Modulo Calculator

Calculate the remainder when dividing a by n (a mod n).

Result
Enter values and click calculate

Quick Examples

Modulo Operation

The modulo operation finds the remainder after division of one number by another.

a mod n = r where a = qn + r and 0 ≤ r < n

Clock Arithmetic

Modulo is used in clock arithmetic. For example, to find what time it is 25 hours after 10:00:

(10 + 25) mod 12 = 35 mod 12 = 11 o'clock

Applications

  • Cryptography: RSA encryption, hash functions
  • Computer Science: Hash tables, random number generation
  • Music: Calculating chord progressions
  • Scheduling: Day-of-week calculations

Frequently Asked Questions

What is the difference between mod and remainder?
For positive numbers, mod and remainder give the same result. For negative numbers, modulo typically returns a positive result (wrapping around), while remainder returns a negative value.