Modulo calculator

Find a nonnegative remainder, including for negative integers.

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Integer dividend

Positive integer modulus

Answer

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Euclidean modulo returns r with 0 ≤ r < modulus, so dividend = floor quotient × modulus + r.

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Formula and assumptions

The modulus must be positive. Some programming languages use a remainder with the dividend’s sign; that value is shown separately to make the convention clear.

Automatic precision shows numbers to 12 significant digits. Thousands separators such as 1,000 are accepted; use a dot for decimals.

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Updated 2026-09-26

Using Modulo calculator

Euclidean modulo returns r with 0 ≤ r < modulus, so dividend = floor quotient × modulus + r.

The modulus must be positive. Some programming languages use a remainder with the dividend’s sign; that value is shown separately to make the convention clear.

Next: Prime factorization calculator

A worked example

With integer dividend = -17, positive integer modulus = 5, the euclidean remainder is 3.

Next: Ratio calculator

Before you use the result

The modulus must be positive. Some programming languages use a remainder with the dividend’s sign; that value is shown separately to make the convention clear.

Example results for integer dividend

These examples use Positive integer modulus: 5. They are reference calculations, not recommended settings.

Integer dividend	Euclidean remainder
-17	3
-34	1

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