Base 32 to Decimal (Base 10) Converter
Convert base 32 numbers to decimal.
7V (base 32) = 255 (base 10)
Digits in base 32: 0 to 9 and A to V. Digits in base 10: 0 to 9.
How to convert Base 32 to Decimal
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.
To get from base 32 to decimal, multiply each digit by 32 raised to the power of its position, counting from 0 on the right, and add the results.
The method
decimal value = each digit × its place value, all added upplace values in base 32: 1, 32, 1024, 32768, 1048576, and so ondigits in base 32: 0 to 9 and A to Vdigits in base 10: 0 to 9
Worked example 1: 1D from base 32 to decimal
1D (base 32) = 1 × 321 + 13 × 320= 32 + 13= 451D (base 32) = 45 (base 10)
Letters stand for values from 10 up: A = 10, B = 11, C = 12 and so on. 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 decimal
7V (base 32) = 7 × 321 + 31 × 320= 224 + 31= 2557V (base 32) = 255 (base 10)
Worked example 3: V8 from base 32 to decimal
V8 (base 32) = 31 × 321 + 8 × 320= 992 + 8= 1,000V8 (base 32) = 1000 (base 10)
Need the other direction? Open the Decimal to Base 32 converter.
Base 32 to Decimal examples
The decimal number 255 is written 7V in base 32 and 255 in decimal.
| Base 32 | Decimal |
|---|---|
| 1 | 1 |
| 2 | 2 |
| 7 | 7 |
| 8 | 8 |
| A | 10 |
| F | 15 |
| G | 16 |
| 10 | 32 |
| 20 | 64 |
| 34 | 100 |
| 7V | 255 |
| V8 | 1000 |
Where Base 32 to Decimal 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.
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.
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 decimal.
Base 32 to Decimal FAQ
How do I convert base 32 to decimal?
Multiply each base 32 digit by 32 raised to the power of its position, counting from 0 on the right, then add everything up.
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 decimal number be longer or shorter?
Longer. Going to a smaller base spreads the same value over more digits, so the result is longer. Roughly 1.51 decimal digits for every base 32 digit. The number 255 needs 2 digits in base 32 and 3 in decimal.
What is 7V in decimal?
7V in base 32 is 255 in decimal. 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.