Remaining Calculator
Remaining calculator works out Remainder and Integer quotient from Dividend (a), Divisor / modulus (n) and Remainder convention. The default figures on this page give remainder of 2; change any entry and the result, the working and the sources update together.
Your figures
Updates as you typeHow this is worked out
3 steps
- Exact quotient: 17 / 5 = 3.4.
- Round toward zero to get the integer quotient q = 3.
- Remainder r = a - n x q = 17 - (5 x 3) = 2.
Its 6 worked examples are re-run on every release, last on 15 September 2026. What changed
Sources and references
4 sources
What the remaining calculator calculates
Computes the remainder and integer quotient of a division under the truncated, floored and Euclidean conventions, handles negative and decimal operands exactly, and also does modular exponentiation and modular inverses.
How to use this remaining calculator
Enter Dividend (a), Divisor / modulus (n), Remainder convention and Operation. Remainder updates as you type, and “Use a worked example” loads checked figures you can adjust. Change one figure at a time to see what drives the result.
How the result is worked out
Open “How this is worked out” beside the result for the step-by-step calculation behind Remainder, Integer quotient and Truncated remainder (C / JavaScript).
The method follows D. E. Knuth, The Art of Computer Programming, Vol. 1, §1.2.4 (the floored definition of mod), R. T. Boute, "The Euclidean definition of the functions div and mod", ACM TOPLAS 14(2), 1992, 127-144, ECMA-262 (ECMAScript) §13.15.3, the % operator - truncated remainder; ISO/IEC 9899 (C) §6.5.5 and NIST Digital Library of Mathematical Functions, §27.1-27.2 (congruences and modular inverses).
17 mod 5 example
With Dividend (a): 17, Divisor / modulus (n): 5, the calculator returns Remainder: 2, Integer quotient: 3, Divides exactly: No. This example is checked against an independent source in the test suite.
What you can compare
Change one input at a time to see how it affects Remainder, Integer quotient and Truncated remainder (C / JavaScript). The inputs you can vary are Dividend (a), Divisor / modulus (n), Remainder convention, Operation, Exponent and Decimal places.
Results are general information, not financial, tax, legal, medical or engineering advice. Check any decision that matters with a qualified professional.
See something wrong? Report a problem with this calculator
Frequently asked questions
How many hours remaining calculator?
Computes the remainder and integer quotient of a division under the truncated, floored and Euclidean conventions, handles negative and decimal operands exactly, and also does modular exponentiation and modular inverses. Open “How this is worked out” beside the result to see each step for your own figures.
How much is the mortgage remaining calculator?
It needs Dividend (a), Divisor / modulus (n), Remainder convention, Operation, Exponent and Decimal places. Nothing else is required, and the figures stay in your browser.
What information do I need for the remaining calculator?
You need Dividend (a), Divisor / modulus (n), Remainder convention, Operation, Exponent and Decimal places. The page opens with default figures that give remainder of 2, so you can see the scale before entering your own.
What does this remaining calculator show?
It shows Remainder, Integer quotient, Truncated remainder (C / JavaScript), Floored remainder (Python / Excel), Euclidean remainder (never negative), Truncated quotient, Floored quotient and Euclidean quotient, with the working and any warnings for your entries.
Can I check how the remaining calculator result was calculated?
Yes. The “How this is worked out” section shows the calculation steps, and the sources section identifies the references used for the method.