Enter any number, decimal, or fraction into the Reciprocal Calculator and get its multiplicative inverse back immediately. Choose your input type (integer/decimal, simple fraction, or mixed number), fill in the relevant fields, and see the reciprocal result expressed as both a fraction and a decimal.
Reciprocal (Fraction)
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Reciprocal (Decimal)
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Original Number (Decimal)
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Verification (n × 1/n)
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A reciprocal (also called the multiplicative inverse) of a number x is simply 1 divided by x, written as 1/x. The defining property is that when you multiply a number by its reciprocal, the result is always 1. For example, the reciprocal of 4 is 1/4, and 4 × 1/4 = 1.
To find the reciprocal of a fraction, simply swap (flip) the numerator and denominator. For example, the reciprocal of 3/4 is 4/3. This works because (3/4) × (4/3) = 12/12 = 1.
First convert the mixed number to an improper fraction, then flip it. For example, 4 and 1/2 becomes 9/2 as an improper fraction, so its reciprocal is 2/9, which equals approximately 0.2222.
The reciprocal of 5 is 1/5, which equals 0.2 as a decimal. You can verify this because 5 × 0.2 = 1.
The reciprocal of 2/3 is 3/2, which equals 1.5 as a decimal. Flipping the numerator and denominator gives you the multiplicative inverse of any simple fraction.
The reciprocal of 1 is 1 itself, since 1/1 = 1. It is the only positive number that is its own reciprocal. Negative one (−1) also shares this property.
No. Zero does not have a reciprocal because 1/0 is undefined in mathematics. Division by zero is not allowed, so the reciprocal of 0 does not exist.
To find the reciprocal of a decimal, divide 1 by that decimal. For example, the reciprocal of 1.25 is 1 ÷ 1.25 = 0.8. You can also convert the decimal to a fraction first (1.25 = 5/4) and then flip it (4/5 = 0.8).