Quick answer
The reciprocal of x is 1 ÷ x, the number that multiplies with x to give 1. The reciprocal of 4 is 0.25.
Enter a number. The calculator returns its reciprocal.
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 Reciprocal Calculator
- Enter number.
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Number | A number | — |
Formula and method
Formula
1 ÷ x
IEEE-754 double precision; shown to at most 6 decimal places.
Division; zero has no reciprocal.
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Number = 4.
| Result | Value |
|---|---|
| Reciprocal | 0.25 |
Example 2
Inputs: Number = -0.5.
| Result | Value |
|---|---|
| Reciprocal | -2 |
Example 3
Inputs: Number = 3.
| Result | Value |
|---|---|
| Reciprocal | 0.333333 |
The first line is the headline result (reciprocal). IEEE-754 double precision; shown to at most 6 decimal places.
Reciprocals of fractions
Flip the fraction: the reciprocal of 3/5 is 5/3. Dividing by a number is the same as multiplying by its reciprocal, so 8 ÷ 4 = 8 × 0.25 = 2.
Edge cases
Zero has no reciprocal, because division by zero is undefined. The reciprocal of 1 is 1 and of −1 is −1. Numbers greater than 1 have reciprocals between 0 and 1.
Reciprocals in practice
The reciprocal of 4 is 0.25 and the reciprocal of 0.25 is 4; multiplying a number by its reciprocal always gives 1. The reciprocal of a fraction flips it, so 3/4 becomes 4/3.
Zero has no reciprocal because 1 ÷ 0 is undefined. Dividing by a fraction is the same as multiplying by its reciprocal, which is why 6 ÷ 2/3 = 6 × 3/2 = 9.
How the result changes with number
Holding every other input at the first worked example, this table changes only number. It shows how sensitive the answer is to that one value; each row was produced by running this calculator.
| Number | Reciprocal |
|---|---|
| 2 | 0.5 |
| 4 | 0.25 |
| 8 | 0.125 |
| 16 | 0.0625 |
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Number: entering "0" shows "Zero has no reciprocal." beside that field and no result.
Choosing between the Reciprocal 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
- 0 is invalid
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 number to confirm this.
Frequently asked questions
What is the reciprocal of 0.5?
The reciprocal of 0.5 is 1 ÷ 0.5 = 2.
What is the reciprocal of −2?
The reciprocal of −2 is −1/2 = −0.5.
What is a multiplicative inverse?
Another name for the reciprocal.
Does zero have a reciprocal?
No. 1 ÷ 0 is undefined, so zero is the one real number without a reciprocal.
How do reciprocals help with dividing fractions?
Dividing by a fraction equals multiplying by its reciprocal, so 6 ÷ 2/3 becomes 6 × 3/2 = 9.
What does the Reciprocal Calculator calculate?
The multiplicative inverse of a number. It returns Reciprocal.
What formula does the Reciprocal Calculator use?
1 ÷ x. Division; zero has no reciprocal.
How is the result rounded or limited?
IEEE-754 double precision; shown to at most 6 decimal places. 0 is invalid.
What is an example of a reciprocal result?
With number 4, the reciprocal is 0.25.
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.