal screen size for a 12-foot distance is between 78 and 108-inches.

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Pixels per inch (ppi) and pixels per centimetre (ppcm or pixels/cm) are measurements of the pixel density of an electronic image device, such as a computer monitor or television display, or image digitizing device such as a camera or image scanner. Horizontal and vertical density are usually the same, as most devices have square pixels, but differ on devices that have non-square pixels. Note that pixel density is not the same as pixel has no inherent size or unit (a pixel is actually a sample), but when it is printed, displayed, or scanned, then the pixel has both a physical size (dimension) and a pixel density (ppi).

Since most digital hardware devices use dots or pixels, the size of the media (in inches) and the number of pixels (or dots) are directly related by the "pixels per inch". The following formula gives the number of pixels, horizontally or vertically, given the physical size of a format and the pixels per inch of the output:

Pixels per inch (or pixels per centimetre) describes the detail of an image file when the print size is known. For example, a 100×100 pixel image printed in a 2 inch square has a resolution of 50 pixels per inch. Used this way, the measurement is meaningful when printing an image. In many applications, such as Adobe Photoshop, the program is designed so that one creates new images by specifying the output device and PPI (pixels per inch). Thus the output target is often defined upon creating the image.

Now, let us imagine the artist wishes to print a larger banner at 48″ horizontally. We know the number of pixels in the image, and the size of the output, from which we can use the same formula again to give the PPI of the printed poster:

Printing on paper is accomplished with different technologies. Newspapers and magazines were traditionally printed using a screen called a lines per inch (LPI) by using a purely analog process in which a photographic print is converted into variable sized dots through interference patterns passing through a screen. Modern inkjet printers can print microscopic dots at any location, and don"t require a screen grid, so they use a metric called dots per inch (DPI). These are both different from pixel density or pixels per inch (PPI) because a pixel is a single sample of any color, whereas an inkjet print can only print a dot of a specific color either on or off. Thus a printer translates the pixels into a series of dots using a process called

Often one wishes to know the image quality in pixels per inch (PPI) that would be suitable for a given output device. If the choice is too low, then the quality will be below what the device is capable of—loss of quality—and if the choice is too high then pixels will be stored unnecessarily—wasted disk space. The ideal pixel density (PPI) depends on the output format, output device, the intended use and artistic choice. For inkjet printers measured in dots per inch it is generally good practice to use half or less than the DPI to determine the PPI. For example, an image intended for a printer capable of 600 dpi could be created at 300 ppi. When using other technologies such as AM or FM screen printing, there are often published screening charts that indicate the ideal PPI for a printing method.

The outside of the square shown above is 200 pixels by 200 pixels. To determine a monitor"s ppi, set the OS DPI scaling setting at 100% and the browser"s zoom at 100%, then measure the width and height, in inches, of the square as displayed on a given monitor. Dividing 200 by the measured width or height gives the monitor"s horizontal or vertical ppi, respectively, at the current screen resolution.

The PPI/PPCM of a computer display is related to the size of the display in inches/centimetres and the total number of pixels in the horizontal and vertical directions. This measurement is often referred to as dots per inch, though that measurement more accurately refers to the resolution of a computer printer.

For example, a 15-inch (38 cm) display whose dimensions work out to 12 inches (30.48 cm) wide by 9 inches (22.86 cm) high, capable of a maximum 1024×768 (or XGA) pixel resolution, can display around 85 PPI, or 33.46PPCM, in both the horizontal and vertical directions. This figure is determined by dividing the width (or height) of the display area in pixels by the width (or height) of the display area in inches. It is possible for a display to have different horizontal and vertical PPI measurements (e.g., a typical 4:3 ratio CRT monitor showing a 1280×1024 mode computer display at maximum size, which is a 5:4 ratio, not quite the same as 4:3). The apparent PPI of a monitor depends upon the screen resolution (that is, the number of pixels) and the size of the screen in use; a monitor in 800×600 mode has a lower PPI than does the same monitor in a 1024×768 or 1280×960 mode.

Typical circa-2000 cathode ray tube or LCD computer displays range from 67 to 130 PPI, though desktop monitors have exceeded 200 PPI, and certain smartphone manufacturers" flagship mobile device models have been exceeding 500 PPI since 2014.

