Remainder Calculator

Your details

The number you are dividing up. It can be positive or negative.
The number you are dividing by. It cannot be zero.
Truncated rounds toward zero (matches most languages for positive numbers). Floored rounds toward negative infinity. Euclidean always returns a non-negative remainder.
RemainderHas a remainder
2
Quotient (whole)3
Exact quotient (decimal)3.4
Remainder as fraction3 2/5
R-notation3 R 2
Division identity17 = 3 x 5 + 2
Quotient (whole groups)3
Remainder (leftover)2

The divisor fits 3 whole times with 2 left over.

  • As a mixed number the result is 3 2/5, where 2/5 is the fractional part.
  • The remainder is always smaller in absolute value than the divisor.
  • Multiply the quotient by the divisor and add the remainder to recover the dividend.
  • Switch to the Euclidean convention if you need the remainder to always be non-negative.

Next stepUse the Euclidean convention to guarantee a non-negative remainder, which is required in many cryptography and hash functions.

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