What is the modulo operation?

The modulo operation (a mod b) returns the remainder after dividing a by b. For example, 17 mod 5 = 2 because 17 = 3 × 5 + 2.

How are negative numbers handled?

This calculator uses truncated division, meaning the quotient is rounded toward zero. So -7 mod 3 = -1 (because -7 = -2 × 3 + (-1)). Some languages like Python use floored division and would return 2 — the step-by-step panel notes both conventions.

What happens when the divisor is zero?

Division by zero is undefined. The calculator will display an error if you enter 0 as the divisor.

What is the difference between remainder and modulo?

They differ only for negative inputs. Remainder follows the sign of the dividend (truncated division); modulo follows the sign of the divisor (floored division). For non-negative integers they are identical.

Can I use decimal numbers?

This tool is designed for integers. Decimal inputs are truncated to their integer part before calculation.

Modulo Calculator

Enter two integers to instantly compute the remainder (a mod b) with a full step-by-step breakdown.

Enter Values

Dividend (a)

mod

Divisor (b)

Quick Examples

Enter values and click Calculate

Summary

The Modulo Calculator computes the remainder when one integer (the dividend) is divided by another (the divisor). It supports both positive and negative integers and follows the truncated-division convention used in most programming languages. Results are shown instantly with a clear step-by-step breakdown.

How it works

Enter the dividend (a) — the number to be divided.
Enter the divisor (b) — the number to divide by.
Click "Calculate" or press Enter to compute a mod b.
The result panel shows the quotient, remainder, and a full step-by-step explanation.
Use the quick-examples buttons to explore common modulo patterns.

Use cases

Check whether a number is even or odd (n mod 2).
Wrap array indices or cyclic counters in programming.
Determine divisibility of large numbers quickly.
Compute clock arithmetic (e.g. 25 mod 12 = 1 for hours).
Verify hash or checksum calculations by hand.
Understand how negative-number remainders behave in different languages.
Teach or learn the division algorithm in math courses.
Debug modular arithmetic in cryptography exercises.

Frequently Asked Questions

Last updated: 2026-05-28 · Reviewed by Nham Vu