Modulo Calculator

Calculate Remainder Operations

Calculate modulo (remainder) operations with detailed step-by-step explanations and visual breakdown.

Modulo Operation

Modulo Format:
a mod n
Also written as: a % n

What is Modulo?

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

Formula:

a mod n = r

where r is the remainder

Example:

17 mod 5 = 2

Because 17 ÷ 5 = 3 remainder 2

Features

  • Step-by-step solutions
  • Detailed explanations
  • Quotient and remainder
  • Verification formula
  • Quick examples
  • Copy result
  • Negative number support
  • Decimal number support

Common Uses

Programming:

Check even/odd, array indexing

Cryptography:

Encryption algorithms

Time:

12-hour clock calculations

Mathematics:

Number theory, modular arithmetic

Properties

Range:

0 ≤ (a mod n) < n

Identity:

a mod 1 = 0

Self:

a mod a = 0

Distributive:

(a + b) mod n = ((a mod n) + (b mod n)) mod n

Use Cases

  • Programming and algorithms
  • Cryptography and security
  • Hash functions
  • Circular arrays and buffers
  • Time and calendar calculations
  • Check digit validation
  • Random number generation
  • Number theory problems

Examples

Real-World Examples:

Even/Odd:

n mod 2 = 0 (even) or 1 (odd)

12-Hour Clock:

15:00 mod 12 = 3:00 PM

Day of Week:

Day number mod 7 gives weekday

Array Wrap:

index mod length keeps in bounds