There’s this humongous article called Keyboard Trivia that has collected many of the theories and stories. The summary of *facts*:

- Touch-tone key pad was designed to mimic the rotary dial with the “1” on top and the 7-8-9 on the bottom, and AT&T conducted user testing to confirm that this configuration helped eliminate dialing errors.
- By the time when the touch-tone telephone was being designed in the late 1950s, the calculator and adding-machine designers had already established a layout that had 7, 8 and 9 across the top row.
- Back then, the industry-standard typical calculator had nine columns of numbers, with 10 numbers in a column, the lowest digits at the bottom, starting with 0 and moving up to 9, and was basically a mechanical adding machine that closely resembled a cash register.
- It is common practice today to use the telephone-keypad layout when designing new products that utilize a keypad, such as Automated Teller Machines.
- When Bell Labs began exploring keypad layouts in the late 1950s they contacted all of the leading calculator manufacturers to find out why they had chosen to put low numbers at the bottom and high numbers at the top rather than the other way around. The answer, apparently, was a big shrug. It turns out that decision was largely arbitrary: no one had done any research about which layout was most convenient for users. Still, when it came time to place a numeric keypad on a computer keyboard, the calculator model with 7-8-9 at the top prevailed.

There’s also a *theory* that phone engineers wanted to slow down people who were fast at entering numerical data, which would jam lines and produce dialing errors, so they reversed the layout. However, records of AT&T Labs’ research clearly invalidate it.

One additional possible explanation is that with the calculator layout many calculations can be performed along the bottom two rows and the plus button only; zeroes, decimal points and the enter/equals button.

Since the main buttons are all at the bottom, it makes reasonable sense that the other numbers would count up from the bottom too.

I suspect (but have no proof) that the phone keypad layout would make typing on a calculator more difficult for most simple calculations.

I have a reasonable explanation. Since I come from mathematics background, this is the first thing that comes to mind.

# Calculators

You probably have heard of the Benford’s law, also known as the “First digit law”. It says, that digits 1,2,3 occur more often than 7,8,9 when dealing with random, arbitrarily big numbers, which numbers that users type into calculators, in fact, are.

The graph is something like this and shows heavy bias against the digit “1”. Therefore it’s sensible to put digits 1, 2, and 3 to the bottom row, as it’s closer to the enter and also user reaches them easier.

Benford’s law (wikipedia)

# Phone numbers

Since phone numbers are have limited number of digits and are in fact, randomly scattered, the Benford’s law doesn’t apply here, which means all the digits occur with similar frequencies. This might be the reason that the more natural ordering is used, since there’s no reason to complicate.