Dozenal (Base 12) Converter — Decimal ↔ Base-12, X/E and A/B Notation
Convert integers between decimal and dozenal (base 12) two ways, live in your browser. Uses the standard X = ten, E = eleven digits (with an A/B toggle and the ↊/↋ glyphs), accepts either notation on input, handles huge numbers with BigInt, and shows the positional-expansion working both ways.
How to Use
- Type a whole number in either box — decimal on the left, dozenal (base 12) on the right.
- The other box updates live as you type; conversion runs both ways.
- Pick your two extra digits: <strong>X/E</strong> (ten / eleven, the default) or the <strong>A/B</strong> style.
- Input accepts either notation, so “1E” and “1B” both read as decimal 23.
- Open “Show work” to see the positional expansion, and use the Copy buttons to grab a value.
1E and 1B both read as 23, and the Unicode glyphs ↊ (ten) and ↋ (eleven) work too.Counting in twelves
Dozenal (also called duodecimal or base 12) counts in groups of twelve rather than ten. Because a base needs as many digit symbols as its size, dozenal requires two extra digits beyond 0–9 — one for ten and one for eleven. After 9 you count X (ten) and E (eleven), and only then does the number roll over to 10, which in dozenal means twelve. So 10₁₂ = 12₁₀, E₁₂ = 11₁₀, and 100₁₂ = 144₁₀ (a “gross”). Everything here runs in your browser — nothing is uploaded — and BigInt arithmetic keeps even hundred-digit numbers exact.
Why twelve, and how the conversion works
Twelve is unusually convenient because it divides evenly by 2, 3, 4 and 6, while ten only divides cleanly by 2 and 5. That is why a third is the tidy 0.4 in dozenal but the endless 0.333… in decimal, and it is the reason eggs, hours, months and inches all come in twelves. Decimal → dozenal uses repeated division: divide by 12, keep each remainder (writing X for 10 and E for 11), repeat, and read the remainders bottom-to-top — so 1000 → 83 r4, 6 rE, 0 r6 → 6E4. Dozenal → decimal is positional expansion: multiply each digit by a power of twelve and add — 6E4₁₂ = 6×144 + 11×12 + 4 = 1000. There is no single agreed notation for the two extra digits, so this converter offers the common X/E pair, a hex-style A/B toggle, and accepts the Unicode dek and el glyphs ↊ (U+218A) and ↋ (U+218B) on input.
Quick reference
About the Dozenal (Base 12) Converter — Decimal ↔ Base-12, X/E and A/B Notation
The Dozenal (Base 12) Converter — Decimal ↔ Base-12, X/E and A/B Notation is a simple, free helper for everyday tasks that runs entirely on your own device. Convert integers between decimal and dozenal (base 12) two ways, live in your browser. Uses the standard X = ten, E = eleven digits (with an A/B toggle and the ↊/↋ glyphs), accepts either notation on input, handles huge numbers with BigInt, and shows the positional-expansion working both ways.
How it works
Type a value, then pick what you want to change it into. The answer appears straight away. It all happens on your own device, so it is fast and nothing you type is sent away. Just check that you picked the right “from” and “to” so you get the answer you wanted.
Want the deeper story? The Knowledge Base explains the ideas behind the tools in more detail.
Frequently Asked Questions
What is dozenal (base 12)?
Dozenal — also called duodecimal — counts in twelves instead of tens. It needs twelve digit symbols, so two new ones are added for ten and eleven. After 9 comes ten (written X), then eleven (written E), and the next number rolls over to “10”, which means twelve. Twelve is a popular base because it divides evenly by 2, 3, 4 and 6, whereas ten only divides by 2 and 5.
What do X and E mean, and what about A/B or ↊/↋?
There is no single official notation. This tool defaults to X = ten and E = eleven (the Dozenal Societies’ common ASCII choice). The A/B toggle borrows the hex-style letters (A = ten, B = eleven) which some programmers prefer. The Unicode dek and el glyphs ↊ (U+218A) and ↋ (U+218B) are the “proper” typographic forms; you can paste those in too and they will be read correctly.
How do I convert decimal to dozenal by hand?
Divide the number by 12 repeatedly, writing down each remainder; reading the remainders from bottom to top gives the dozenal digits (using X for a remainder of 10 and E for 11). For example 100 → 8 r4, 0 r8 → 84. The reverse is positional expansion: 84 in base 12 = 8×12 + 4 = 100.
How large a number can it handle?
Conversion uses JavaScript BigInt, so there is no practical size limit — values with hundreds of digits convert exactly. This tool handles whole numbers (integers); it does not convert dozenal fractions.
Is anything uploaded?
No. The whole conversion runs in your browser with JavaScript — nothing is sent to a server.
How do I use the Dozenal (Base 12) Converter — Decimal ↔ Base-12, X/E and A/B Notation?
Just type or paste your value. The answer shows up right away — there is no button to press. Change anything and it updates by itself.
Does it cost anything or need an account?
No. The tool is completely free, there is no account to create, and it keeps working offline after the page first loads.
Is anything I type uploaded?
No. The tool works entirely on your device, so the values you enter never leave your browser.
Common Use Cases
Learning number bases
See how the same value looks in base 10 and base 12 side by side, with the repeated-division and positional working spelled out.
Dozenal enthusiasts
Convert quickly between decimal and dozenal in whichever notation you favour — X/E, A/B, or the ↊/↋ Unicode glyphs.
Teaching divisibility
Demonstrate why twelfths are “nicer” than tenths — a third is 0.4 in dozenal but 0.333… in decimal.
Puzzles & recreational math
Decode base-12 numbers in puzzles, ciphers and number-theory exercises.
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