Duodecimal (Base 12) to Base 36 Converter
Convert duodecimal numbers to base 36.
193 (base 12) = 73 (base 36)
Digits in base 12: 0 to 9 and A to B. Digits in base 36: 0 to 9 and A to Z.
How to convert Duodecimal to Base 36
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 12 the place values, from the right, are 120 = 1, 121 = 12, 122 = 144 and so on.
Most pairs have no direct trick, so go through decimal, the base we all calculate in. First turn the base 12 number into decimal, then divide by 36 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 12: 1, 12, 144, 1728, 20736, and so ondivide by 36, keep the remainder, repeat until the quotient is 0the answer is the remainders read from last to firstdigits in base 12: 0 to 9 and A to Bdigits in base 36: 0 to 9 and A to Z
Worked example 1: 39 from duodecimal to base 36
Step 1: base 12 to decimal39 (base 12) = 3 × 121 + 9 × 120= 36 + 9= 45Step 2: decimal to base 3645 ÷ 36 = 1 remainder 91 ÷ 36 = 0 remainder 1Read the remainders from the bottom up: 1939 (base 12) = 19 (base 36)
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: 193 from duodecimal to base 36
Step 1: base 12 to decimal193 (base 12) = 1 × 122 + 9 × 121 + 3 × 120= 144 + 108 + 3= 255Step 2: decimal to base 36255 ÷ 36 = 7 remainder 37 ÷ 36 = 0 remainder 7Read the remainders from the bottom up: 73193 (base 12) = 73 (base 36)
Worked example 3: 6B4 from duodecimal to base 36
Step 1: base 12 to decimal6B4 (base 12) = 6 × 122 + 11 × 121 + 4 × 120= 864 + 132 + 4= 1,000Step 2: decimal to base 361,000 ÷ 36 = 27 remainder 28 (S)27 ÷ 36 = 0 remainder 27 (R)Read the remainders from the bottom up: RS6B4 (base 12) = RS (base 36)
Need the other direction? Open the Base 36 to Duodecimal converter.
Duodecimal to Base 36 examples
The decimal number 255 is written 193 in duodecimal and 73 in base 36.
| Duodecimal | Base 36 | Decimal |
|---|---|---|
| 1 | 1 | 1 |
| 2 | 2 | 2 |
| 7 | 7 | 7 |
| 8 | 8 | 8 |
| A | A | 10 |
| 13 | F | 15 |
| 14 | G | 16 |
| 28 | W | 32 |
| 54 | 1S | 64 |
| 84 | 2S | 100 |
| 193 | 73 | 255 |
| 6B4 | RS | 1000 |
Where Duodecimal to Base 36 comes up
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.
Base 36 uses 0 to 9 and A to Z, the largest base you can write with digits and letters alone. Short IDs and URL slugs often use it, and JavaScript number.toString(36) and parseInt(text, 36) work in base 36.
Going to a larger base packs more value into each digit, so the result is shorter. The number 255 needs 3 digits in duodecimal and 2 in base 36.
Duodecimal to Base 36 FAQ
How do I convert duodecimal to base 36?
Convert to decimal first by adding up each digit times its place value, then divide that decimal number by 36 repeatedly and read the remainders from last to first.
Which digits does duodecimal use?
Base 12 uses the digits 0 to 9 and A to B. For example, C is not a valid digit in base 12. Letters are not case sensitive on this converter, and results are shown in capitals.
Will the base 36 number be longer or shorter?
Shorter. Going to a larger base packs more value into each digit, so the result is shorter. Roughly 0.69 base 36 digits for every duodecimal digit. The number 255 needs 3 digits in duodecimal and 2 in base 36.
What is 193 in base 36?
193 in duodecimal is 73 in base 36. 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.