Remainder Calculator

Enter a dividend and divisor to see the quotient and remainder immediately, including the negative-number convention.

Dividend

Divisor

Signed remainder

—

Truncated integer division result

—Truncated quotient

—Euclidean remainder

—Divides evenly?

—|divisor|

a = bq + r

Long division

Negative-number remainder conventions

Signed remainderSame sign as dividend

Euclidean remainder0 ≤ r < |divisor|

Why show both?Math and programming languages can use different sign conventions.

Modulo calculator Divisibility

Modulo rule & batch audit

Compare truncated remainder with Euclidean modulo for signed values and test many dividends against the same divisor.

Signed modulo

Batch dividends

Rule

a	divisor	trunc q / r	Euclidean q / r

Use the tool above, then refresh this audit.

Audit uses the visible inputs plus the assumptions shown here.

Practical guide and verification

What the remainder means

For integer division, dividend = divisor × quotient + remainder. That identity is the quickest way to check a result.

Negative numbers

Programming languages and mathematical conventions can differ in how they define quotient and remainder for negative inputs. If negatives matter, verify the convention required by your application rather than assuming every `%` operator behaves the same.

Decimal inputs

A classic integer remainder is different from a floating-point remainder. Decide whether you need Euclidean division, modulo arithmetic, or a programming-language remainder before interpreting the output.

How to use this Remainder Calculator

Enter an integer dividend and a nonzero divisor. The signed remainder, quotient, Euclidean remainder, divisibility status, and exact a = bq + r identity update immediately.

What the result means

For negative inputs, signed programming-style remainder and Euclidean remainder can differ. Both stay visible so the sign convention is explicit rather than hidden.