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