Decimal (Base 10) to Duodecimal (Base 12) Converter
Convert decimal numbers to duodecimal.
255 (base 10) = 193 (base 12)
Digits in base 10: 0 to 9. Digits in base 12: 0 to 9 and A to B.
How to convert Decimal to Duodecimal
Every positional number system works the same way: a digit is worth its own value times the base raised to the power of its position. In base 10 the place values, from the right, are 100 = 1, 101 = 10, 102 = 100 and so on.
To get from decimal to base 12, divide the number by 12 over and over. Every remainder is one digit of the answer, starting with the last digit, so you read the remainders from the bottom up.
The method
divide by 12, keep the remainder, repeat until the quotient is 0the answer is the remainders read from last to firstdigits in base 10: 0 to 9digits in base 12: 0 to 9 and A to B
Worked example 1: 45 from decimal to duodecimal
45 ÷ 12 = 3 remainder 93 ÷ 12 = 0 remainder 3Read the remainders from the bottom up: 3945 (base 10) = 39 (base 12)
Letters stand for values from 10 up: A = 10, B = 11, C = 12 and so on. Remainders come out last digit first, which is why you read them from the bottom up.
Worked example 2: 255 from decimal to duodecimal
255 ÷ 12 = 21 remainder 321 ÷ 12 = 1 remainder 91 ÷ 12 = 0 remainder 1Read the remainders from the bottom up: 193255 (base 10) = 193 (base 12)
Worked example 3: 1000 from decimal to duodecimal
1,000 ÷ 12 = 83 remainder 483 ÷ 12 = 6 remainder 11 (B)6 ÷ 12 = 0 remainder 6Read the remainders from the bottom up: 6B41000 (base 10) = 6B4 (base 12)
Need the other direction? Open the Duodecimal to Decimal converter.
Decimal to Duodecimal examples
The decimal number 255 is written 255 in decimal and 193 in duodecimal.
| Decimal | Duodecimal |
|---|---|
| 1 | 1 |
| 2 | 2 |
| 7 | 7 |
| 8 | 8 |
| 10 | A |
| 15 | 13 |
| 16 | 14 |
| 32 | 28 |
| 64 | 54 |
| 100 | 84 |
| 255 | 193 |
| 1000 | 6B4 |
Where Decimal to Duodecimal comes up
Decimal is the base 10 system everyone learns first, with the digits 0 to 9. It is the form people read: prices, measurements, ages and IDs. It is also the base we calculate in by hand, which is why the worked steps on this page pass through decimal.
Duodecimal (base 12) uses 0 to 9 plus A for ten and B for eleven. Twelve divides evenly by 2, 3, 4 and 6. That is why dozens, the 12-hour clock, twelve inches to a foot and twelve months feel natural. A few mathematicians even argue it is a better base than ten.
Going to a larger base packs more value into each digit, so the result is shorter. The number 255 needs 3 digits in decimal and 3 in duodecimal.
Decimal to Duodecimal FAQ
How do I convert decimal to duodecimal?
Divide the decimal number by 12, write down the remainder, and repeat with the quotient until it reaches 0. The remainders, read from last to first, are the base 12 number.
Which digits does decimal use?
Base 10 uses the digits 0 to 9. For example, A is not a valid digit in base 10.
Will the duodecimal number be longer or shorter?
Shorter. Going to a larger base packs more value into each digit, so the result is shorter. Roughly 0.93 duodecimal digits for every decimal digit. The number 255 needs 3 digits in decimal and 3 in duodecimal.
What is 255 in duodecimal?
255 in decimal is 193 in duodecimal. Both are the decimal number 255.
Can I convert negative numbers or fractions?
The converter handles whole numbers, and a leading minus sign works for negatives. Fractions use a different method, where you repeatedly multiply the fractional part by the new base, and they are not supported here.