Holography applications demand even greater pixel density, as higher pixel density produces a larger image size and wider viewing angle. Spatial light modulators can reduce pixel pitch to 2.5 μm, giving a pixel density of 10,160 PPI.

High pixel density display technologies would make supersampled antialiasing obsolete, enable true WYSIWYG graphics and, potentially enable a practical “paperless office” era.screen size would have to display more than four Full HD screens (or WQUXGA resolution).

The PPI pixel density specification of a display is also useful for calibrating a monitor with a printer. Software can use the PPI measurement to display a document at "actual size" on the screen.

PPI can be calculated from knowing the diagonal size of the screen in inches and the resolution in pixels (width and height). This can be done in two steps:

Note that these calculations may not be very precise. Frequently, screens advertised as “X inch screen” can have their real physical dimensions of viewable area differ, for example:

Camera manufacturers often quote view screens in "number of dots". This is not the same as the number of pixels, because there are 3 "dots" per pixel – red, green and blue. For example, the Canon 50D is quoted as having 920,000 dots.

Length refers to horizontal and vertical size in inches, centimeters, etc., whereas pixel refers only to the number of pixels found along the horizontal and vertical dimension.

Support in SVG differs. The standard supports the floats pixelUnitToMillimeterX, pixelUnitToMillimeterY, screenPixelToMillimeterX and screenPixelToMillimeterY for use in CSS2.

This article is about the electronic device. For mechanical precursors to the modern calculator, see mechanical calculator. For other uses, see Calculator (disambiguation).

An electronic calculator is typically a portable electronic device used to perform calculations, ranging from basic arithmetic to complex mathematics.

The first solid-state electronic calculator was created in the early 1960s. Pocket-sized devices became available in the 1970s, especially after the Intel 4004, the first microprocessor, was developed by Intel for the Japanese calculator company Busicom.

Modern electronic calculators vary from cheap, give-away, credit-card-sized models to sturdy desktop models with built-in printers. They became popular in the mid-1970s as the incorporation of integrated circuits reduced their size and cost. By the end of that decade, prices had dropped to the point where a basic calculator was affordable to most and they became common in schools.

Computer operating systems as far back as early Unix have included interactive calculator programs such as dc and hoc, and interactive BASIC could be used to do calculations on most 1970s and 1980s home computers. Calculator functions are included in most personal digital assistant (PDA) type devices.

In addition to general purpose calculators, there are those designed for specific markets. For example, there are scientific calculators which include trigonometric and statistical calculations. Some calculators even have the ability to do computer algebra. Graphing calculators can be used to graph functions defined on the real line, or higher-dimensional Euclidean space. As of 2016

With the very wide availability of smartphones, tablet computers and personal computers, dedicated hardware calculators, while still widely used, are less common than they once were. In 1986, calculators still represented an estimated 41% of the world"s general-purpose hardware capacity to compute information. By 2007, this had diminished to less than 0.05%.

Electronic calculators contain a keyboard with buttons for digits and arithmetical operations; some even contain "00" and "000" buttons to make larger or smaller numbers easier to enter. Most basic calculators assign only one digit or operation on each button; however, in more specific calculators, a button can perform multi-function working with key combinations.

Calculators usually have liquid-crystal displays (LCD) as output in place of historical light-emitting diode (LED) displays and vacuum fluorescent displays (VFD); details are provided in the section

Large-sized figures are often used to improve readability; while using decimal separator (usually a point rather than a comma) instead of or in addition to vulgar fractions. Various symbols for function commands may also be shown on the display. Fractions such as 1⁄3 are displayed as decimal approximations, for example rounded to 0.33333333. Also, some fractions (such as 1⁄7, which is 0.14285714285714; to 14 significant figures) can be difficult to recognize in decimal form; as a result, many scientific calculators are able to work in vulgar fractions or mixed numbers.

Calculators also have the ability to store numbers into computer memory. Basic calculators usually store only one number at a time; more specific types are able to store many numbers represented in variables. The variables can also be used for constructing formulas. Some models have the ability to extend memory capacity to store more numbers; the extended memory address is termed an array index.

Power sources of calculators are batteries, solar cells or mains electricity (for old models), turning on with a switch or button. Some models even have no turn-off button but they provide some way to put off (for example, leaving no operation for a moment, covering solar cell exposure, or closing their lid). Crank-powered calculators were also common in the early computer era.

