Quick answer
Division gives a = q × b + r with 0 ≤ r < b. 17 ÷ 5 has a quotient of 3 and a remainder of 2.
Enter a non-negative dividend and a positive divisor. The calculator returns the quotient and remainder.
Related tools: Fraction Calculator: Add, subtract, multiply and divide fractions with simplified and mixed-number results. Ratio Calculator: Simplify a ratio of two whole numbers. Average Calculator: Arithmetic mean, sum, count, minimum and maximum of a list of numbers.
How to use the Remainder Calculator
- Enter dividend (a whole number, 0 or more).
- Enter divisor (a whole number, above 0).
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Dividend | A whole number | ≥ 0 |
| Divisor | A whole number | > 0 |
Formula and method
Formula
a = q × b + r, with 0 ≤ r < b
IEEE-754 double precision; shown to at most 6 decimal places.
q = floor(a ÷ b); r = a − q × b.
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Dividend = 17; Divisor = 5.
| Result | Value |
|---|---|
| Remainder | 2 |
| Quotient | 3 |
Example 2
Inputs: Dividend = 20; Divisor = 5.
| Result | Value |
|---|---|
| Remainder | 0 |
| Quotient | 4 |
Example 3
Inputs: Dividend = 3; Divisor = 7.
| Result | Value |
|---|---|
| Remainder | 3 |
| Quotient | 0 |
The first line is the headline result (remainder). Below it the remainder Calculator lists quotient, which describe the same case from other angles. IEEE-754 double precision; shown to at most 6 decimal places.
Check
3 × 5 + 2 = 17 ✓. The remainder is always smaller than the divisor. A remainder of 0 means the divisor goes in exactly.
Uses
Share 17 sweets among 5 children: 3 each, 2 left over. Remainders drive clock arithmetic, repeating patterns and divisibility tests. For negative numbers use the Modulo calculator.
How the result changes with dividend
Holding every other input at the first worked example, this table changes only dividend. It shows how sensitive the answer is to that one value; each row was produced by running this calculator.
| Dividend | Remainder | Quotient |
|---|---|---|
| 9 | 4 | 1 |
| 17 | 2 | 3 |
| 34 | 4 | 6 |
| 68 | 3 | 13 |
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Divisor: entering "0" shows "Divisor must be greater than 0." beside that field and no result.
Choosing between the Remainder Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Fraction Calculator](/math/fraction-calculator/) | numerator 1, denominator 1 and operation | Result |
| [Ratio Calculator](/math/ratio-calculator/) | first number and second number | Simplified ratio |
| [Average Calculator](/math/average-calculator/) | numbers | Average (mean) |
| [Long Division Calculator](/math/long-division-calculator/) | dividend and divisor | Quotient |
| [Percent Off Calculator](/math/percent-off-calculator/) | original price and discount | Sale price |
Background: rounding and basic arithmetic
Rounding to a place looks at the digit just to its right: 0 to 4 rounds down and 5 to 9 rounds up (the half-up convention, so 2.5 becomes 3). Rounding 838.274 gives 800 to the nearest hundred, 840 to the nearest ten and 838 to the nearest one.
Some systems use banker's rounding (half to even), which sends 2.5 to 2 and 3.5 to 4; check which convention your task requires, and round only at the end of a multi-step calculation.
Assumptions and limitations
- Divisor must be greater than 0
- Non-negative dividend
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for divisor to confirm this.
Frequently asked questions
What is the remainder of 100 ÷ 7?
100 = 14 × 7 + 2, so the remainder is 2.
Can the remainder be larger than the divisor?
No. The remainder is always smaller than the divisor, otherwise the quotient could be one larger.
What does remainder 0 mean?
A remainder of 0 means the divisor goes into the dividend exactly, so it is a factor.
What does the Remainder Calculator calculate?
Quotient and remainder of a whole-number division. It returns Remainder and Quotient.
What formula does the Remainder Calculator use?
a = q × b + r, with 0 ≤ r < b. q = floor(a ÷ b); r = a − q × b.
What do I need to enter in the remainder Calculator?
You enter Dividend and Divisor.
How is the result rounded or limited?
IEEE-754 double precision; shown to at most 6 decimal places. Divisor must be greater than 0.
What are the limits of this calculator?
Divisor must be greater than 0. Non-negative dividend.
What is an example of a remainder result?
With dividend 17 and divisor 5, the remainder is 2.
Related calculators
- Fraction Calculator — Add, subtract, multiply and divide fractions with simplified and mixed-number results.
- Ratio Calculator — Simplify a ratio of two whole numbers.
- Average Calculator — Arithmetic mean, sum, count, minimum and maximum of a list of numbers.
- Long Division Calculator — Divide whole numbers to a chosen number of decimal places.
- Percent Off Calculator — Find the sale price and savings after a percentage discount.
- Rounding Calculator — Round a number to decimal places, with up, down or nearest modes.
Sources
- OpenStax, Algebra and Trigonometry 2e (Rice University): exponents, radicals, logarithms and inverse trigonometric functions
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.