Base 32 to Hexadecimal (Base 16) Converter
Convert base 32 numbers to hexadecimal.
7V (base 32) = FF (base 16)
Digits in base 32: 0 to 9 and A to V. Digits in base 16: 0 to 9 and A to F.
How to convert Base 32 to Hexadecimal
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 16 and read the remainders from the bottom up. Two short steps, and you can check the number in the middle.
Both 32 and 16 are powers of 2, so there is a faster way that skips decimal. Write each digit as 5 bits, then regroup the bits in groups of 4 from the right and replace each group with a base 16 digit.
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 16, keep the remainder, repeat until the quotient is 0the answer is the remainders read from last to first1 base 32 digit = 5 bits1 base 16 digit = 4 bitsdigits in base 32: 0 to 9 and A to Vdigits in base 16: 0 to 9 and A to F
Worked example 1: 1D from base 32 to hexadecimal
Step 1: base 32 to decimal1D (base 32) = 1 × 321 + 13 × 320= 32 + 13= 45Step 2: decimal to base 1645 ÷ 16 = 2 remainder 13 (D)2 ÷ 16 = 0 remainder 2Read the remainders from the bottom up: 2D1D (base 32) = 2D (base 16)
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 hexadecimal
Step 1: base 32 to decimal7V (base 32) = 7 × 321 + 31 × 320= 224 + 31= 255Step 2: decimal to base 16255 ÷ 16 = 15 remainder 15 (F)15 ÷ 16 = 0 remainder 15 (F)Read the remainders from the bottom up: FF7V (base 32) = FF (base 16)
Worked example 3: V8 from base 32 to hexadecimal
Step 1: base 32 to decimalV8 (base 32) = 31 × 321 + 8 × 320= 992 + 8= 1,000Step 2: decimal to base 161,000 ÷ 16 = 62 remainder 862 ÷ 16 = 3 remainder 14 (E)3 ÷ 16 = 0 remainder 3Read the remainders from the bottom up: 3E8V8 (base 32) = 3E8 (base 16)
Worked example 4: 5L with the bit-group shortcut
5L (base 32)Write each digit as 5 bits: 5 = 00101, L = 10101Join them and drop leading zeros: 10110101Split into groups of 4 from the right: 1011 0101Replace each group with its digit: 1011 = B, 0101 = 55L (base 32) = B5 (base 16)
Both bases are powers of 2, so there is no need to go through decimal. Groups of 4 bits make one base 16 digit.
Need the other direction? Open the Hexadecimal to Base 32 converter.
Base 32 to Hexadecimal examples
The decimal number 255 is written 7V in base 32 and FF in hexadecimal.
| Base 32 | Hexadecimal | Decimal |
|---|---|---|
| 1 | 1 | 1 |
| 2 | 2 | 2 |
| 7 | 7 | 7 |
| 8 | 8 | 8 |
| A | A | 10 |
| F | F | 15 |
| G | 10 | 16 |
| 10 | 20 | 32 |
| 20 | 40 | 64 |
| 34 | 64 | 100 |
| 7V | FF | 255 |
| V8 | 3E8 | 1000 |
Where Base 32 to Hexadecimal 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.
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.
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 2 in hexadecimal.
Base 32 to Hexadecimal FAQ
How do I convert base 32 to hexadecimal?
Convert to decimal first by adding up each digit times its place value, then divide that decimal number by 16 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 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 hexadecimal number be longer or shorter?
Longer. Going to a smaller base spreads the same value over more digits, so the result is longer. Roughly 1.25 hexadecimal digits for every base 32 digit. The number 255 needs 2 digits in base 32 and 2 in hexadecimal.
Is there a shortcut for base 32 to hexadecimal?
Yes. Both 32 and 16 are powers of 2, so there is a faster way that skips decimal. Write each digit as 5 bits, then regroup the bits in groups of 4 from the right and replace each group with a base 16 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.