The following keys are common to most pocket calculators. While the arrangement of the digits is standard, the positions of other keys vary from model to model; the illustration is an example.

Display panel (output device) – displays input numbers, commands and results. Liquid-crystal displays (LCDs), vacuum fluorescent displays (VFDs), and light-emitting diode (LED) displays use seven segments to represent each digit in a basic calculator. Advanced calculators may use dot matrix displays.

A printing calculator, in addition to a display panel, has a printing unit that prints results in ink onto a roll of paper, using a printing mechanism.

Clock rate of a processor chip refers to the frequency at which the central processing unit (CPU) is running. It is used as an indicator of the processor"s speed, and is measured in clock cycles per second or hertz (Hz). For basic calculators, the speed can vary from a few hundred hertz to the kilohertz range.

Most pocket calculators do all their calculations in binary-coded decimal (BCD) rather than binary. BCD is common in electronic systems where a numeric value is to be displayed, especially in systems consisting solely of digital logic, and not containing a microprocessor. By employing BCD, the manipulation of numerical data for display can be greatly simplified by treating each digit as a separate single sub-circuit. This matches much more closely the physical reality of display hardware—a designer might choose to use a series of separate identical seven-segment displays to build a metering circuit, for example. If the numeric quantity were stored and manipulated as pure binary, interfacing to such a display would require complex circuitry. Therefore, in cases where the calculations are relatively simple, working throughout with BCD can lead to a simpler overall system than converting to and from binary. (For example, CDs keep the track number in BCD, limiting them to 99 tracks.)

Where calculators have added functions (such as square root, or trigonometric functions), software algorithms are required to produce high precision results. Sometimes significant design effort is needed to fit all the desired functions in the limited memory space available in the calculator chip, with acceptable calculation time.

The fundamental difference between a calculator and computer is that a computer can be programmed in a way that allows the program to take different branches according to intermediate results, while calculators are pre-designed with specific functions (such as addition, multiplication, and logarithms) built in. The distinction is not clear-cut: some devices classed as programmable calculators have programming functions, sometimes with support for programming languages (such as RPL or TI-BASIC).

For instance, instead of a hardware multiplier, a calculator might implement floating point mathematics with code in read-only memory (ROM), and compute trigonometric functions with the CORDIC algorithm because CORDIC does not require much multiplication. Bit serial logic designs are more common in calculators whereas bit parallel designs dominate general-purpose computers, because a bit serial design minimizes chip complexity, but takes many more clock cycles. This distinction blurs with high-end calculators, which use processor chips associated with computer and embedded systems design, more so the Z80, MC68000, and ARM architectures, and some custom designs specialized for the calculator market.

In 1642, the Renaissance saw the invention of the mechanical calculator (by Wilhelm SchickardBlaise Pascalarithmetic operations with minimal human intervention.Pascal"s calculator could add and subtract two numbers directly and thus, if the tedium could be borne, multiply and divide by repetition. Schickard"s machine, constructed several decades earlier, used a clever set of mechanised multiplication tables to ease the process of multiplication and division with the adding machine as a means of completing this operation. There is a debate about whether Pascal or Shickard should be credited as the known inventor of a calculating machine due to the differences (like the different aims) of both inventions.Gottfried Leibniz who spent forty years designing a four-operation mechanical calculator, the stepped reckoner, inventing in the process his leibniz wheel, but who couldn"t design a fully operational machine.

The 18th century saw the arrival of some notable improvements, first by Poleni with the first fully functional calculating clock and four-operation machine, but these machines were almost always one of a kind. Luigi Torchi invented the first direct multiplication machine in 1834: this was also the second key-driven machine in the world, following that of James White (1822).Industrial Revolution that real developments began to occur. Although machines capable of performing all four arithmetic functions existed prior to the 19th century, the refinement of manufacturing and fabrication processes during the eve of the industrial revolution made large scale production of more compact and modern units possible. The Arithmometer, invented in 1820 as a four-operation mechanical calculator, was released to production in 1851 as an adding machine and became the first commercially successful unit; forty years later, by 1890, about 2,500 arithmometers had been soldcomptometers.

In 1921, Edith Clarke invented the "Clarke calculator", a simple graph-based calculator for solving line equations involving hyperbolic functions. This allowed electrical engineers to simplify calculations for inductance and capacitance in power transmission lines.

