How Calculators Work

Imagine trying to do your taxes or plan a budget without at least a basic calculator. See more essential gadgets pictures.

There may have been a time when the most complicated computations people needed to do could be performed on their fingers and toes. But these days, it's all but impossible for many people to imagine doing anything involving numbers -- from math homework to tax returns to tipping servers in restaurants -- without the help of at least a basic pocket calculator. In fact, electronic calculators are so widespread now that it's hard to believe they didn't become commonplace until the late 20th century.

Before the invention of the modern calculator, people used some other tools for computation. The abacus, for example, is one ancestor of the calculator. Probably of Babylonian origin, early abaci are believed to have been boards on which the position of counters stood for numerical values. However, the modern abacus -- which some people still use today in China, Japan and the Middle East -- works by moving beads along wires that are strung on a frame [source: Britannica: Abacus].


Throughout much of the last century, some people performed calculations using motor-assisted mechanical adding machines and others used mathematical tables and slide rules -- devices with movable, graduated scales that, depending on what type you have, can handle everything from multiplication to trigonometry [source: Britannica: Slide Rule].

Finally, in the 1960s, advancements in integrated circuitry led to the development of electronic calculators, but the early versions of these devices -- created by companies such as Sharp and Texas Instruments -- looked very little like the one you may be carrying around today in your briefcase or backpack.

To learn more about the evolution of the modern electronic calculator -- and see how consumer demand for smaller calculators led to the creation of microchips that power the appliances we use every day -- read on.


Evolution of the Electronic Calculator

Graphing calculators have many advanced functions, including solving and graphing equations.

Several electronics companies and inventors may claim a first when it comes to the development of the electronic calculator. Japanese company Sharp is said to have created the first desktop calculator, the CS-10A, in 1964. This model resembled a cash register and cost about as much as mid-sized car [sources: Lewis, Sharp]. In 1967, Texas Instruments developed what is known as the first portable, handheld calculator -- a device that could perform addition, subtraction, multiplication and division -- in a project that the company nicknamed "Cal Tech" [sources: Courier Mail, Texas Instruments].

Using "Cal Tech" technology, Canon developed the first handheld calculator for commercial use, which debuted in 1970 with a price tag of $400 [source: Texas Instruments]. The next few years became something of a race between manufacturers to make calculators smaller, more accessible and less expensive. In 1972, British inventor Sir Clive Sinclair introduced the Sinclair Executive, which is considered by many to be the world's first affordable pocket calculator [sources: The Press, Western Daily Press]. Its thickness was that of a pack of cigarettes.


These continued advancements in calculator technology were largely made possible by the development of the single-chip microprocessor in the late 1960s. Before this time, engineers built the computing "brains" of calculators (and computers) with multiple chips or other components. Basically, a single-chip microprocessor allows an entire central processing unit (CPU) to exist on one silicon microchip. (To learn more about this technology, check out How Microprocessors Work.)

Intel Corp. created the first commercially available single-chip microprocessor -- the Intel 4004 -- in 1971 [sources: Behar, Intel]. It was capable of performing basic arithmetic, 4 bits of information at time. However, Intel's co-founder, Gordon Moore, predicted that the capacity of a single chip would double about every two years. This theory is known as "Moore's Law," and so far it still holds true. Not only did calculators become smaller over the years, they became capable of increasingly advanced applications [source: Intel].

Today, in addition to modern versions of the basic pocket calculator, complex scientific and graphing calculators are available and used by both students and professionals such as engineers. Many use well-known computer languages and are programmable according to the user's needs. In fact, when Texas Instruments introduced its TI-92 model in 1995, they called it "a calculator with the power of a computer lab" [source: Texas Instruments]. Many scientific and graphing calculators may be capable of some of these functions:

  • Switching from the usual base-ten to other number systems (hexadecimal counting, is a base-16 system)
  • Using scientific notation to calculate very large numbers
  • Using logarithms and trigonometric functions directly
  • Working with constants like pi and e at a much higher degree of accuracy
  • Using complex numbers, fractions and formulas
  • Solving equations
  • Analyzing statistics
  • Using larger displays to work out formulas and graph equations

Read on to the next section to find out more about solar cells, circuit boards, and some of the other parts that make up a calculator.


