Base 32 to Duodecimal (Base 12) Converter
Convert base 32 numbers to duodecimal.
7V (base 32) = 193 (base 12)
Digits in base 32: 0 to 9 and A to V. Digits in base 12: 0 to 9 and A to B.
How to convert Base 32 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 32 the place values, from the right, are 320 = 1, 321 = 32, 322 = 1024 and so on.
Most pairs have no direct trick, so go through decimal, the base we all calculate in. First turn the base 32 number into decimal, then divide by 12 and read the remainders from the bottom up. Two short steps, and you can check the number in the middle.
The method
decimal value = each digit × its place value, all added upplace values in base 32: 1, 32, 1024, 32768, 1048576, and so ondivide by 12, keep the remainder, repeat until the quotient is 0the answer is the remainders read from last to firstdigits in base 32: 0 to 9 and A to Vdigits in base 12: 0 to 9 and A to B
Worked example 1: 1D from base 32 to duodecimal
Step 1: base 32 to decimal1D (base 32) = 1 × 321 + 13 × 320= 32 + 13= 45Step 2: decimal to base 1245 ÷ 12 = 3 remainder 93 ÷ 12 = 0 remainder 3Read the remainders from the bottom up: 391D (base 32) = 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. Digits that are 0 add nothing to the sum, so they are left out of the expansion.
Worked example 2: 7V from base 32 to duodecimal
Step 1: base 32 to decimal7V (base 32) = 7 × 321 + 31 × 320= 224 + 31= 255Step 2: decimal to base 12255 ÷ 12 = 21 remainder 321 ÷ 12 = 1 remainder 91 ÷ 12 = 0 remainder 1Read the remainders from the bottom up: 1937V (base 32) = 193 (base 12)
Worked example 3: V8 from base 32 to duodecimal
Step 1: base 32 to decimalV8 (base 32) = 31 × 321 + 8 × 320= 992 + 8= 1,000Step 2: decimal to base 121,000 ÷ 12 = 83 remainder 483 ÷ 12 = 6 remainder 11 (B)6 ÷ 12 = 0 remainder 6Read the remainders from the bottom up: 6B4V8 (base 32) = 6B4 (base 12)
Need the other direction? Open the Duodecimal to Base 32 converter.
Base 32 to Duodecimal examples
The decimal number 255 is written 7V in base 32 and 193 in duodecimal.
| Base 32 | Duodecimal | Decimal |
|---|---|---|
| 1 | 1 | 1 |
| 2 | 2 | 2 |
| 7 | 7 | 7 |
| 8 | 8 | 8 |
| A | A | 10 |
| F | 13 | 15 |
| G | 14 | 16 |
| 10 | 28 | 32 |
| 20 | 54 | 64 |
| 34 | 84 | 100 |
| 7V | 193 | 255 |
| V8 | 6B4 | 1000 |
Where Base 32 to Duodecimal comes up
Base 32 here uses 0 to 9 and A to V, and each digit stands for exactly five bits. It is handy for compact IDs. The text encodings called Base32 in RFC 4648 work on bytes and use their own alphabets, so their output is not the same as converting a whole number.
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 smaller base spreads the same value over more digits, so the result is longer. The number 255 needs 2 digits in base 32 and 3 in duodecimal.
Base 32 to Duodecimal FAQ
How do I convert base 32 to duodecimal?
Convert to decimal first by adding up each digit times its place value, then divide that decimal number by 12 repeatedly and read the remainders from last to first.
Which digits does base 32 use?
Base 32 uses the digits 0 to 9 and A to V. For example, W is not a valid digit in base 32. Letters are not case sensitive on this converter, and results are shown in capitals.
Will the duodecimal number be longer or shorter?
Longer. Going to a smaller base spreads the same value over more digits, so the result is longer. Roughly 1.39 duodecimal digits for every base 32 digit. The number 255 needs 2 digits in base 32 and 3 in duodecimal.
What is 7V in duodecimal?
7V in base 32 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.