The Curta calculator was developed in 1948 and, although costly, became popular for its portability. This purely mechanical hand-held device could do addition, subtraction, multiplication and division. By the early 1970s electronic pocket calculators ended manufacture of mechanical calculators, although the Curta remains a popular collectable item.

The first mainframe computers, using firstly vacuum tubes and later transistors in the logic circuits, appeared in the 1940s and 1950s. This technology was to provide a stepping stone to the development of electronic calculators.

The Casio Computer Company, in Japan, released the Model 14-A calculator in 1957, which was the world"s first all-electric (relatively) compact calculator. It did not use electronic logic but was based on relay technology, and was built into a desk.

In October 1961, the world"s first all-electronic desktop calculator, the British Bell Punch/Sumlock Comptometer ANITA (A New Inspiration To Arithmetic/Accounting) was announced.vacuum tubes, cold-cathode tubes and Dekatrons in its circuits, with 12 cold-cathode "Nixie" tubes for its display. Two models were displayed, the Mk VII for continental Europe and the Mk VIII for Britain and the rest of the world, both for delivery from early 1962. The Mk VII was a slightly earlier design with a more complicated mode of multiplication, and was soon dropped in favour of the simpler Mark VIII. The ANITA had a full keyboard, similar to mechanical comptometers of the time, a feature that was unique to it and the later Sharp CS-10A among electronic calculators. The ANITA weighed roughly 33 pounds (15 kg) due to its large tube system.Pilot ACE computer project, to lead the development. The ANITA sold well since it was the only electronic desktop calculator available, and was silent and quick.

The tube technology of the ANITA was superseded in June 1963 by the U.S. manufactured Friden EC-130, which had an all-transistor design, a stack of four 13-digit numbers displayed on a 5-inch (13 cm) cathode ray tube (CRT), and introduced Reverse Polish Notation (RPN) to the calculator market for a price of $2200, which was about three times the cost of an electromechanical calculator of the time. Like Bell Punch, Friden was a manufacturer of mechanical calculators that had decided that the future lay in electronics. In 1964 more all-transistor electronic calculators were introduced: Sharp introduced the CS-10A, which weighed 25 kilograms (55 lb) and cost 500,000 yen ($4555.81), and Industria Macchine Elettroniche of Italy introduced the IME 84, to which several extra keyboard and display units could be connected so that several people could make use of it (but apparently not at the same time). The Victor 3900 was the first to use integrated circuits in place of individual transistors, but production problems delayed sales until 1966.

There followed a series of electronic calculator models from these and other manufacturers, including Canon, Mathatronics, Olivetti, SCM (Smith-Corona-Marchant), Sony, Toshiba, and Wang. The early calculators used hundreds of germanium transistors, which were cheaper than silicon transistors, on multiple circuit boards. Display types used were CRT, cold-cathode Nixie tubes, and filament lamps. Memory technology was usually based on the delay-line memory or the magnetic-core memory, though the Toshiba "Toscal" BC-1411 appears to have used an early form of dynamic RAM built from discrete components. Already there was a desire for smaller and less power-hungry machines.

Bulgaria"s ELKA 6521,Sofia. The name derives from ELektronen KAlkulator, and it weighed around 8 kg (18 lb). It is the first calculator in the world which includes the square root function. Later that same year were released the ELKA 22 (with a luminescent display)ELKA 101, was released in 1974. The writing on it was in Roman script, and it was exported to western countries.

The first desktop programmable calculators were produced in the mid-1960s. They included the Mathatronics Mathatron (1964) and the Olivetti Programma 101 (late 1965) which were solid-state, desktop, printing, floating point, algebraic entry, programmable, stored-program electronic calculators.

Another early programmable desktop calculator (and maybe the first Japanese one) was the Casio (AL-1000) produced in 1967. It featured a nixie tubes display and had transistor electronics and ferrite core memory.

The branch instruction was an implied unconditional branch (GOTO) at the end of the operation stack, returning the program to its starting instruction. Thus, it was not possible to include any conditional branch (IF-THEN-ELSE) logic. During this era, the absence of the conditional branch was sometimes used to distinguish a programmable calculator from a computer.

