Quick answer
Long division divides step by step: find how many times the divisor fits into the leading digits, subtract, bring down the next digit and repeat. 22 ÷ 7 gives a quotient of 3 and a remainder of 1, and continuing with decimals gives 3.142857…
Enter a dividend, a divisor and the number of decimal places. The calculator returns the quotient, the whole-number quotient and the remainder.
Related tools: Polynomial Long Division Calculator: Quotient and remainder of one polynomial divided by another. Fraction Calculator: Add, subtract, multiply and divide fractions with simplified and mixed-number results. Ratio Calculator: Simplify a ratio of two whole numbers.
How to use the Long Division Calculator
- Enter dividend (a whole number, between 0 and 1000000000000).
- Enter divisor (a whole number, between 0 and 1000000000000).
- Optionally, enter decimal places (a whole number, between 0 and 30). It starts at 6.
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Dividend | A whole number | ≥ 0, ≤ 1000000000000 |
| Divisor | A whole number | > 0, ≤ 1000000000000 |
| Decimal places (optional) | A whole number | ≥ 0, ≤ 30, starts at 6 |
Formula and method
Formula
a ÷ b = q remainder r; decimals by bringing down zeros
IEEE-754 double precision; shown to at most 6 decimal places.
Digit-by-digit division using BigInt arithmetic so no precision is lost.
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Dividend = 22; Divisor = 7; Decimal places = 6.
| Result | Value |
|---|---|
| Quotient | 3.142857 |
| Quotient | 3 |
| Remainder | 1 |
Example 2
Inputs: Dividend = 100; Divisor = 8; Decimal places = 6.
| Result | Value |
|---|---|
| Quotient | 12.5 |
| Quotient | 12 |
| Remainder | 4 |
Example 3
Inputs: Dividend = 1; Divisor = 3; Decimal places = 4.
| Result | Value |
|---|---|
| Quotient | 0.3333 |
| Quotient | 0 |
| Remainder | 1 |
The first line is the headline result (quotient). Below it the long Division Calculator lists quotient and remainder, which describe the same case from other angles. IEEE-754 double precision; shown to at most 6 decimal places.
The steps for 22 ÷ 7
7 goes into 22 three times (21), leaving 1. To continue, add a decimal point and bring down a 0: 10 ÷ 7 = 1 remainder 3, 30 ÷ 7 = 4 remainder 2, 20 ÷ 7 = 2 remainder 6, 60 ÷ 7 = 8 remainder 4, 40 ÷ 7 = 5 remainder 5, 50 ÷ 7 = 7 remainder 1. The remainder 1 has appeared before, so the digits 142857 repeat.
Remainder or decimal
Use the remainder when you need whole numbers (22 ÷ 7 = 3 R 1) and decimals for measurements. The decimal places setting rounds the quotient; the calculator allows up to 30. The divisor must be greater than 0.
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 | Quotient | Quotient | Remainder |
|---|---|---|---|
| 11 | 1.571428 | 1 | 4 |
| 22 | 3.142857 | 3 | 1 |
| 44 | 6.285714 | 6 | 2 |
| 88 | 12.571428 | 12 | 4 |
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 Long Division 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 |
|---|---|---|
| [Polynomial Long Division Calculator](/math/polynomial-division/) | dividend coefficients and divisor coefficients | Quotient |
| [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) |
| [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 greater than 0
- Up to 30 decimal places
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 in 22 ÷ 7?
The remainder is 1, because 7 × 3 = 21 and 22 − 21 = 1.
Why do some divisions repeat?
A fraction in lowest terms repeats when its denominator has prime factors other than 2 and 5.
Does it show every step?
It returns the quotient and remainder; the steps are explained on this page.
What does the Long Division Calculator calculate?
Divide whole numbers to a chosen number of decimal places. It returns Quotient, Quotient and Remainder.
What formula does the Long Division Calculator use?
a ÷ b = q remainder r; decimals by bringing down zeros. Digit-by-digit division using BigInt arithmetic so no precision is lost.
What do I need to enter in the long Division Calculator?
You enter Dividend and Divisor. Optional: Decimal places.
How is the result rounded or limited?
IEEE-754 double precision; shown to at most 6 decimal places. Divisor greater than 0.
What are the limits of this calculator?
Divisor greater than 0. Up to 30 decimal places.
What is an example of a long Division result?
With dividend 22, divisor 7 and decimal places 6, the quotient is 3.142857.
Related calculators
- Polynomial Long Division Calculator — Quotient and remainder of one polynomial divided by another.
- 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.
- 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.
- Letters to Numbers Converter — A=1 … Z=26 letter-number cipher.
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.