Remainder calculator
Divide with remainder and see the quotient and the check.
Fill in the fields and the result will appear here automatically.
Divides integer a by nonzero integer b and shows the exact quotient q, remainder r and identity a = bq + r. This calculator truncates the quotient towards zero, as JavaScript integer operations do: a nonzero remainder has the dividend’s sign. Other conventions for negative numbers can give a different result.
How it works
Formula and logic
The quotient is the division truncated towards zero; the remainder is what the identity a = b × q + r leaves over.
Example
17 divided by 5 gives quotient 3 and remainder 2, because 17 = 5 × 3 + 2.
Fields and units
- Dividend — unitless
- Divisor — unitless
How to use
- — Enter the dividend.
- — Enter the divisor.
- — Read the remainder and the quotient.
Method and limitations
- Calculation method
- Formula and logic
- Data or methodology source
- ECMAScript draft specification: integer quotient truncation and remainder sign
- Limitation
- Each input must be an integer with magnitude at most 9007199254740991; b ≠ 0. Inputs are not rounded to integers. Division and remainder use exact integer arithmetic. Truncation gives q = −3, r = 2 for 17 ÷ −5; the convention does not require a nonnegative remainder for every sign.
FAQ
What happens with negative numbers?
The remainder takes the sign of the dividend: −17 and 5 give quotient −3 and remainder −2, since −17 = 5 × (−3) + (−2).
Is this the same as the modulo in Python?
No. Python returns a remainder with the sign of the divisor, so −17 mod 5 is 3 there. This calculator follows the truncating convention.
Can I use decimals?
No. Division with remainder is defined for whole numbers, so decimal input is rejected instead of being rounded.
Why is the check line shown?
It makes the answer verifiable at a glance: multiply the divisor by the quotient, add the remainder and you get the dividend back.