Why Are There Two Answers For Negative Numbers?

Different conventions choose different quotients. The Euclidean remainder is nonnegative for a positive modulus; many languages truncate the quotient toward zero.

Modulo Calculator

Compare Euclidean modulo with truncated language-style remainders, including negative dividends and divisors.

Division Ledger

Whole-Number Inputs

Compare mathematical Euclidean modulo with the signed remainder used by many programming languages.

DividendDivisor

For a positive modulus, Euclidean modulo always returns a remainder from zero through modulus minus one. `%` behavior with negative values varies by language.

Two Conventions

-17 mod 5 = 3

Both identities are shown so the chosen convention is explicit.

Euclidean Identity

-17 = 5 × -4 + 3

Truncated Identity

-17 = 5 × -3 + -2

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What Is the Modulo Calculator?

The Modulo Calculator shows both Euclidean division and truncation-toward-zero division. That distinction matters for negative values because mathematical modulo and the percent operator in common programming languages can return different signed remainders.

How It Works

Enter whole-number dividend and divisor values. Compare the two quotient-and-remainder identities and export the convention you need.

When to Use It

Use it for programming, cyclic indexing, modular arithmetic, clock calculations and debugging negative remainder behavior.

Frequently Asked Questions

Why Are There Two Answers For Negative Numbers?: Different conventions choose different quotients. The Euclidean remainder is nonnegative for a positive modulus; many languages truncate the quotient toward zero.

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