# Reciprocal Calculator

URL: https://speedycalculator.com/calculators/math/reciprocal/
Last updated: 2026-10-30

> The reciprocal calculator gives 1/x for a whole number, decimal, fraction or mixed number, as a simplified fraction and as a decimal.

## Inputs

- Type of number
- Number
- Whole number
- Numerator
- Denominator

## Results

- Reciprocal (fraction)
- Reciprocal (decimal)
- As a mixed number
- Steps

## Formula

```
Reciprocal of x = 1/x;  of a/b = b/a
```

## Explanation

Reciprocals turn division into multiplication and appear in rates (seconds per metre versus metres per second), lens equations, parallel resistors and unit conversions.

### How to use the Reciprocal Calculator

- **Type of number**
- **Number**
- **Whole number**
- **Numerator**
- **Denominator**

Everything is calculated in your browser, so results appear instantly and nothing you type is sent to a server.

### How it works

The number is written as an exact fraction and inverted. The product of a number and its reciprocal is always 1.

## Worked example

Inputs — Type of number: An integer or decimal; Number: 8.

Results — **Reciprocal (fraction) = 1/8**; Reciprocal (decimal) = 0.125; As a mixed number = 1/8; Steps = 1. Write the number as a fraction: 8
2. Swap numerator and denominator: 1/8
3. Check: 8 × 1/8 = 1.

## Key terms

- **Reciprocal**: 1 divided by a number.

## FAQ

**What is the reciprocal of 8?**
1/8 = 0.125.

**What is the reciprocal of 2/5?**
5/2 = 2.5.

**What is the reciprocal of a negative number?**
Also negative: the reciprocal of −4 is −1/4.

**Which number is its own reciprocal?**
1 and −1.


## Sources

- [OpenStax – Prealgebra 2e](https://openstax.org/details/books/prealgebra-2e)
- [Wolfram MathWorld – Reciprocal](https://mathworld.wolfram.com/Reciprocal.html)