How it's read: each place is a power of twelve — units, twelves, gross (144s), great gross (1,728s) — instead of powers of ten. The remainders from repeated division spell out the answer from the last digit backwards, which is why the steps above read bottom-to-top. Dozenalists write the fraction point as a semicolon, so 6;6 means six-and-a-half.
Whole numbers, decimals, and negatives all work. Base 12 needs two extra digits beyond 9 — pick the style you like below.
Every digit times its power of twelve — whole-part places in blue, fraction places in orange. Shown for up to 16 places.
Digits 0–9 plus ten and eleven in any spelling: ↊ ↋, X E, A B, or T E — upper or lower case, with ; or . as the fraction point.
Same rules, different base: carry whenever a column reaches twelve instead of ten, borrow twelve instead of ten. That's the whole difference. Multiplication builds one partial product per digit of the second number, each shifted one place left, then adds them up.
Add, subtract, or multiply two dozenal whole numbers — and watch the carries work column by column, just like school arithmetic in a different base.
Notice how much cleaner the patterns are: the 3, 4, and 6 rows all end in repeating cycles of just two or three digits.
Hover any cell for its decimal translation.
Landmarks: 10 is a dozen (12), 100 is a gross (144), and 1000 is a great gross (1,728). Egg cartons, clock faces, and inches on a ruler all still count this way — the table above is what arithmetic looks like when the number system agrees with them.
The times table every dozenal schoolkid would memorize — plus addition and a counting chart. Hover or tap any cell for its decimal translation.
Digits needed to write 1/n exactly, for n = 2 through 12. Short bars are clean, terminating fractions; red bars never terminate — they repeat forever. Base 12 turns thirds, sixths, and ninths from endless decimals into one or two digits.
Dozenal isn't a novelty — mathematicians have argued for centuries that twelve divides more evenly than ten. Pick a topic to see why.