The electronic calculators of the mid-1960s were large and heavy desktop machines due to their use of hundreds of transistors on several circuit boards with a large power consumption that required an AC power supply. There were great efforts to put the logic required for a calculator into fewer and fewer integrated circuits (chips) and calculator electronics was one of the leading edges of semiconductor development. U.S. semiconductor manufacturers led the world in large scale integration (LSI) semiconductor development, squeezing more and more functions into individual integrated circuits. This led to alliances between Japanese calculator manufacturers and U.S. semiconductor companies: Canon Inc. with Texas Instruments, Hayakawa Electric (later renamed Sharp Corporation) with North-American Rockwell Microelectronics (later renamed Rockwell International), Busicom with Mostek and Intel, and General Instrument with Sanyo.

By 1970, a calculator could be made using just a few chips of low power consumption, allowing portable models powered from rechargeable batteries. The first handheld calculator was a 1967 prototype called Cal Tech, whose development was led by Jack Kilby at Texas Instruments in a research project to produce a portable calculator. It could add, multiply, subtract, and divide, and its output device was a paper tape.

The first commercially produced portable calculators appeared in Japan in 1970, and were soon marketed around the world. These included the Sanyo ICC-0081 "Mini Calculator", the Canon Pocketronic, and the Sharp QT-8B "micro Compet". The Canon Pocketronic was a development from the "Cal-Tech" project. It had no traditional display; numerical output was on thermal paper tape.

Sharp put in great efforts in size and power reduction and introduced in January 1971 the Sharp EL-8, also marketed as the Facit 1111, which was close to being a pocket calculator. It weighed 1.59 pounds (721 grams), had a vacuum fluorescent display, rechargeable NiCad batteries, and initially sold for US$395.

However, integrated circuit development efforts culminated in early 1971 with the introduction of the first "calculator on a chip", the MK6010 by Mostek,vacuum fluorescent display, LED, and LCD), led within a few years to the cheap pocket calculator available to all.

In 1971, Pico ElectronicsGeneral Instrument also introduced their first collaboration in ICs, a full single chip calculator IC for the Monroe Royal Digital III calculator. Pico was a spinout by five GI design engineers whose vision was to create single chip calculator ICs. Pico and GI went on to have significant success in the burgeoning handheld calculator market.

The first truly pocket-sized electronic calculator was the Busicom LE-120A "HANDY", which was marketed early in 1971.Mostek MK6010, and the first electronic calculator to run off replaceable batteries. Using four AA-size cells the LE-120A measures 4.9 by 2.8 by 0.9 inches (124 mm × 71 mm × 23 mm).

The first European-made pocket-sized calculator, DB 800Digitron in Buje, Croatia (former Yugoslavia) with four functions and an eight-digit display and special characters for a negative number and a warning that the calculation has too many digits to display.

The first American-made pocket-sized calculator, the Bowmar 901B (popularly termed The Bowmar Brain), measuring 5.2 by 3.0 by 1.5 inches (132 mm × 76 mm × 38 mm), came out in the Autumn of 1971, with four functions and an eight-digit red LED display, for US$240, while in August 1972 the four-function Sinclair Executive became the first slimline pocket calculator measuring 5.4 by 2.2 by 0.35 inches (137.2 mm × 55.9 mm × 8.9 mm) and weighing 2.5 ounces (71 g). It retailed for around £79 (US$194 at the time). By the end of the decade, similar calculators were priced less than £5 ($6.85). Following protracted development over the course of two years including a botched partnership with Texas Instruments, Eldorado Electrodata released five pocket calculators in 1972. One called the Touch Magic was "no bigger than a pack of cigarettes" according to Administrative Management.

One of the first low-cost calculators was the Sinclair Cambridge, launched in August 1973. It retailed for £29.95 ($41.03), or £5 ($6.85) less in kit form. The Sinclair calculators were successful because they were far cheaper than the competition; however, their design led to slow and inaccurate computations of transcendental functions.

Meanwhile, Hewlett-Packard (HP) had been developing a pocket calculator. Launched in early 1972, it was unlike the other basic four-function pocket calculators then available in that it was the first pocket calculator with scientific functions that could replace a slide rule. The $395 HP-35, along with nearly all later HP engineering calculators, uses reverse Polish notation (RPN), also called postfix notation. A calculation like "8 plus 5" is, using RPN, performed by pressing 8, Enter↑, 5, and +; instead of the algebraic infix notation: 8, +, 5, =. It had 35 buttons and was based on Mostek Mk6020 chip.

