Constructive Calculator

Ordinary calculators round. Constructive Calculator doesn’t.

It computes with constructive real numbers, an arbitrary-precision engine that keeps every result exact and gives you as many correct digits as you ask for. The rounding errors that quietly accumulate in ordinary calculators simply never happen.

exp(pi times sqrt 163) scrolled to its decimal point, showing twelve nines

1 divided by 243 showing 0.004115226337, the start of a repeating pattern

Left: exp(π√163) looks like a whole number, but scroll past the decimal point and twelve 9s appear before it diverges. Right: 1/243, whose digits weave two simple sequences together before the block repeats.

The number a wartime censor mistook for a code

In Surely You’re Joking, Mr. Feynman!, Richard Feynman recalls spotting this on an adding machine at Los Alamos: 1/243 = 0.00 4 11 5 22 6 33 7 44 8 55 9… Two sequences interleave: 4, 5, 6, 7, 8, 9… woven through 11, 22, 33, 44, 55… In his words it “goes a little cockeyed after 559 when you’re carrying, but it soon straightens itself out and repeats itself nicely” (the block is 27 digits long). He slipped it into a letter; the censors flagged the digits as a suspected code, and he wrote back that it couldn’t be one, because “there’s no more information in the number .004115226337… than there is in the number 243.” Constructive Calculator lets you see the pattern; a rounding calculator shows just 0.00412.

What it does

As many digits as you want. A pocket calculator stops at about 15 digits and rounds. Here every result is computed on demand and kept exact, so you can swipe √2, π, or any answer to pull in tens, hundreds, or thousands more.
A scientific keypad. Trigonometry in degrees or radians and their inverses, exponentials and logarithms, powers and roots, factorials, percentages, π and e.
Exact big integers. 52! (the number of ways to shuffle a deck) prints in full, all 68 digits.
Built for clarity. A running tape of recent calculations, locale-aware digit grouping, and copy at any precision.

Constructive Calculator is an independent port of Hans Boehm’s constructive-reals calculator, the arbitrary-precision engine behind Android’s Calculator, rebuilt natively for iPhone.