Calculator Components

If you've read the previous page, you know by now that handheld calculators need single-chip microprocessors to function. But how do you activate the microprocessor? It all starts with what's on the outside of the device.

Many modern calculators have a durable plastic casing, with simple openings in the front that allow rubber to push through, just like a television remote. By pressing a button, you complete a circuit underneath the rubber, which sends electrical impulses through a circuit board below. Those impulses are routed through the microprocessor, which interprets the information and sends a readout to the calculator's display screen.


The displays of most early electronic calculators were made up of LEDs, or light-emitting diodes. Newer models that use less power incorporate the liquid crystal display, or LCD. Rather than producing light, LCDs rearrange light molecules to create a pattern on the display and ultimately don't require as much electricity.

Early calculators also had to be plugged in or used bulky battery power. But by the late 1970s, solar cell technology had become cheap and efficient enough to use in consumer electronics. A solar cell creates electricity when the photons of sunlight are absorbed by semiconductors, such as silicon, in the cell. This knocks loose electrons, and the electric field of the solar cell keeps them all traveling in the same direction, thus creating an electric current. (Something like an LCD calculator would only need a low-level current, which explains why their solar cells are so small.) By the 1980s, most manufacturers of simple calculators were taking advantage of solar cell technology. More powerful scientific and graphing calculators, however, still use battery power.

In the next section, we'll look more closely into binary code and how the calculator actually does its job.


How a Calculator Calculates

As you learned on previous pages, most calculators depend on integrated circuits, commonly known as chips. These circuits use transistors to add and subtract, as well as to perform computations on logarithms in order to accomplish multiplication, division and more complicated operations such as using exponents and finding square roots. Basically, the more transistors an integrated circuit has, the more advanced its functions may be. Most standard pocket calculators have identical, or very similar, integrated circuitry.

Like any electronic device, the chips inside a calculator work by reducing any information you give it to its binary equivalent. Binary numbers translate our numbers in a base-two system, in which we represent each digit by a 1 or a 0, doubling each time we move up a digit. By "turning on" each of the positions -- in other words, by putting a 1 in it -- we can say that that digit is included in our overall number.


Microchips use binary logic by turning transistors on and off literally, with electricity. So, for example, if you wanted to add 2 + 2, your calculator would convert each "2" to binary (which looks like this: 10) and then add them together. Adding the "ones" column (the two 0s), gives you 0: The chip can see that there is nothing in the first position. When it adds the digits in the "tens" column, the chip gets 1+1. It sees that both are positive, and -- since there are no 2's in binary notation -- moves the positive reply one digit to the left, getting a sum of 100 -- which, in binary terms, equals 4 [source: Wright].

This sum is routed through the input/output chip in our integrated circuit, which applies the same logic to the display itself. Have you ever noticed the way the numbers on a calculator or alarm clock are made up of segmented lines? Each one of those parts of the numerals can be turned on or off using this same binary logic. So, the processor takes that "100" and translates it by lighting up or turning on certain segments of the lines in the display to create the numeral 4.

On the next page, we'll look at the calculator's impact on the world and how we can expect to see them develop in the future.


Impact of Calculator Technology

The calculator has had a profound impact on the world, making computations quicker and more exact. In the classroom, calculators have given many students the ability to learn about and put complex formulas and concepts into practice more easily. Especially in lower-grade mathematics courses, some instructors still don't allow their use to make sure students truly understand mathematical concepts and learn problem-solving techniques. But for many calculus and trigonometry courses in high school, for example, graphing calculators are a requirement.

