Division Remainder Calculator
Dividing one number by another gives both a whole-number quotient and a leftover remainder. This calculator applies the Euclidean division identity, dividend equals divisor times quotient plus remainder, to return the integer quotient, the non-negative remainder (mathematical modulo), and the exact decimal result in one place. It is useful for arithmetic homework, splitting items into equal groups, working out clock and calendar arithmetic, and any situation where you need to know both how many whole times something fits and what is left over.
Division with remainder formula
quotient = floor(dividend / divisor)
remainder = dividend - divisor * quotient
(Euclidean: 0 <= remainder < |divisor|)
decimal result = dividend / divisor
check = quotient * divisor + remainder = dividend
The floor function takes the largest integer not greater than the value, which keeps the remainder non-negative for positive divisors.
Division remainder context
- The remainder is always less than the absolute value of the divisor.
- A remainder of zero means the divisor divides the dividend exactly.
- The check column should always equal the dividend, confirming the identity holds.
- This tool reports a non-negative (mathematical) modulo; some programming languages differ for negatives.
- Dividing by zero is undefined and returns n/a.
Division remainder: frequently asked questions
What is a remainder in division?
When you divide one whole number (the dividend) by another (the divisor), the remainder is what is left over after taking out as many whole copies of the divisor as possible. For 17 divided by 5, the quotient is 3 and the remainder is 2, because 3 times 5 is 15 and 17 minus 15 is 2.
What is the division identity?
Euclidean division states dividend = divisor times quotient plus remainder, where the remainder is at least 0 and less than the absolute value of the divisor. The quotient is the integer part (floor for positive divisors), and the remainder makes the equation balance exactly.
How does the modulo operation handle negative numbers?
This calculator reports a mathematical (non-negative) modulo: the result always lies between 0 and the divisor minus 1, matching Euclidean division. Many programming languages instead return a remainder with the sign of the dividend, so -7 mod 3 may show as 2 here but -1 in some languages.
What happens if I divide by zero?
Division by zero is undefined in mathematics, so the calculator shows n/a for every output when the divisor is 0. There is no quotient or remainder for a zero divisor.
Does this work with decimals?
The decimal result works for any numbers. The integer quotient and remainder are most meaningful for whole-number inputs; if you enter decimals, the calculator floors the quotient and computes the remainder consistently with the division identity.
Official sources
- NIST Digital Library of Mathematical Functions: DLMF home.
- NIST: National Institute of Standards and Technology.
Reviewed by the CalculatorHub team, edited by James Graham, 17 June 2026. See our methodology.