Remainder Calculator
Euclidean Integer Remainder Calculator works out Remainder and Integer quotient from Dividend (a), Divisor / modulus (n) and Decimal places. 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 -infinity on |n| 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 Euclidean Integer Remainder 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 Euclidean Integer Remainder Calculator
Enter Dividend (a), Divisor / modulus (n) and Decimal places. Remainder updates as you type. 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).
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) 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 to do remainders on a 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 to do remainder on TI 84?
It needs Dividend (a), Divisor / modulus (n) and Decimal places. Nothing else is required, and the figures stay in your browser.
How do you calculate a remainder?
The result gives Remainder, Integer quotient, Truncated remainder (C / JavaScript), Floored remainder (Python / Excel), Euclidean remainder (never negative) and Truncated quotient, each labelled with its unit so the figure can be read on its own.
How to get remainder in Casio calculator?
The page opens with worked default figures: remainder of 2. Replace them with your own and every figure updates as you type.
What information do I need for the Euclidean Integer Remainder Calculator?
You need Dividend (a), Divisor / modulus (n) 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 Euclidean Integer Remainder 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.