Modulo Calculator

Formula

Nonnegative remainder = ((Dividend % Divisor)+abs(Divisor))%abs(Divisor)

Worked example

With Dividend: 17, Divisor: 5, nonnegative remainder is 2.

Calculation method

The rule is Nonnegative remainder = ((Dividend % Divisor)+abs(Divisor))%abs(Divisor).

For this modulo example, changing dividend from 17 to 18 while keeping the other inputs fixed changes nonnegative remainder from 2 to 3.

Reading nonnegative remainder

The remainder is smaller than the absolute divisor. It tells where the dividend falls within repeating groups of that size. In the worked values on this page, dividend 17, divisor 5 produce nonnegative remainder 2.

Practical use

Use it for periodic patterns, grouping, and checks such as whether a number is divisible by another. The specific task here is to find nonnegative remainder from dividend, divisor.

Limits and common mistakes

The divisor cannot be zero. Different programming languages may define a negative-input remainder differently; this page uses a nonnegative convention. Verify dividend before interpreting nonnegative remainder; a value measured on another basis would answer a different question.

Why the relationship works

A remainder describes what is left after whole multiples of the divisor are removed. This tool reports a nonnegative remainder, including for a negative dividend. That convention should be distinguished from programming languages or textbooks that use a signed remainder operator. The modulo rule uses dividend, divisor in Nonnegative remainder = ((Dividend % Divisor)+abs(Divisor))%abs(Divisor); read each symbol as the field named on this page.

Interpreting another set of values

For modulo, the fields labeled dividend, divisor are the known quantities. The calculator solves for nonnegative remainder using Nonnegative remainder = ((Dividend % Divisor)+abs(Divisor))%abs(Divisor). Interpret the answer in the context of the entered equation or coordinate system. A root, signed slope, intercept, distance, and remainder have different meanings and different valid domains. When comparing two calculations, keep their units and input definitions identical.

For a second modulo check, keep the other default inputs fixed and change dividend from 17 to 19. Nonnegative remainder changes from 2 to 4. This is a comparison of two particular cases. Repeat it near the values relevant to your task; do not assume that every formula changes at a constant rate.

Checks and limits

The divisor cannot be zero. This page chooses a nonnegative remainder convention; confirm the convention used in any programming language or reference you compare with. The remainder must be smaller than the absolute divisor. The reported nonnegative remainder is 2 in the worked example. Keep its stated unit or counting convention when checking it against another calculation.