However, there has been some controversy regarding the use of powerful calculators in class, because some believe that using the devices to do the work that people's brains once did can result in the loss of true mathematical ability. Recent research suggests that advanced physics students, for example, can often be hampered in their learning by an overreliance on mathematical aids [Source: Bing]. Graphing calculators have even been banned in some classes because of their high memory capability. Students can use their calculators' memory to cheat by storing other information -- like periodic tables or test answers -- in them.


Engineers continue to make advancements in calculator technology, and as they become more and more complex, the lines between personal computers and classic calculators may continue to blur. For their current models, some companies are exploring more ecologically sound components, including the development of more efficient and recyclable power sources, and even using materials like recycled cellular phones in their manufacturing.

Calculators have even moved online and have a number of practical applications. Here are some specific types of calculators you might find online:

  • Weight-loss calculators can measure body mass, caloric content and workout impact.
  • College loan and mortgage calculators that can help you determine the cost and length of a loan according to a wide array of variables.
  • Conversion calculators give you everything from measurements of volume and length to up-to-the-minute currency exchanges.
  • Carbon footprint calculators may help you get an idea of your impact on the environment.

These online versions all use the same principles as your hand-held calculator, but present information in easy-to-use ways with access to massive databases of related information. Pretty much anyone can use them, which just goes to show that calculators truly aren't just tools for the likes of engineers, scientists and accountants anymore.

For more information on calculator technology and related topics, check out the links on the next page.


Frequently Answered Questions

Can a calculator be wrong?
A calculator can be wrong if it is not properly calibrated or if it is not functioning properly.

Lots More Information

Related HowStuffWorks Articles

More Great Links

  • Behar, Richard. "Who Invented Microprocessors?" Time. June 14, 2001. (Accessed 2/3/10),9171,155487,00.html
  • Bing, Thomas J. and Redish, Edward F. "Symbolic Manipulators Affect Mathematical Mindsets." American Journal of Physics, 2008. (Accessed 12/21/09)
  • The Courier Mail (Australia). "'60s Tech." June 1, 2009 (Accessed 2/3/10)
  • Ifrah, Georges. "The Universal History of Numbers." Wiley Press, 2000.
  • Encyclopedia Britannica. "Abacus." Encyclopedia Britannica Online. 2010. (Accessed 2/3/10)
  • Encyclopedia Britannica. "Calculator." Encyclopedia Britannica Online. 2010. (Accessed 2/3/10)
  • Encyclopedia Britannica. "Slide Rule." Encyclopedia Britannica Online. 2010. (Accessed 2/3/10)
  • Greenia, Mark W. "Computers and Computing: A Chronology of the Men and Machines that Made Computer History." Lexikon Services Publications, 1990.
  • Hamrick, Kathy B. "The History of the Hand-Held Electronic Calculator." Mathematical Association of America, 1996.
  • Intel Corporate Site. “About Intel.” (Accessed 2/3/2010)
  • Lewis, Leo. "The Eccentric Japanese Inventor." The Times (London). January, 31, 2004. (Accessed 2/3/10)
  • The Press. "Let's Get Inventin'." January 29, 2008. (Accessed 2/3/10)
  • Sharp Corporate Web site. "30th Anniversary of the Calculator." (Accessed 2/3/10)
  • Texas Instruments Corporate Web site. "History of Innovation." (Interactive Timeline) (Accessed 2/3/10)
  • Tout, Nigel. "The Calculator That Spawned The Microprocessor." Vintage Calculators Web Museum, 2009. (Accessed 12/21/09)
  • Vergano, Dan. "Nobels Recognize Information Age Pioneers; Physics, Chemistry Prizes Presented for Revolutionary Devices." USA Today. October 11, 2000. (Accessed 2/3/10)
  • Wright, Christine R. and Samuel A. Rebelsky. "A Tutorial on Binary Numbers." Grinnell College Math Department Web site.