Base 32 to Base 36 Converter
Convert base 32 numbers to base 36.
7V (base 32) = 73 (base 36)
Digits in base 32: 0 to 9 and A to V. Digits in base 36: 0 to 9 and A to Z.
How to convert Base 32 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 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 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 32: 1, 32, 1024, 32768, 1048576, 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 32: 0 to 9 and A to Vdigits in base 36: 0 to 9 and A to Z
Worked example 1: 1D from base 32 to base 36
Step 1: base 32 to decimal1D (base 32) = 1 × 321 + 13 × 320= 32 + 13= 45Step 2: decimal to base 3645 ÷ 36 = 1 remainder 91 ÷ 36 = 0 remainder 1Read the remainders from the bottom up: 191D (base 32) = 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: 7V from base 32 to base 36
Step 1: base 32 to decimal7V (base 32) = 7 × 321 + 31 × 320= 224 + 31= 255Step 2: decimal to base 36255 ÷ 36 = 7 remainder 37 ÷ 36 = 0 remainder 7Read the remainders from the bottom up: 737V (base 32) = 73 (base 36)
Worked example 3: V8 from base 32 to base 36
Step 1: base 32 to decimalV8 (base 32) = 31 × 321 + 8 × 320= 992 + 8= 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: RSV8 (base 32) = RS (base 36)
Need the other direction? Open the Base 36 to Base 32 converter.
Base 32 to Base 36 examples
The decimal number 255 is written 7V in base 32 and 73 in base 36.
| Base 32 | Base 36 | Decimal |
|---|---|---|
| 1 | 1 | 1 |
| 2 | 2 | 2 |
| 7 | 7 | 7 |
| 8 | 8 | 8 |
| A | A | 10 |
| F | F | 15 |
| G | G | 16 |
| 10 | W | 32 |
| 20 | 1S | 64 |
| 34 | 2S | 100 |
| 7V | 73 | 255 |
| V8 | RS | 1000 |
Where Base 32 to Base 36 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.
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 2 digits in base 32 and 2 in base 36.
Base 32 to Base 36 FAQ
How do I convert base 32 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 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 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 0.97 base 36 digits for every base 32 digit. The number 255 needs 2 digits in base 32 and 2 in base 36.
What is 7V in base 36?
7V in base 32 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.