Modular Hashing Calculator
The division method, or modular hashing, is the simplest and most common way to map a numeric key to a slot in a hash table. The hash is just the remainder when the key is divided by the table size, written key modulo table size, which always lands in the range from zero up to one less than the table size. This calculator computes that slot for any key and table size, and it also reports the quotient so you can see the full division. The choice of table size matters: a prime number that is not close to a power of two tends to spread keys evenly and reduce clustering, because it avoids common factors with the keys, whereas a power-of-two size only keeps the low bits and can collide badly with patterned data. You enter the key and the table size, and the calculator returns the slot index and notes whether the table size is prime, a small but useful guide to good hashing. Every figure is computed deterministically by integer division, never guessed, so the same key and size always give the same slot. The method and a worked example that reconciles to the calculator default are shown in full below so you can follow the arithmetic.
Modular hashing maps a key to a slot with slot = key mod table size. With the default key 1234 and table size 17, the slot is 10, since 1234 = 72 x 17 + 10.
Formula
slot = key mod table size
The slot is always between 0 and (table size - 1)
A prime table size, not near a power of two, spreads keys best
The key is divided by the table size; the remainder is the slot and the whole-number part is the quotient. Using a prime size avoids common factors with the keys and reduces clustering of slots.
Worked example
Hash the key 1234 into a table of size 17.
- 1234 divided by 17 is 72 with a remainder
- 72 x 17 = 1224
- 1234 - 1224 = 10, so the slot is 10
- 17 is prime, which helps spread keys evenly
These are the calculator's default inputs, so the slot of 10 matches the widget exactly.
Modular Hashing Calculator: frequently asked questions
What is modular hashing?
Modular hashing, or the division method, maps a key to a hash table slot by taking the remainder of the key divided by the table size. The result is always a valid slot index.
Why does the table size matter?
A prime table size that is not close to a power of two spreads keys evenly and reduces clustering, because it shares no common factors with typical keys. Power-of-two sizes only use the low bits and can collide badly.
What range does the slot fall in?
The slot is always between zero and one less than the table size, since a remainder is always smaller than the divisor. That keeps it within the table.
What does the quotient tell me?
The quotient is the whole-number part of the division. It is not used as the slot, but it shows the full division so you can verify the remainder.
Is the result reproducible?
Yes. Integer division is exact and deterministic, so the same key and table size always produce the same slot.
Official sources
- Hashing and data structure reference: US National Institute of Standards and Technology (NIST). As at 25 June 2026.
Reviewed by the CalculatorHub team, edited by James Graham, 25 June 2026. See our methodology. This is general information, not financial, tax, legal or investment advice.