What kind of machine is a calculator

That's why calculators and phones have different number fields

By Adrian Mühlroth | December 28, 2017, 6:04 p.m.

What starts with 123 and ends in 0? The number field of a telephone is known to everyone. But why is it in a different order than that of a calculator?

Hardly anyone notices, but there is one major difference between the keypads on a telephone and a calculator - the order is reversed. While the numbers on a telephone run from 1-9 and top left to bottom right, the world is wrong with a pocket calculator. Here the numbers are counted from top right to bottom left in descending order from 9 to 1. TECHBOOK explains why that is.

Early calculators without standardized keys

Mechanical calculators with levers and wheels saw the light of day as early as 1642, but it wasn't until 1844 that the French Jean-Baptiste Schwilguć managed to design a computer prototype with numeric input keys. The calculator had keys from 1 to 9 arranged in a horizontal line. Although there were machines that could do more complex calculations at that time, this revolutionary input method made calculating much easier and faster, as each key actually only corresponded to one number.

Despite this invention, there was no standardized input field for calculating machines for a long time. Regardless of whether sliders, wheels or buttons, in a horizontal or vertical arrangement, every inventor gave his computing device its own look, often driven by mechanical necessities. So where does the 3-by-3-key field with a zero underneath that can be found in (almost) every pocket calculator come from? While there is no clear evidence that the number field was created, it is believed that cash registers may have played a role in it.

Cash registers as a model for calculating machines

The first mechanical cash register was invented in Ohio in 1879 by James Ritty, who wanted to prevent his saloon employees from helping themselves at the cash register. However, the cash register was little more than a calculating machine that rang after calculating the price to signal the owner that a purchase was taking place. So while the tills lagged behind the calculating machines in terms of functionality, they had one important distinguishing feature: the zero. The cash registers needed zero in order to correctly display cents, while calculating machines only calculated zero by adding, for example "10" by adding 5 + 5. Initially, however, there was no dedicated button for the zero. Instead, there were fixed amounts like 10, 20, 30, etc.

Operation is simplified

The development of calculating machines continued rapidly. In 1884 inventor Dorr Felt presented the so-called comptometer, which arranged the numbers from 1 to 9 vertically from bottom to top. The vertical rows each represented a decimal place, the device came with up to 16 parallel rows of numbers. This arrangement was unusual for the time, but probably arose from a mixture of mechanical necessity and more efficient operation. The smaller numbers needed a shorter rotation than the higher ones, so they could sit further down.

Perhaps when Dorr Felt was developing his device, he knew that smaller numbers are used more often than higher numbers, a theory proposed by Simon Newcomb as early as 1881 and later known as Benford's Law. To make operation easier and more efficient, the smaller numbers are therefore closer to the user's hands. The fact that Dorr Felt intended this is confirmed by the operating instructions for the device, in which it says that smaller numbers should simply be added instead of entering the higher ones. Due to the smaller distance, a higher input speed should be achieved.

The introduction of zero

The first adding machine to have its own key for zero was the Dalton adding machine from 1902. The device had an unusual keypad with the numbers 24579 in the top row and 13068 in the bottom row. Only twelve years later, in 1914, the American David Sundstrand applied for patent no. 1198487 for a more logical and user-friendly keypad. According to the patent, the numbers 1-9 should be arranged from bottom to top in a 3-by-3 grid, with another row below for the zero. This design, which emerged from 70 years of development, ultimately caught on and is still used today for pocket calculators.

From the rotary dial to the button

The first telephone with a rotary dial dates back to 1891, even before the 3-to-3 keypad had established itself in calculating machines. In the dial, the numbers 1-9 were arranged counterclockwise with a zero at the end, so the zero already existed as the bottom number on the control panel. As the American Telephone and Telegraph Company AT&T wanted to change the input method from a rotary dial to buttons, studies were commissioned by Bell Labs in 1950 and 1960 to find out which button arrangement users would find most intuitive. In addition to the already established pocket calculator arrangement of 9-1, there was also a choice of the reverse pocket calculator arrangement of 1-9, as well as many other suggestions such as crosses, circles, trapezoids and triangles.

When preparing the studies, Bell Labs also asked leading calculating machine manufacturers why they would always equip their devices with the input field with the lower numbers at the lower end and the higher numbers at the upper end. The answer, unsurprisingly, was that the decision was made arbitrarily. This arrangement was known and prevailed, but no one had researched which arrangement is best for the user.

According to studies, the phone number field is better for the user

The Bell Labs studies showed that users preferred the 3-by-3 grid arrangement with the lower numbers at the top, but the pocket calculator arrangement was seen as less than intuitive. It was therefore decided that phones should follow the preferred order that is still used in all phones, smartphones and cell phones to this day. The already established pocket calculator arrangement was retained for adding machines, pocket calculators and later computers, so it happens that pocket calculators and telephones have different number fields.

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