Reciprocal Calculator
Find the reciprocal (multiplicative inverse) of a number or fraction.
Inputs
Set to 1 if entering a whole number.
Reciprocal
8/5
As Decimal
1.60000000
Verification (should be 1)
1.000000
Step by step
Simplify original fraction
5/8 = 5/8
Flip numerator and denominator
Reciprocal of 5/8 = 8/5
Verify: original × reciprocal = 1
(5/8) × (8/5) = 1.0000
How it works
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)
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.