Reverse Percentages: How to Find the Original Value

Calculating 20% of 100 is easy. But what if you know 20% of a number is 20, and you need to find the number? That's called a reverse percentage, and it's one of the most useful math skills you can have.

When Do You Use Reverse Percentages?

• Finding original prices: "This shirt is $40 after a 20% discount. What was the original price?"
• Income before taxes: "My take-home pay is $3,000, which is 75% of my gross salary. What is my total salary?"
• Test scores: "I got 18 questions right, which is 90%. How many questions were on the test?"

The "Divider" Method

The easiest way to solve any reverse percentage problem is to turn the percentage into a decimal and divide.

Steps:

1. Identify the percentage you have left (for discounts) or the target percentage.
2. Divide the result by that percentage (as a decimal).

Discount Example:

A jacket costs $120 after a 40% discount.

• If it's 40% off, you are paying 60% of the original price.
• Calculation: $120 / 0.60 = $200 (Original Price).

Result Example:

You know that 15% of a bill is $9.

• Calculation: $9 / 0.15 = $60 (Total Bill).

Common Mistakes to Avoid

Never try to find the "missing" amount by calculating 40% of the $120 and adding it back. 40% of $120 is $48, which gives you $168—incorrect! Because the 40% discount was taken from the original $200, you must work backward using division.

Get Instant Results

Struggling with the decimal points? Our Reverse Percentage Calculator lets you find the original value instantly without any manual division. Perfect for shopping trips or financial planning!