Quotient and Remainder Calculator

How it is calculated

The tool divides and rounds the quotient down to a whole number, q = ⌊dividend ÷ divisor⌋, then finds what is left with r = dividend − divisor × q, so dividend = divisor × q + r always holds exactly. With a positive divisor, r runs from 0 to divisor − 1, even for a negative dividend (−100 ÷ 7 gives −15 remainder 5, not −14). With a negative divisor the remainder is 0 or negative (100 ÷ −7 gives −15 remainder −5). Both numbers must be whole; a decimal such as 100.5, a zero divisor, or an empty box shows no result. Whole numbers up to 9,007,199,254,740,992 (2⁵³) are handled exactly and larger ones show no result, even when typed as an exact integer such as 9007199254740993; the tool refuses rather than rounds. Results are printed with thousands separators.

Common mistakes

• Rounding the quotient to the nearest whole number instead of down. 20 ÷ 7 is 2.86, which rounds to 3, but the quotient is 2 with remainder 6.
• Entering a negative dividend and expecting a negative remainder. Here −100 ÷ 7 gives quotient −15 and remainder 5, because the quotient is floored and the remainder takes the divisor's sign.
• Entering decimals such as 7.5. The tool works on whole numbers only and shows nothing for a fractional dividend or divisor.
• Swapping dividend and divisor. 7 ÷ 100 gives quotient 0 and remainder 7.
• Treating the remainder as a decimal part. A remainder of 2 means 2 left over, not 0.2.