Reciprocal Calculator
Key takeaway: This reciprocal calculator is able to determine the reciprocal of any number (except 0, of course). This free Reciprocal Calculator is designed for students, teachers, and anyone who needs quick math answers — enter your values above to get instant results.
If you're wondering how to find the reciprocal, we're here to help with this easy-to-use reciprocal calculator.
Below, you can find an explanation of what a reciprocal is and examples of how to calculate and find reciprocals, be it the reciprocal of a fraction or a number.
As you're interested in reciprocals, we suspect that fraction calculators may also be interesting to you. So why not check out our other tools!
- Decimal to fractions calculator — Converts any decimal to a fraction instantly.
- Adding fractions calculator — Useful to determine the sum of up to five fractions.
- Equivalent fractions calculator — Finds a list of fractions equivalent to the one you provided. Also, you can check there if two fractions are equivalent or not.
What is a reciprocal?
A reciprocal in math is one divided by the number in question (also known as the multiplicative inverse).
The reciprocal of x = 1/x
Alternatively, you can say that if you multiply a number by its reciprocal, you'll get 1:
For example, if our chosen number is 5, its reciprocal is 1/5. The multiplication of these two numbers will give us 1:
5 × 1/5 = 5 × 0.2 = 1
The name reciprocal comes from Latin, possibly from the phrase reque proque, meaning back and forth. The reciprocal number to x may be denoted simply as 1/x but also as x-1. Thus, raising the number to the power of minus one is the same as finding its reciprocal.
How to find the reciprocal?
So, in short, how to find the reciprocal of a number?
-
Reciprocal of a fraction
To find the reciprocal of a fraction, switch the numerator and the denominator (the top and bottom of the fraction, respectively). So, simply speaking, the reciprocal of a/b is b/a.
Example: the reciprocal of 3/4 is 4/3
-
Reciprocal of a number
To find the reciprocal of a number, divide 1 by the number.
Example: the reciprocal of 7 is 1/7
-
Reciprocal of a decimal
To find the reciprocal of a decimal, you need to do the same as before - divide 1 by your decimal number.
Example: the reciprocal of 3.25 is 1/3.25
Additionally, our reciprocal calculator will show you the fraction in its simplified form.
Remember that 0 doesn't have the reciprocal, as 1/0 is undefined.
Examples: what is the reciprocal of 4 and 1/2?
We hope that, after our explanation, you now understand the concept of a reciprocal. In that case, let's look at two examples to check how this calculator works!
Example 1: What is the reciprocal of 4?
- Is your number a fraction? Not this time! Choose No from the drop-down list. (If you really want, you can leave it as the fraction option and then choose 1 as the denominator).
- Input the number for which you'd like to find the reciprocal, which is 4.
- Tadaa! That's all you need to do! The reciprocal calculator shows that the reciprocal of your number is 0.25, or, as a fraction, 1/4.
Example 2: What is the reciprocal of 1/2?
- Again, start with the question: is the number a fraction? Pick Yes this time.
- Enter the numerator (top) and denominator (bottom) of your fraction into the appropriate fields. So, in our case, input 1 as the numerator and 2 in the denominator box.
- The reciprocal calculator finds the answer - the reciprocal of 1/2 is 2.
FAQs
- What is the reciprocal of 5?
- 0.2. Since we can write 5 as 5/1, if we take the reciprocal, it becomes 1/5, which is 0.2 in decimal form.
- What is the reciprocal of 2/3?
- 3/2 or 1.5. Taking the reciprocal of a fraction means swapping the numerator and the denominator around.
- What is the reciprocal of 1?
- 1. Since 1 in fractional form is written as 1/1, taking the reciprocal (swapping around the numerator and the dominator) results in the same thing, 1/1, which is 1.
- How do you find the inverse of a fraction?
- You find the inverse of a fraction by exchanging the numerator (top number) with the denominator (bottom number) – taking the reciprocal of the fraction. For example, the inversion of the fraction 5/4 is 4/5.
Related calculators
Remainder
Use the remainder calculator to find the quotient and remainder of division.
Math
Slope
Calculate the slope of a line from two given points using the slope calculator. Discover the slope formula and learn how to find a slope with two points.
Math
Average
Calculate the average (mean) with our user-friendly tool. Discover how to find averages or perform quick calculations effortlessly.
Math
Circumference
Use this free circumference calculator to find the area, circumference and diameter of a circle.
Math