Modulo Calculator
Calculate the modulo (remainder) of any two integers: a mod n = r.
Shows quotient, remainder, step-by-step division, and clock arithmetic examples.
Modulo Result
Modulo (mod) returns the remainder after dividing one number by another.
a mod b = a − b × floor(a / b)
Or equivalently:
a = b × quotient + remainder
Examples:
17 mod 5 = 2(17 = 5 × 3 + 2)25 mod 7 = 4(25 = 7 × 3 + 4)100 mod 10 = 0(100 = 10 × 10 + 0)7 mod 3 = 1(7 = 3 × 2 + 1)
Clock arithmetic (mod 12):
- If it is 10 o’clock and you add 5 hours: (10 + 5) mod 12 = 3 o’clock
- If it is 7 o’clock and you add 20 hours: (7 + 20) mod 12 = 3 o’clock
Common uses:
- Even/odd check:
n mod 2→ 0 = even, 1 = odd - Cycling/wrapping: array indices, day of week
- Digit extraction:
n mod 10gives the last digit - Divisibility test:
n mod d = 0means n is divisible by d - Cryptography: RSA encryption uses modular exponentiation
Negative numbers:
- In mathematics:
−7 mod 3 = 2(remainder is always non-negative) - In some programming languages:
−7 % 3 = −1(sign matches dividend) - This calculator uses the mathematical definition
How we build and check this calculator
This calculator runs entirely in your browser, so the numbers you enter stay on your device. The math behind it is written by hand and tested against worked examples and standard references before the page goes live.
SuperGlobalCalculator is independently built and maintained. See how we build and verify our calculators.