Omni Calculator logo

Reciprocal Calculator

Created by Hanna Pamuła, PhD
Reviewed by Steven Wooding and Jack Bowater
Last updated: Mar 04, 2024

If you're wondering how to find the reciprocal, we're here to help with this easy-to-use reciprocal calculator.
Below, you can find an explanation of what a reciprocal is and examples of how to calculate and find reciprocals, be it the reciprocal of a fraction or a number.

As you're interested in reciprocals, we suspect that fraction calculators may also be interesting to you. So why not check out our other tools!

What is a reciprocal?

A reciprocal in math is one divided by the number in question (also known as the multiplicative inverse).

The reciprocal of x = 1/x

Alternatively, you can say that if you multiply a number by its reciprocal, you'll get 1:

explanation what is a reciprocal: number (x) * reciprocal (1/x) = 1

For example, if our chosen number is 5, its reciprocal is 1/5. The multiplication of these two numbers will give us 1:

  • 5 × 1/5 = 5 × 0.2 = 1

The name reciprocal comes from Latin, possibly from the phrase reque proque, meaning back and forth. The reciprocal number to x may be denoted simply as 1/x but also as x-1. Thus, raising the number to the power of minus one is the same as finding its reciprocal.

How to find the reciprocal?

So, in short, how to find the reciprocal of a number?

  1. Reciprocal of a fraction

    To find the reciprocal of a fraction, switch the numerator and the denominator (the top and bottom of the fraction, respectively). So, simply speaking, the reciprocal of a/b is b/a.

    Example: the reciprocal of 3/4 is 4/3

  2. Reciprocal of a number

    To find the reciprocal of a number, divide 1 by the number.

    Example: the reciprocal of 7 is 1/7

  3. Reciprocal of a decimal

    To find the reciprocal of a decimal, you need to do the same as before - divide 1 by your decimal number.

    Example: the reciprocal of 3.25 is 1/3.25

Additionally, our reciprocal calculator will show you the fraction in its simplified form.

Remember that 0 doesn't have the reciprocal, as 1/0 is undefined.

Examples: what is the reciprocal of 4 and 1/2?

We hope that, after our explanation, you now understand the concept of a reciprocal. In that case, let's look at two examples to check how this calculator works!

Example 1: What is the reciprocal of 4?

  • Is your number a fraction? Not this time! Choose No from the drop-down list. (If you really want, you can leave it as the fraction option and then choose 1 as the denominator).
  • Input the number for which you'd like to find the reciprocal, which is 4.
  • Tadaa! That's all you need to do! The reciprocal calculator shows that the reciprocal of your number is 0.25, or, as a fraction, 1/4.

Example 2: What is the reciprocal of 1/2?

  • Again, start with the question: is the number a fraction? Pick Yes this time.
  • Enter the numerator (top) and denominator (bottom) of your fraction into the appropriate fields. So, in our case, input 1 as the numerator and 2 in the denominator box.
  • The reciprocal calculator finds the answer - the reciprocal of 1/2 is 2.


What is the reciprocal of 5?

0.2. Since we can write 5 as 5/1, if we take the reciprocal, it becomes 1/5, which is 0.2 in decimal form.

What is the reciprocal of 2/3?

3/2 or 1.5. Taking the reciprocal of a fraction means swapping the numerator and the denominator around.

What is the reciprocal of 1?

1. Since 1 in fractional form is written as 1/1, taking the reciprocal (swapping around the numerator and the dominator) results in the same thing, 1/1, which is 1.

How do you find the inverse of a fraction?

You find the inverse of a fraction by exchanging the numerator (top number) with the denominator (bottom number) – taking the reciprocal of the fraction. For example, the inversion of the fraction 5/4 is 4/5.

Hanna Pamuła, PhD
Related calculators
Input in the form of
an integer/decimal
Check out 75 similar arithmetic calculators ➗
Absolute changeAbsolute valueAdding and subtracting fractions… 72 more
People also viewed…

Helium balloons

Wondering how many helium balloons it would take to lift you up in the air? Try this helium balloons calculator! 🎈

Multiplying fractions

Use this multiplying fractions calculator to multiply up to 5 fractions. You can multiply simple fractions by whole numbers, mixed numbers, improper numbers, or negative fractions.

Scalene triangle

The scalene triangle calculator will answer all the important questions regarding the triangles of unequal sides.

Test grade

With this test grade calculator, you'll quickly determine the test percentage score and grade.