Modulo Calculator

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 10 gives the last digit
• Divisibility test: n mod d = 0 means 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