In 1973, Texas Instruments (TI) introduced the SR-10, (SR signifying slide rule) an algebraic entry pocket calculator using scientific notation for $150. Shortly after the SR-11 featured an added key for entering pi (π). It was followed the next year by the SR-50 which added log and trig functions to compete with the HP-35, and in 1977 the mass-marketed TI-30 line which is still produced.

The first programmable pocket calculator was the HP-65, in 1974; it had a capacity of 100 instructions, and could store and retrieve programs with a built-in magnetic card reader. Two years later the HP-25C introduced CMOS memory during power-off. In 1979, HP released the first expandable calculator, the HP-41C. It could be expanded with random-access memory (RAM, for memory) and read-only memory (ROM, for software) modules, and peripherals like bar code readers, microcassette and floppy disk drives, paper-roll thermal printers, and miscellaneous communication interfaces (RS-232, HP-IL, HP-IB).

The first Soviet pocket battery-powered programmable calculator, Elektronika Elektronika B3-34 wasn"t backward compatible with B3-21, even if it kept the reverse Polish notation (RPN). Thus B3-34 defined a new command set, which later was used in a series of later programmable Soviet calculators. Despite very limited abilities (98 bytes of instruction memory and about 19 stack and addressable registers), people managed to write all kinds of programs for them, including adventure games and libraries of calculus-related functions for engineers. Hundreds, perhaps thousands, of programs were written for these machines, from practical scientific and business software, which were used in real-life offices and labs, to fun games for children. The Elektronika MK-52 calculator (using the extended B3-34 command set, and featuring internal EEPROM memory for storing programs and external interface for EEPROM cards and other periphery) was used in Soviet spacecraft program (for Soyuz TM-7 flight) as a backup of the board computer.

This series of calculators was also noted for a large number of highly counter-intuitive mysterious undocumented features, somewhat similar to "synthetic programming" of the American HP-41, which were exploited by applying normal arithmetic operations to error messages, jumping to nonexistent addresses and other methods. A number of respected monthly publications, including the popular science magazine Наука и жизнь, Science and Life), featured special columns, dedicated to optimization methods for calculator programmers and updates on undocumented features for hackers, which grew into a whole esoteric science with many branches, named "yeggogology" ("еггогология"). The error messages on those calculators appear as a Russian word "YEGGOG" ("ЕГГОГ") which, unsurprisingly, is translated to "Error".

Through the 1970s the hand-held electronic calculator underwent rapid development. The red LED and blue/green vacuum fluorescent displays consumed a lot of power and the calculators either had a short battery life (often measured in hours, so rechargeable nickel-cadmium batteries were common) or were large so that they could take larger, higher capacity batteries. In the early 1970s liquid-crystal displays (LCDs) were in their infancy and there was a great deal of concern that they only had a short operating lifetime. Busicom introduced the Busicom LE-120A "HANDY" calculator, the first pocket-sized calculator and the first with an LED display, and announced the Busicom LC with LCD. However, there were problems with this display and the calculator never went on sale. The first successful calculators with LCDs were manufactured by Rockwell International and sold from 1972 by other companies under such names as: Dataking LC-800, Harden DT/12, Ibico 086, Lloyds 40, Lloyds 100, Prismatic 500 (a.k.a. P500), Rapid Data Rapidman 1208LC. The LCDs were an early form using the Dynamic Scattering Mode DSM with the numbers appearing as bright against a dark background. To present a high-contrast display these models illuminated the LCD using a filament lamp and solid plastic light guide, which negated the low power consumption of the display. These models appear to have been sold only for a year or two.

A more successful series of calculators using a reflective DSM-LCD was launched in 1972 by Sharp Inc with the Sharp EL-805, which was a slim pocket calculator. This, and another few similar models, used Sharp"s Calculator On Substrate (COS) technology. An extension of one glass plate needed for the liquid crystal display was used as a substrate to mount the needed chips based on a new hybrid technology. The COS technology may have been too costly since it was only used in a few models before Sharp reverted to conventional circuit boards.

