Modulo Calculator
Calculate the modulo of two numbers (a mod b) — the result always takes the sign of the divisor, matching the convention used in mathematics and languages like Python.
- Free to use
- Accurate results
- No registration required
- Works on all devices
Your result
2
a mod b
AI explanation
Formula
modulo = a − b × floor(a / b) — the result takes the sign of the divisor bWorked example
-7 mod 3
| Field | Value |
|---|---|
| Dividend (a) | -7 |
| Divisor (b) | 3 |
| a mod b | 2 |
| Remainder (a % b, sign follows dividend) | -1 |
Assumptions
- The divisor cannot be zero.
- When the dividend and divisor have the same sign, modulo and remainder give the same result — they only differ when the signs differ. See the Remainder Calculator for the other convention.
Frequently asked questions
What is the difference between modulo and remainder?
They agree when the dividend and divisor have the same sign. When the signs differ, modulo (this calculator's primary result) always takes the sign of the divisor, while remainder (see the Remainder Calculator) always takes the sign of the dividend.
Why does -7 mod 3 equal 2, not -1?
Modulo is defined using floor division: -7 ÷ 3 floors to -3, and -7 − (3 × -3) = -7 + 9 = 2. This convention (used by Python's % operator) always returns a result with the same sign as the divisor.
Where is modulo commonly used?
It's used for cyclic calculations like clock arithmetic, checking divisibility, hashing, and wrapping array indices — anywhere a value needs to "wrap around" within a fixed range.