Reverse percentage is used to find an original amount when the final amount and percentage change are known. If a price after a 20% increase is $120, divide $120 by 1.20 to recover the original price of $100. If a sale price after a 20% discount is $80, divide $80 by 0.80 to find the original price of $100.
Use the Percentage Calculator on the homepage to check the percentage relationship between the known final value and the original amount.
A final value of $120 after a 20% increase represents 120% of the unknown original value.
What Reverse Percentage Means
Reverse percentage means working backwards from a final value to find the original value before a percentage increase or decrease was applied.
A normal percentage calculation begins with the original amount. A reverse calculation begins with the amount after the change.
This method is useful for recovering original prices, pre-tax amounts, values before markup, previous salaries, earlier populations, and amounts before discounts.
Why Subtracting the Percentage Is Not Enough
Suppose a value after a 20% increase is $120. Subtracting 20% of $120 gives $96, not the original $100.
The reason is that the 20% increase was calculated from the original value, not from the final value.
Reverse percentage therefore requires division by a percentage multiplier rather than subtraction of the percentage from the final amount.
Reverse Percentage After an Increase
After a percentage increase, the final amount represents more than 100% of the original.
Convert the final percentage into a decimal multiplier. After a 20% increase, the final value is 120% of the original, which equals 1.20.
Divide the final value by that multiplier to recover the original amount.
Worked Example: $120 After a 20% Increase
A final price of $120 represents 120% of the original price.
Convert 120% to the decimal multiplier 1.20.
Divide $120 by 1.20. The original price was $100.
Reverse Percentage After a Decrease
After a percentage decrease, the final amount represents less than 100% of the original.
A 20% decrease leaves 80% of the original value. The decimal multiplier is therefore 0.80.
Divide the final amount by 0.80 to recover the original value.
Worked Example: $80 After a 20% Discount
A sale price of $80 after a 20% discount represents 80% of the original price.
Convert 80% to the decimal multiplier 0.80.
Divide $80 by 0.80. The original price was $100.
Step 1: Determine Whether the Value Increased or Decreased
The multiplier depends on the direction of the change.
For an increase, add the percentage to 100%. For a decrease, subtract the percentage from 100%.
Using the wrong direction can produce a result that is larger or smaller than logically expected.
Step 2: Convert the Remaining Percentage to a Decimal
Divide the final percentage by 100.
After a 15% increase, the final percentage is 115%, which becomes 1.15.
After a 15% decrease, the final percentage is 85%, which becomes 0.85.
Step 3: Divide the Final Amount by the Multiplier
Division reverses the multiplication that created the final value.
If a salary after a 10% raise is $55,000, divide $55,000 by 1.10.
The original salary was $50,000.
How to Reverse a Percentage on a Calculator
Convert the percentage after the change into a decimal multiplier, then divide the final value by that multiplier.
For $170 after a 15% decrease, calculate 170 ÷ 0.85. The original value is $200.
Use the Percentage Calculator to verify that the calculated original amount produces the known final percentage.
Finding an Original Price Before a Discount
Suppose a product costs $126 after a 30% discount.
A 30% discount leaves 70% of the original price, so the decimal multiplier is 0.70.
Divide $126 by 0.70. The original price was $180.
Finding a Price Before Tax
Suppose a total of $108 includes 8% tax and you need the pre-tax amount.
The final total represents 108% of the original price, or a multiplier of 1.08.
Divide $108 by 1.08. The amount before tax was $100.
Finding a Value Before Markup
Suppose a selling price of $156 includes a 30% markup on cost.
The selling price represents 130% of the original cost, or 1.30.
Divide $156 by 1.30. The original cost was $120.
Reverse Salary Increase Example
An employee earns $64,800 after an 8% salary increase.
The final salary represents 108% of the previous salary.
Divide $64,800 by 1.08. The previous salary was $60,000.
How to Check a Reverse Percentage Answer
Apply the original percentage change to the recovered amount.
If the calculated original value is $100 and the increase was 20%, calculate $100 × 1.20.
The result should return the known final value of $120.
Common Mistakes
The most common mistake is subtracting the percentage directly from the final value.
Another is dividing by the percentage itself rather than the percentage multiplier.
It is also easy to use 1.20 for a 20% decrease when the correct remaining multiplier is 0.80.
Conclusion
To calculate reverse percentage, convert the final percentage into a decimal multiplier and divide the final value by it.
Use a multiplier above 1 after an increase and below 1 after a decrease.
Check the recovered amount using the Percentage Calculator on the Percentage.click homepage.
Related percentage guides
FAQs
What is reverse percentage?
Reverse percentage is a method for finding the original value when the final value and percentage change are known.
How do I find the original value after a percentage increase?
Divide the final value by one plus the percentage increase expressed as a decimal.
How do I find the original price after a discount?
Divide the sale price by the percentage remaining expressed as a decimal.
What was the original price if $80 is after a 20% discount?
A 20% discount leaves 80%, so divide $80 by 0.80. The original price was $100.
Why can I not simply subtract the percentage?
The percentage change was calculated from the original value, not the final value.