Find the reciprocal of any number or fraction — 1 divided by x — shown as a decimal, a simplified fraction and a percentage.
For a number, the reciprocal is simply 1 ÷ x. Switch to Fraction mode to enter something like 3/4.
reciprocal (1 ÷ x)
How to use this tool
Type any non-zero number. The reciprocal is 1 divided by that number — for example, the reciprocal of 0.5 is 2.
Switch to Fraction mode and enter a numerator and denominator. The reciprocal of a fraction is the fraction flipped: 3/4 becomes 4/3.
The result is shown as a decimal, as a simplified fraction and as a percentage, so you can use whichever form your working needs.
A number times its reciprocal is always exactly 1. If your check is not 1, something was typed wrong.
Formula & worked example
Worked example: the reciprocal of 0.5 is 1 ÷ 0.5 = 2. As a fraction, 0.5 is 1/2, flipped to 2/1 = 2. Check: 0.5 × 2 = 1. For a fraction: the reciprocal of 3/4 is 4/3 = 1.3333, and 3/4 × 4/3 = 12/12 = 1.
Limitations — read this before you rely on it
Fractions from decimals are shown as the closest fraction with a denominator up to 10,000, which is exact for ordinary decimals but an approximation for repeating decimals like 1/3. Very large or very small numbers may lose precision in the decimal display — the fraction form stays exact where it applies.
Frequently asked questions
The reciprocal of a number x is 1 ÷ x. It is also called the multiplicative inverse, because multiplying a number by its reciprocal always gives 1.
It does not exist. 1 ÷ 0 is undefined in mathematics, so zero is the one number with no reciprocal.
Flip it: the reciprocal of a/b is b/a. So the reciprocal of 3/4 is 4/3, and the reciprocal of 1/2 is 2/1 = 2.
Still 1 ÷ x, and it keeps the sign: the reciprocal of −4 is −0.25, because −4 × −0.25 = 1.
Everywhere division appears: rates (miles per gallon vs gallons per mile), unit conversion, resistances in parallel circuits (1/R = 1/R1 + 1/R2), and solving equations by multiplying both sides by a reciprocal.