Remainder Calculator

How it is calculated

The tool computes the remainder as r = dividend − divisor × ⌊dividend / divisor⌋, where ⌊ ⌋ rounds down to a whole number. It shows r first and the whole-number quotient second. Both inputs must be whole numbers: a decimal such as 59.5 gives no result, and so does a divisor of zero or a number beyond about 9 quadrillion (2⁵³). With positive numbers the remainder is always from 0 up to divisor − 1, and a remainder of 0 means the divisor divides the dividend evenly. Because the quotient is rounded down, the remainder takes the sign of the divisor: −3 mod 7 gives 4 with quotient −1, and 3 divided by −7 gives a remainder of −4. Many programming languages instead give −3 for −3 % 7, so the results can differ.

Common mistakes

• Reading the quotient as the answer when you need the remainder. The remainder is listed first; the quotient is the number of complete groups.
• Expecting a negative remainder from a negative dividend. Here −3 ÷ 7 gives remainder 4, since the quotient rounds down to −1.
• Entering a decimal, such as 8.43 for 59 / 7, or a decimal dividend. The tool shows no result; the remainder is the leftover whole amount, 3, not the fractional part.
• Swapping dividend and divisor. 4 divided by 9 has remainder 4, but 9 divided by 4 has remainder 1.
• Comparing with a programming language and assuming a mismatch is a bug. For negative numbers many languages truncate the quotient instead of rounding it down, so the signs of the remainder differ.