Modulo Calculator

Calculate a mod n for positive and negative numbers using the mathematical (always non-negative) definition.

Enter values

Result

-17 mod 5

Truncated remainder (JavaScript/C %): -2

Step-by-stepShow

-17 = 5 × -4 + 3

About the Modulo Calculator

Calculate a mod n for positive and negative numbers using the mathematical (always non-negative) definition.

Also known as: mod calculator, modulus calculator, a mod b, modular operation.

How to use this calculator

Enter a, n (modulus).
The result updates instantly as you type — press Calculate (or Enter) at any time.
Open “Step-by-step” to see how the answer was worked out.
Use Copy result or Share to save the answer or send a link with your inputs.

Formula

a mod n = a − n × ⌊a / n⌋

Worked example

Using the values pre-filled in the calculator above:

a = -17
n (modulus) = 5

the calculator returns:

-17 mod 5: 3
Truncated remainder (JavaScript/C %): -2

Working

-17 = 5 × -4 + 3

Frequently asked questions

Why does −17 mod 5 give 3 and not −2?

Mathematically, the result of a mod n (for positive n) is always between 0 and n − 1. Many programming languages instead return a truncated remainder (−2), which keeps the sign of the dividend.