Modulo calculator (a mod n)
Enter the dividend and divisor to get the remainder. The tool shows how the math definition differs from some programming languages for negative numbers.
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How to use it
- Enter dividend a and divisor n.
- The result appears straight away and updates as you edit.
- Copy the result, or copy a link that keeps the same values to share it.
How it is calculated
a mod n = a - n × ⌊a ÷ n⌋ (the result takes the sign of n). Truncated remainder = a - n × trunc(a ÷ n) (sign of a, like % in JavaScript and C).
Example
Inputs: Dividend a = 17, Divisor n = 5. Result: a mod n: 2; Integer quotient ⌊a ÷ n⌋: 3; Truncated remainder (a % n in code): 2.
Limits and caveats
- Uses floored division, so the result takes the sign of the divisor.
- Decimal inputs use standard floating point precision.
Questions about this tool
What is 17 mod 5?
2, because 17 = 5 × 3 + 2.
Why is -17 mod 5 equal to 3 and not -2?
In math the result lies between 0 and n, and -17 = 5 × (-4) + 3. JavaScript and C return -2 because they truncate the quotient.
Where is modulo used?
In weekday and clock arithmetic, check digits, cryptography and round-robin scheduling.