Reverse a percentage: find the original amount before a percentage increase or discount, or the whole when you know a part and its percentage.

Display precision

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Reverse Percentage Formula

Percentages are numbers that are expressed as fractions. They are denoted by the symbol %. These numbers have no units and are therefore dimensionless. For example, the percentage of 25% is equal to a fraction of 1/4 and can be written as .25.

To recover a whole from a part, divide the known amount by its percentage divided by 100. To reverse an increase, divide the final amount by 1 plus the rate divided by 100; to reverse a decrease, divide by 1 minus the rate divided by 100. A decrease must be below 100% and a known-part percentage must be positive.

How to calculate reverse percentages?

Below are two different examples of how to calculate numbers from percentages, otherwise known as a reverse percentage.

  1. Let’s assume we have a number of 100. We find that this number is 25% of some original number. To determine the original number, we simply need to multiply 100 by the inverse of the fraction equivalent to 25%. So, 25%= 1/4, and the inverse of 1/4 = 4. Therefore the original number can be calculated as 100*4=400.
  2. In this example, we are going to use a more abstract number and percentage. Say we have a number that is some percent of another number. We will assume our number is 121 and that is 32% of another number X. To calculate x we must use the same process as the previous example. 121 * 100/32 (the inverse of .32) = 378.125. Select at least 3 maximum decimal places in Display precision to show this value; the default shows 378.13.

FAQ

What is a reverse percentage?

A reverse percentage is a method of determining an original number from the percentage and new number.

Calculator Change Log:

  • Improved UI for better understanding of the reverse percentage calculator.