Hexadecimal (Base 16) to Base 32 Converter
Convert hexadecimal numbers to base 32.
FF (base 16) = 7V (base 32)
Digits in base 16: 0 to 9 and A to F. Digits in base 32: 0 to 9 and A to V.
How to convert Hexadecimal 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 16 the place values, from the right, are 160 = 1, 161 = 16, 162 = 256 and so on.
Most pairs have no direct trick, so go through decimal, the base we all calculate in. First turn the base 16 number into decimal, then divide by 32 and read the remainders from the bottom up. Two short steps, and you can check the number in the middle.
Both 16 and 32 are powers of 2, so there is a faster way that skips decimal. Write each digit as 4 bits, then regroup the bits in groups of 5 from the right and replace each group with a base 32 digit.
The method
decimal value = each digit × its place value, all added upplace values in base 16: 1, 16, 256, 4096, 65536, and so ondivide by 32, keep the remainder, repeat until the quotient is 0the answer is the remainders read from last to first1 base 16 digit = 4 bits1 base 32 digit = 5 bitsdigits in base 16: 0 to 9 and A to Fdigits in base 32: 0 to 9 and A to V
Worked example 1: 2D from hexadecimal to base 32
Step 1: base 16 to decimal2D (base 16) = 2 × 161 + 13 × 160= 32 + 13= 45Step 2: decimal to base 3245 ÷ 32 = 1 remainder 13 (D)1 ÷ 32 = 0 remainder 1Read the remainders from the bottom up: 1D2D (base 16) = 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. Digits that are 0 add nothing to the sum, so they are left out of the expansion.
Worked example 2: FF from hexadecimal to base 32
Step 1: base 16 to decimalFF (base 16) = 15 × 161 + 15 × 160= 240 + 15= 255Step 2: decimal to base 32255 ÷ 32 = 7 remainder 31 (V)7 ÷ 32 = 0 remainder 7Read the remainders from the bottom up: 7VFF (base 16) = 7V (base 32)
Worked example 3: 3E8 from hexadecimal to base 32
Step 1: base 16 to decimal3E8 (base 16) = 3 × 162 + 14 × 161 + 8 × 160= 768 + 224 + 8= 1,000Step 2: decimal to base 321,000 ÷ 32 = 31 remainder 831 ÷ 32 = 0 remainder 31 (V)Read the remainders from the bottom up: V83E8 (base 16) = V8 (base 32)
Worked example 4: B5 with the bit-group shortcut
B5 (base 16)Write each digit as 4 bits: B = 1011, 5 = 0101Join them and drop leading zeros: 10110101Pad the left with zeros and split into groups of 5: 00101 10101Replace each group with its digit: 00101 = 5, 10101 = LB5 (base 16) = 5L (base 32)
Both bases are powers of 2, so there is no need to go through decimal. Groups of 5 bits make one base 32 digit.
Need the other direction? Open the Base 32 to Hexadecimal converter.
Hexadecimal to Base 32 examples
The decimal number 255 is written FF in hexadecimal and 7V in base 32.
| Hexadecimal | Base 32 | Decimal |
|---|---|---|
| 1 | 1 | 1 |
| 2 | 2 | 2 |
| 7 | 7 | 7 |
| 8 | 8 | 8 |
| A | A | 10 |
| F | F | 15 |
| 10 | G | 16 |
| 20 | 10 | 32 |
| 40 | 20 | 64 |
| 64 | 34 | 100 |
| FF | 7V | 255 |
| 3E8 | V8 | 1000 |
Where Hexadecimal to Base 32 comes up
Hexadecimal (base 16) uses 0 to 9 and A to F, and each hex digit stands for exactly four bits, so one byte is always two hex digits. You see it in web colours like #FF8800, memory addresses, MAC addresses, hash values and byte dumps.
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 2 digits in hexadecimal and 2 in base 32.
Hexadecimal to Base 32 FAQ
How do I convert hexadecimal to base 32?
Convert to decimal first by adding up each digit times its place value, then divide that decimal number by 32 repeatedly and read the remainders from last to first. Because both bases are powers of 2, you can also skip decimal and work with groups of bits.
Which digits does hexadecimal use?
Base 16 uses the digits 0 to 9 and A to F. For example, G is not a valid digit in base 16. Letters are not case sensitive on this converter, and results are shown in capitals.
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 0.8 base 32 digits for every hexadecimal digit. The number 255 needs 2 digits in hexadecimal and 2 in base 32.
Is there a shortcut for hexadecimal to base 32?
Yes. Both 16 and 32 are powers of 2, so there is a faster way that skips decimal. Write each digit as 4 bits, then regroup the bits in groups of 5 from the right and replace each group with a base 32 digit.
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.