Dozenal Converter (Base 12)

2026 in dozenal. 2026 ÷ 12 = 168 r 10; 168 ÷ 12 = 14 r 0; 14 ÷ 12 = 1 r 2; 1 ÷ 12 = 0 r 1. Reading upwards and writing ten as ↊: 120↊. Check: 1 × 1,728 + 2 × 144 + 0 × 12 + 10 = 2,026.

A fifth in dozenal. 0.2 × 12 = 2.4 → 2; 0.4 × 12 = 4.8 → 4; 0.8 × 12 = 9.6 → 9; 0.6 × 12 = 7.2 → 7; then 0.2 again, so 1/5 = 0.249724972497…, repeating 2497. A third, by contrast, is just 0.4, because 1/3 × 12 = 4 exactly.

The common mistake: reading 10 as ten. In dozenal “10” is twelve and “100” is 144. Writing a value without saying which base it is in, or mixing a dozenal 10 into a decimal sum, is off by a factor that grows with every digit.

Twelve is everywhere in old measures: twelve inches to a foot, twelve pence to a shilling, twelve months, twelve hours on a clock face and the dozen and gross of the market. Some suggest people counted twelve finger joints with the thumb. The Romans used twelfths, unciae, for their fractions, the root of both “inch” and “ounce”.

Proposals to count fully in base 12 go back at least to the 17th century. Isaac Pitman, the shorthand inventor, designed the turned digits ↊ and ↋ in the 19th century, and they entered Unicode in 2015 at the request of the dozenal societies. Decimal won because of the metric system and ten fingers, but the arithmetic advantages of twelve still make it the favourite alternative base.

This converter turns whole numbers, decimals and fractions into dozenal and back, exactly, marking repeating digits and explaining whether a fraction ends in base 12. You can write ten and eleven as ↊ and ↋, X and E, A and B or * and #, and any of them is accepted as input.

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Related calculators: Number Base Converter, Babylonian Numerals, and Maya Numerals.