Hex Modulo Calculator
Find the remainder of dividing one hex value by another — the modulo operation, useful for bitmasks, hashing, and cyclic indexing.
How Hex Modulo Works
Modulo (often written mod or %) finds what's left over after dividing as many whole times as possible. Convert both hex values to decimal, divide, and whatever remains — the remainder — is the modulo result, converted back to hex.
Hex Modulo Example, Step by Step
1D2 mod A = 6
0x1D2 mod 0xA = 0x6
1D2 hex = 466 decimal A hex = 10 decimal 466 / 10 = 46 remainder 6 Result: 6
| Step | Description | Result |
|---|---|---|
| Convert 1D2 | 1D2 (hex) = 466 (decimal) | 466 |
| Convert A | A (hex) = 10 (decimal) | 10 |
| Divide and find remainder | 466 / 10 = 46 remainder 6 | 6 |
This is the same division already covered on the Hex Division Calculator — modulo just keeps the remainder and discards the quotient.
Common Mistakes With Hex Modulo
- Confusing modulo's remainder with division's quotient — they're different parts of the same calculation.
- Forgetting the result is always smaller than the second value (the divisor).
- Attempting modulo by zero, which is undefined.
Frequently Asked Questions
What does modulo actually compute?
The remainder left over after dividing one value by another as many whole times as possible. 1D2 mod A is 6, because A (10) fits into 1D2 (466) exactly 46 times with 6 left over.
How is modulo different from division?
Division gives you the quotient (how many times it fits); modulo gives you only the remainder. This calculator's division tool already shows both — modulo isolates just the remainder as its own operation.
What happens with modulo by zero?
It's undefined, the same as regular division by zero — the calculator flags it as an error.
Where does hex modulo come up in programming?
Bitmasking with powers of 2 (x mod 0x100 isolates the low byte), hash table indexing, cyclic buffers, and checksum calculations all lean on modulo arithmetic, often with hex-formatted operands.
Is x mod 0x10 the same as reading the last hex digit?
Yes — dividing by 16 (0x10) always leaves the last hex digit as the remainder, since one hex digit represents exactly the ones place in base 16.
Can the remainder ever be negative?
Not with this calculator — both inputs are treated as non-negative hex values, so the remainder is always in the range from 0 up to (but not including) the second value.