In the mid-1970s the first calculators appeared with field-effect, twisted nematic (TN) LCDs with dark numerals against a grey background, though the early ones often had a yellow filter over them to cut out damaging ultraviolet rays. The advantage of LCDs is that they are passive light modulators reflecting light, which require much less power than light-emitting displays such as LEDs or VFDs. This led the way to the first credit-card-sized calculators, such as the Casio Mini Card LC-78 of 1978, which could run for months of normal use on button cells.

There were also improvements to the electronics inside the calculators. All of the logic functions of a calculator had been squeezed into the first "calculator on a chip" integrated circuits (ICs) in 1971, but this was leading edge technology of the time and yields were low and costs were high. Many calculators continued to use two or more ICs, especially the scientific and the programmable ones, into the late 1970s.

The power consumption of the integrated circuits was also reduced, especially with the introduction of CMOS technology. Appearing in the Sharp "EL-801" in 1972, the transistors in the logic cells of CMOS ICs only used any appreciable power when they changed state. The LED and VFD displays often required added driver transistors or ICs, whereas the LCDs were more amenable to being driven directly by the calculator IC itself.

With this low power consumption came the possibility of using solar cells as the power source, realised around 1978 by calculators such as the Royal Solar 1, Sharp EL-8026, and Teal Photon.

The interior of a Casio fx-20 scientific calculator from the mid-1970s, using a VFD. The processor integrated circuit (IC) is made by NEC (marked μPD978C). Discrete electronic components like capacitors and resistors and the IC are mounted on a printed circuit board (PCB). This calculator uses a battery pack as a power source.

The processor chip (integrated circuit package) inside a 1980s Sharp pocket calculator, marked SC6762 1•H. An LCD is directly under the chip. This was a PCB-less design. No discrete components are used. The battery compartment at the top can hold two button cells.

Inside a Casio scientific calculator from the mid-1990s, showing the processor chip (small square; top-middle; left), keypad contacts, right (with matching contacts on the left), the back of the LCD (top; marked 4L102E), battery compartment, and other components. The solar cell assembly is under the chip.

The interior of a newer (c.2000) pocket calculator. It uses a button battery in combination with a solar cell. The processor is a "Chip on Board" type, covered with dark epoxy.

At the start of the 1970s, hand-held electronic calculators were very costly, at two or three weeks" wages, and so were a luxury item. The high price was due to their construction requiring many mechanical and electronic components which were costly to produce, and production runs that were too small to exploit economies of scale. Many firms saw that there were good profits to be made in the calculator business with the margin on such high prices. However, the cost of calculators fell as components and their production methods improved, and the effect of economies of scale was felt.

By 1976, the cost of the cheapest four-function pocket calculator had dropped to a few dollars, about 1/20 of the cost five years before. The results of this were that the pocket calculator was affordable, and that it was now difficult for the manufacturers to make a profit from calculators, leading to many firms dropping out of the business or closing. The firms that survived making calculators tended to be those with high outputs of higher quality calculators, or producing high-specification scientific and programmable calculators.

The Elektronika MK-52 was a programmable RPN-style calculator that accepted extension modules; it was manufactured in the Soviet Union from 1985 to 1992

The first calculator capable of symbolic computing was the HP-28C, released in 1987. It could, for example, solve quadratic equations symbolically. The first graphing calculator was the Casio fx-7000G released in 1985.

The two leading manufacturers, HP and TI, released increasingly feature-laden calculators during the 1980s and 1990s. At the turn of the millennium, the line between a graphing calculator and a handheld computer was not always clear, as some very advanced calculators such as the TI-89, the Voyage 200 and HP-49G could differentiate and integrate functions, solve differential equations, run word processing and PIM software, and connect by wire or IR to other calculators/computers.

The HP 12c financial calculator is still produced. It was introduced in 1981 and is still being made with few changes. The HP 12c featured the reverse Polish notation mode of data entry. In 2003 several new models were released, including an improved version of the HP 12c, the "HP 12c platinum edition" which added more memory, more built-in functions, and the addition of the algebraic mode of data entry.

Calculated Industries competed with the HP 12c in the mortgage and real estate markets by differentiating the key labeling; changing the "I", "PV", "FV" to easier labeling terms such as "Int", "Term", "Pmt", and not using the reverse Polish notation. However, CI"s more successful calculators involved a line of construction calculators, which evolved and expanded in the 1990s to present. According to Mark Bollman,

Personal computers often come with a calculator utility program that emulates the appearance and functions of a calculator, using the graphical user interface to portray a calculator. One such example is Windows Calculator. Most personal data assistants (PDAs) and smartphones also have such a feature.

