Decimal (Base 10) to Base 32 Converter
Convert decimal numbers to base 32.
255 (base 10) = 7V (base 32)
Digits in base 10: 0 to 9. Digits in base 32: 0 to 9 and A to V.
How to convert Decimal to Base 32
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 32, divide the number by 32 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 32, 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 32: 0 to 9 and A to V
Worked example 1: 45 from decimal to base 32
45 ÷ 32 = 1 remainder 13 (D)1 ÷ 32 = 0 remainder 1Read the remainders from the bottom up: 1D45 (base 10) = 1D (base 32)
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 base 32
255 ÷ 32 = 7 remainder 31 (V)7 ÷ 32 = 0 remainder 7Read the remainders from the bottom up: 7V255 (base 10) = 7V (base 32)
Worked example 3: 1000 from decimal to base 32
1,000 ÷ 32 = 31 remainder 831 ÷ 32 = 0 remainder 31 (V)Read the remainders from the bottom up: V81000 (base 10) = V8 (base 32)
Need the other direction? Open the Base 32 to Decimal converter.
Decimal to Base 32 examples
The decimal number 255 is written 255 in decimal and 7V in base 32.
| Decimal | Base 32 |
|---|---|
| 1 | 1 |
| 2 | 2 |
| 7 | 7 |
| 8 | 8 |
| 10 | A |
| 15 | F |
| 16 | G |
| 32 | 10 |
| 64 | 20 |
| 100 | 34 |
| 255 | 7V |
| 1000 | V8 |
Where Decimal to Base 32 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.
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.
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 2 in base 32.
Decimal to Base 32 FAQ
How do I convert decimal to base 32?
Divide the decimal number by 32, write down the remainder, and repeat with the quotient until it reaches 0. The remainders, read from last to first, are the base 32 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 base 32 number be longer or shorter?
Shorter. Going to a larger base packs more value into each digit, so the result is shorter. Roughly 0.66 base 32 digits for every decimal digit. The number 255 needs 3 digits in decimal and 2 in base 32.
What is 255 in base 32?
255 in decimal is 7V in base 32. 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.