Math
Reciprocal Calculator
Enter a whole number, a decimal, a fraction, or a mixed number and get its reciprocal in every useful form: exact fraction, mixed number, and decimal.
The steps show how a decimal or mixed number is first written as a single fraction, how the fraction is flipped, and the check that the product with the original is 1. Zero is flagged because it has no reciprocal.
Any nonzero number, for example 8, -2.5, or 0.75.
Try an example
Result
Reciprocal
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- As a fraction
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- As a mixed number
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- As a decimal
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- Check
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Student quick launch
Grade planning, algebra checks, and formulas students reach for most.
Study path
Use this calculator with
Follow these when you want the formula behind the answer, a short lesson, or nearby tools in the same topic.
What the reciprocal calculator solves
Enter a whole number, a decimal, a fraction, or a A whole number written next to a fraction, like 2 1/3. and get its The number you get by flipping a fraction; 3/4 becomes 4/3, and 5 becomes 1/5. in every useful form: exact fraction, mixed number, and decimal. The steps show how a decimal or mixed number is first written as a single fraction, how the fraction is flipped, and the check that the product with the original is 1. Zero is flagged because it has no reciprocal.
Formula
How to use it
- Choose whether you have a plain number, a fraction, or a mixed number.
- Enter the value. Decimals and negatives are fine; zero is not.
- Read the reciprocal as a fraction, mixed number, and decimal, and use the check line to confirm the product is 1.
How to read the answer
The reciprocal is the number you multiply by to get 1. For a fraction you simply swap The top number of a fraction; it counts how many parts you have. and The bottom number of a fraction; it says how many equal parts make one whole.. Numbers bigger than 1 have reciprocals between 0 and 1 and vice versa; the sign never changes. Only 0 has no reciprocal.
Common mistakes and edge cases
- Flipping a mixed number directly: the reciprocal of 2 3/4 is 4/11, not 4 3/2. Convert to 11/4 first.
- Changing the sign: the reciprocal of -5 is -1/5, not 1/5.
- Treating the reciprocal as the negative: the reciprocal of 4 is 1/4, while the additive inverse is -4.
- Rounding the decimal before flipping: 1/0.3 is 10/3 = 3.333…, not 3.
- Trying to find the reciprocal of 0.
Worked examples
Reciprocal of 0.75
0.75 = 3/4, so the reciprocal is 4/3 ≈ 1.3333.
Reciprocal
4/3 = 1.333333
Reciprocal of a whole number
8 becomes 1/8 = 0.125.
Reciprocal
1/8 = 0.125
Reciprocal of a fraction
3/4 flips to 4/3.
Reciprocal
4/3 = 1.333333
Reciprocal of a mixed number
2 3/4 = 11/4, reciprocal 4/11.
Reciprocal
4/11 = 0.363636
Negative number
-2.5 = -5/2, reciprocal -2/5 = -0.4.
Reciprocal
-2/5 = -0.4
Reciprocal of 1
1 is its own reciprocal.
Reciprocal
1
Zero
No reciprocal exists.
Reciprocal
Error
Frequently asked questions
What is a reciprocal?+
The reciprocal of a number is 1 divided by it, also called the multiplicative inverse. A number times its reciprocal equals 1: 4 × 1/4 = 1.
How do you find the reciprocal of a fraction?+
Swap the numerator and denominator: the reciprocal of 3/4 is 4/3. If the fraction is negative, the reciprocal stays negative.
How do you find the reciprocal of a mixed number?+
Convert it to an improper fraction first, then flip. 2 3/4 = 11/4, so its reciprocal is 4/11.
What is the reciprocal of a decimal?+
Write the decimal as a fraction and flip. 0.75 = 3/4, so the reciprocal is 4/3 ≈ 1.3333. Or just compute 1 ÷ 0.75.
Does 0 have a reciprocal?+
No. 1/0 is undefined because no number times 0 equals 1.
Which numbers are their own reciprocal?+
Only 1 and -1, since 1 × 1 = 1 and (-1) × (-1) = 1.
About this calculator
- Written by
- mathcheck editorial team
- Last reviewed
- September 4, 2026
Method
- Uses the values entered by the user and stable formulas documented on the page.
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Last updated: September 4, 2026