Calculators have evolved over centuries from large computing machines into today’s highly functional, pocket-sized devices capable of performing complex computations, graphing multiple lines at once and analyzing graphs of functions. Modern students of math may not realize that the invention of these tools is relatively recent.
Today’s digital screens and easy-to-read graphs of the calculator bear no resemblance to the earliest calculating tools, which featured stone and beads and couldn’t perform computations.
The earliest tool for performing mathematical operations was likely an abacus, which allowed ancients to add and subtract units on a frame. Calculating machines, which hardly resemble today’s calculators, weren’t invented until the 17th century. Even compared to the calculators available as late as the 1970s, graphing calculators are incredibly advanced and perform operations and analysis that would’ve been unimaginable to users of early arithmetic and algebraic calculators.
Graphing calculators are hand-held computers capable of plotting graphs, solving equations and performing analysis on functions. Graphing calculators include a range of capabilities and can typically be programmed to perform various specialized tasks for science and engineering, such as p-value analysis. In addition, graphing calculators often come with charging cables and can be stored in travel cases for easy transportation.
The two major graphing calculator manufacturers are Texas Instruments and Casio. Both manufacture a range of graphing calculators with varying degrees of functionality. Texas Instruments’ calculators are widely known for their unparalleled programmability, while Casio is most commonly known for its durable and reliable products.
Graphing calculators are ubiquitous in math classrooms today, and many courses even require students to purchase one. Additionally, many courses allow graphing calculators as a supplement while students learn to graph equations by hand.
Graphing calculators include all the functionality of a basic scientific calculator, such as arithmetic and algebraic functions, alongside the capability to graph complex equations.
One of the most common uses of a graphing calculator is solving multiple equations simultaneously to graph their lines against each other and find their intercepts. This allows students to understand equations both algebraically (by solving for intercepts, for example) and visually (by graphing them).
Apart from displaying graphs of plotted equations, one of the major innovations of the graphing calculator was the ability to compute the sine, cosine and tangent trigonometric functions.
Graphing calculators typically have large screens and digital displays to display multiple lines of calculations or a large section of a graph at once.
Graphing calculators became widely available in the 1980s and quickly became essential tools in calculus and trigonometry classes, replacing basic math machines and earlier versions of calculators. Prior to the invention and mass production of graphing calculators, basic calculators evolved through centuries of innovation.
The first tool invented for mathematical operations was likely the abacus, which is a table of columns featuring beads representing units. The earliest abacus dates back to Sumeria in 2500 B.C. Unfortunately, while the abacus could be used efficiently and quickly for addition and subtraction, it’s a limited device and doesn’t lend itself well to division and multiplication.
In 1617, the Scottish mathematician John Napier came up with the idea of a multiplying table that would assist in performing calculations by representing multiplication operations in multiplication tables inscribed on thin rods.
In 1623, Wilhelm Schickard first conceived of a calculating clock, which consisted of a multiplying device and a mechanism for recording the results of operations.
Unlike modern calculators, which can perform an array of complex computations, the first calculators were adding machines that could perform basic arithmetic operations on whole numbers and fractions. However, they were limited to addition, subtraction, multiplication and division.
Operations were entered into the machine using the machine's bulky keyboard.
The first true calculating tool was the Pascal calculator, invented by the French mathematician Blaise Pascal in 1642. Pascal calculators were revolutionary for their innovative calculating ability, but they were never widely produced.
Similar mechanical calculating machines were designed and produced in limited production runs throughout the 18th and 19th centuries.
In 1851, Thomas de Colmar released a calculating machine that was easier to produce than all previous machines and could be used in office settings. However, though it was an improvement, it was far less compact than today’s calculators.
The first widely produced and sold calculators arrived in the 20th century.
The hand-held calculator, called the Curta, was invented by Curt Herzstark in 1945 and looked like a pepper grinder. It was distributed until 1970, when Busicom, a company in Japan, invented the first digital pocket calculator. While the new Japanese calculator was arguably the earliest recognizable ancestor of a modern graphing calculator, it could only perform four functions: addition, subtraction, multiplication and division.
After the invention of the Japanese handheld calculator, US companies like Casio and Texas Instruments began to adapt its design into increasingly slim calculators with more and more functions.
In 1985, Casio introduced the first commercially available graphing calculator, the fx-7000G. Texas Instruments quickly followed and began producing the TI-81 in 1990.
What you need to know: A digital color screen calculator with high resolution and a rechargeable battery.
What you’ll love: For advanced mathematics students such as those enrolled in a Calculus course, the TI-Nspire CX II CAS Color Graphing Calculator is a serious upgrade from other models and a great supplement to math learning. It includes six different graph styles with 15 differentiating graph colors to choose from, allowing you to simultaneously graph lines and analyze each. Lightweight touchpad. Comes with a student software bundle.
What you should consider: This model is significantly pricier than others, but its fast processing power, digital interface and high functionality make it worth it for those who want a serious calculator.
Where to buy: Sold by Amazon
What you need to know: A widely used and user-friendly graphing calculator approved for use on the SAT, PSAT, ACT and AP exams.
What you’ll love: This calculator allows you to compare functions, analyze data with logistic and sine regressions, analyze matrices and more. Known for user-friendliness and its reasonably high memory or 24KB of RAM and 160KB Flash ROM.
What you should consider: The TI-83 Plus calculator doesn’t include the array of functions some pricier models do, but it’s a good entry-level calculator and fine for most students of mathematics.
Where to buy: Sold by Staples
What you need to know: A tried and true, battery-operated graphing calculator from an iconic brand approved for use on the PSAT, SAT and AP tests.
What you’ll love: The Casio graphing calculator allows you to graph functions and inequalities, analyze graphs, solve for intercepts and intersects and more. Includes USB functionality to connect with devices. Includes the ability to recall previous entries.
What you should consider: If you’re used to the digital interactivity of some pricier graphing calculators, you may not find the user experience on this model as satisfying.
Where to buy: Sold by Amazon
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Evelyn Waugh writes for BestReviews. BestReviews has helped millions of consumers simplify their purchasing decisions, saving them time and money.