Dozenal Calc

A "dozenal calculator" with a novel notation for numbers.

A "dozenal calculator" — a scientific calculator that computes not in tens, but in twelves. With its own symbols for the digits.

What base 12 can do that base 10 can't

In the decimal system, 1/3 is an infinite repeating fraction (0.333…). In base 12 it's short and exact: 0.4. Sixths, ninths, and every fraction whose denominator is built from twos and threes also become finite in dozenal. No coincidence: twelve has six divisors, ten only four.

Dozenal Calc computes exactly — a rational track runs in parallel with floating-point arithmetic. Repeating fractions appear with a bar over the recurring digits, for example 1/7 as 0.186A3 with a repetend bar.

Features

• Basic arithmetic, parentheses, signs • Power, square root, nth root, logarithm to any base • Trigonometric and hyperbolic functions including their inverses • Constants π, e, φ, √2; factorial, absolute value, reciprocal, modulo • Parallel addition (a⊕b) for resistor circuits • Memory (STO/RCL/MC) with exact rational preservation • Angle modes DEG / RAD / GRAD • Dozenal/decimal switching for input AND result, with automatic conversion

Unit converter

A second calculator mode converts between imperial/dozenal and metric units — length, area, volume, weight, time, angle, money (£/sh/d) and temperature. New: slope as a percentage in the angle section (0–90°).

Hands-on theory — now with pictures

A richly illustrated read explains why twelve in particular is a special number, in three blocks: • Twelve and the World — from the dodecagon and dodecahedron through pyrite, garnet, viruses and quasicrystals to music, art, architecture and calendars • Dozenal Mathematics — divisors and periods, the number bases compared, a history of place-value systems • Dozenal Society — the movement for twelve, new digits for ten and eleven, the TGM measurement system and related dozenal calculators

Many chapters now show public-domain historical illustrations — from Haüy's pyrite plate through Leonardo's dodecahedron to Vermeer's balance — each with a tappable source citation. Plus a dedicated theory of measurement and number.

Fourteen languages

Deutsch, English, Français, Español, Italiano, فارسی, Русский, Gaeilge, हिन्दी, 简体中文, 繁體中文, Cymraeg, 日本語, العربية — freely selectable in the info menu.

What Dozenal Calc doesn't do

• No ads, no tracking, no analytics • No internet connection, no permissions • No personal data

The app works completely offline. What you type stays on your device.

Who is it for?

For teachers who want to show how a different number system transforms everyday work with fractions — and for anyone who wants to see mathematics from an unfamiliar perspective.

License: MIT. Contact: dozenal@weltanschauung.app