In most countries, students use calculators for schoolwork. There was someelementary arithmetic skills would suffer.in the head, with some curricula restricting calculator use until a certain level of proficiency has been obtained, while others concentrate more on teaching estimation methods and problem-solving. Research suggests that inadequate guidance in the use of calculating tools can restrict the kind of mathematical thinking that students engage in.UK"s Minister of State for Schools, Nick Gibb, voiced concern that children can become "too dependent" on the use of calculators.Curriculum.National Council of Teachers of Mathematics (NCTM) standards and actively promoted the use of classroom calculators from kindergarten through high school.

Ball, Guy; Flamm, Bruce. "The History of Pocket Electronic Calculators". vintagecalculators.com. Vintage Calculators Web Museum. Archived from the original on 3 July 2014. Retrieved 8 July 2014.

Electronic Calculator Invented 40 Years Ago Archived 2008-12-05 at the Wayback Machine All Things Considered, NPR, 30 September 2007. Audio interview with one of the inventors.

"50 Jahre Taschenrechner – Die Erfindung, die niemand haben wollte" [50th anniversary of calculators – the invention not wanted by anyone]. Wirtschaft (in German). Frankfurter Allgemeine Zeitung (FAZ). 27 March 2017. Archived from the original on 29 March 2017. Retrieved 30 March 2017.

Okon, Thomas (27 March 2017). "The First Handheld Digital Calculator Celebrates 50 Years". Electronic Design. Archived from the original on 13 April 2017.

Bellotto, Sam Jr. (August 1972). "Calculators: They Just Keep Multiplying". Administrative Management. Geyer-McAllister Publications. 33 (8): 68–73 – via the Internet Archive.

Reversing Sinclair"s amazing 1974 calculator hack – half the ROM of the HP-35, Ken Shirriff, 2013. See in particular the section "Limited performance and accuracy". For more coverage of Shirriff"s results, see Sharwood, Simon (2 September 2013), "Google chap reverse engineers Sinclair Scientific Calculator", The Register, archived from the original on 23 August 2017

Vasagar, Jeevan; Shepherd, Jessica (1 December 2011). "Subtracting calculators adds to children"s maths abilities, says minister". Archived from the original on 9 March 2016. Retrieved 7 December 2011. The use of calculators will be looked at as part of a national curriculum review, after the schools minister, Nick Gibb, expressed concern that children"s mental and written arithmetic was suffering because of reliance on the devices. Gibb said: "Children can become too dependent on calculators if they use them at too young an age. They shouldn"t be reaching for a gadget every time they need to do a simple sum. [...]"

Hamrick, Kathy B. (October 1996). "The History of the Hand-Held Electronic Calculator". The American Mathematical Monthly. The American Mathematical Monthly, Vol. 103, No. 8. 103 (8): 633–639. doi:10.2307/2974875. JSTOR 2974875.

Miniature electronic calculator – J. S. Kilby, Texas Instruments, 1974 (originally filed 1967), handheld (3 pounds (1.4 kg)) battery operated electronic device with thermal printer

The Japanese Patent Office granted a patent in June 1978 to Texas Instruments (TI) based on US patent 3819921, notwithstanding objections from 12 Japanese calculator manufacturers. This gave TI the right to claim royalties retroactively to the original publication of the Japanese patent application in August 1974. A TI spokesman said that it would actively seek what was due, either in cash or technology cross-licensing agreements. 19 other countries, including the United Kingdom, had already granted a similar patent to Texas Instruments. – New Scientist, 17 August 1978 p455, and Practical Electronics (British publication), October 1978 p1094.

Collectors Guide to Pocket Calculators. by Guy Ball and Bruce Flamm, 1997, ISBN 1-888840-14-5 – includes an extensive history of early pocket calculators and highlights over 1,500 different models from the early 1970s. Book still in print.

Suydam, Marilyn N. (December 1980). Calculators: A Categorized Compilation of References. Supplement 1 (PDF). Columbus, Ohio, USA: Calculator Information Center, Ohio State University. ED199087. SE034434. Archived (PDF) from the original on 19 September 2021. Retrieved 16 October 2022. (64 pages)

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