Math & Algebra Tool

Modulo Calculator

Find the remainder of a division.

Σ The Formula

a mod b = remainder of a ÷ b

Real World Examples

Simple Mod
17 mod 5 = 2 (17 = 3×5 + 2)
Time Calc
14:00 + 13 hours = 27 mod 24 = 3:00
Even/Odd
Any number mod 2: 0=Even, 1=Odd
Cycles
365 days mod 7 = 1 (same day next year + 1)

# About This Calculator

The Modulo operation (often abbreviated as "mod" or represented by %) finds the remainder after division of one number by another. While normal division calculates how many times a number fits, modulo tells you what is left over.

For example, 17 mod 5 is 2, because 5 goes into 17 three times (15) with 2 remaining. This concept is incredibly powerful in computer science (cryptography, hash functions), scheduling (days of the week), and detecting patterns (even vs. odd numbers).

It works like a clock face. On a 12-hour clock, 13 o'clock is actually 1 o'clock (13 mod 12 = 1). This "wrapping around" behavior is the core of modular arithmetic.

This tool computes the modulo for positive and negative numbers instantly, perfect for checking congruences or programming logic.

How To Use

  1. Enter the Dividend (the number being divided).
  2. Enter the Modulus (the divisor).
  3. Click Calculate.
  4. The result is the remainder.

Frequently Asked Questions

What is modulo used for in real life?+

Time (clocks wrap around 12 or 24), Calendars (weeks wrap around 7 days), and Cryptography (securing data online).

How is it different from division?+

Division focuses on the quotient (how many times it fits). Modulo focuses ONLY on the remainder (what is left over).

What is 5 mod 2?+

1. Because 2 goes into 5 twice (4), leaving 1 left over.

How do you handle negative numbers?+

It depends on the definition. In programming, -5 % 3 often gives -2 (truncation). In math, -5 mod 3 is usually 1 (flooring). This tool typically follows standard math conventions.

Is modulo the same as percent (%)?+

In programming (like Python, JS, C++), the % symbol represents the modulo operator. In math text, percents mean '/100'. Don't confuse them!

Is Modulo Calculator free to use?+

Yes, Modulo Calculator on Matheric is completely free to use. We believe in accessible education and utility for everyone.

About

The Modulo operation (often abbreviated as "mod" or represented by %) finds the remainder after division of one number by another. While normal division calculates how many times a number fits, modulo tells you what is left over.

For example, 17 mod 5 is 2, because 5 goes into 17 three times (15) with 2 remaining. This concept is incredibly powerful in computer science (cryptography, hash functions), scheduling (days of the week), and detecting patterns (even vs. odd numbers).

It works like a clock face. On a 12-hour clock, 13 o'clock is actually 1 o'clock (13 mod 12 = 1). This "wrapping around" behavior is the core of modular arithmetic.

This tool computes the modulo for positive and negative numbers instantly, perfect for checking congruences or programming logic.

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