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.
Where Hex Modulo Actually Comes Up
Wrapping an Index in a Cyclic Buffer
Ring buffers and circular queues wrap an index back to the start using modulo — this is the exact calculation that keeps a write or read position inside the buffer's bounds.
0x14 mod 0x10 = 0x4
Isolating the Low Byte of a Value
Taking a value mod 0x100 strips everything except its lowest byte — a quick way to check just the trailing byte of a larger hex number without a full bit mask.
0x1234 mod 0x100 = 0x34
Computing a Hash Table Bucket Index
Basic hash table implementations reduce a hash value to a valid bucket index with modulo against the table size — this is that final step before the lookup or insert happens.
hash mod table_size = bucket
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.
Why Use This Calculator Instead of Doing It by Hand
- Shows the full division alongside the remainder, so you can see how it was derived
- Runs entirely in your browser — nothing you type gets sent anywhere
- Handles multi-digit values without manual long division
- Flags modulo by zero instead of returning a silently wrong result
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.
How does modulo help with wraparound in a cyclic buffer?
Taking an index mod the buffer size wraps any index back into range automatically — index 0x14 mod 0x10 gives 0x4, which is exactly the wrapped position in a 16-slot buffer.
Why is modulo by a power of 2 so fast in hardware?
Because it's equivalent to a bitwise AND with (value - 1) — x mod 0x100 is the same result as x AND 0xFF, which processors compute far faster than a general division.