How calculators work

What is a calculator?

Our brains are amazingly versatile, but we find it hard to calculate in our heads because they can store only so many numbers. According to a famous bit of 1950s research by psychologist George Miller, we can remember typically 5–9 digits (or, as Miller put it: "the magical number seven, plus or minus two") before our brains start to ache and forget. That's why people have been using aids to help them calculate since ancient times. Indeed, the word calculator comes from the Latin calculare, which means to count up using stones.

Mechanical calculators (ones made from gears and levers) were in widespread use from the late-19th to the late-20th century. That's when the first affordable, pocket, electronic calculators started to appear, thanks to the development of silicon microchips in the late 1960s and early 1970s.

Modern calculators have much in common with computers: they share much of the same history and work in a similar way, but there's one crucial difference: a calculator is an entirely human-operated machine for processing math, whereas a computer can be programmed to operate itself and do a whole range of more general-purpose jobs. In short, a computer is programmable and a calculator is not. (A programmable calculator sits somewhere between the two: you can program it, but only to do relatively simple

• Input: Keyboard: About 40 tiny plastic keys with a rubber membrane underneath and a touch-sensitive circuit underneath that.

• Processor: A microchip that does all the hard work. This does the same job as all the hundreds of gears in an early calculator.

• Output: A liquid crystal display (LCD) for showing you the numbers you type in and the results of your calculations.

• Power source: A long-life battery (mine has a thin lithium "button" cell that lasts several years). Some calculators also have a solar cell to provide free power in the daylight.