Reciprocal Calculator
Find the reciprocal (multiplicative inverse) of a number or fraction.
About Reciprocal Calculator
The reciprocal of a number x is 1/x. For a fraction a/b, the reciprocal is b/a. Multiplying any non-zero number by its reciprocal always gives 1. Zero has no reciprocal.
Formula
Reciprocal
Reciprocal of a/b = b/a; Reciprocal of x = 1/x
- a
- Numerator
- b
- Denominator (non-zero)
Worked example
With the default values below, Reciprocal Calculator returns Reciprocal of 8/5. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Numerator (or whole number)
- 5
- Denominator (1 for whole numbers)
- 8
Results
- Reciprocal
- 8/5
- As Decimal
- 1.60000000
- Verification (should be 1)
- 1.000000
Step by step
- 1Simplify original fraction
- 2Flip numerator and denominator
- 3Verify: original × reciprocal = 1
Assumptions and limits
- The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
- Figures are rounded for display to 8 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
Frequently Asked Questions
Why does zero have no reciprocal?
Because 1/0 is undefined — there is no number that multiplied by 0 gives 1.
Is the reciprocal the same as the inverse?
The reciprocal is specifically the multiplicative inverse (1/x). The additive inverse is −x. These are different operations.