Reverse Percentage Calculator
Find the original value before a percentage increase or decrease was applied.
How to Find the Original Value Before a Percentage Change
Sometimes you know the final value after a percentage increase or decrease, but you need to find the original value. This is called reverse percentage calculation and is useful in many real-world scenarios — from finding original prices after discounts to understanding pre-tax amounts or calculating starting values from known changes.
The Reverse Percentage Formula
To find the original after an increase: Original = New Value / (1 + Percentage / 100). To find the original after a decrease: Original = New Value / (1 - Percentage / 100). For example, if a price increased by 25% to $150, the original was $150 / 1.25 = $120.
Real-World Examples
A shirt is on sale for $45 after a 25% discount. What was the original price? $45 / 0.75 = $60. Your salary increased by 8% to $54,000. What was your previous salary? $54,000 / 1.08 = $50,000. A cities population grew by 15% to 230,000. What was it before? 230,000 / 1.15 = 200,000.
Common Mistakes to Avoid
The most common error is dividing by the percentage itself instead of (1 + percentage). For a 20% increase, you divide by 1.20, not by 0.20. Another mistake is applying the wrong formula — use the increase formula when the value went up and the decrease formula when it went down. Our calculator handles this automatically.
When You Need Reverse Percentage
Reverse percentage is needed when analyzing discounts and sales, calculating pre-tax amounts, determining original values before markups, finding starting populations after growth, recovering original measurements after percentage adjustments, and in many financial and scientific calculations where you work backwards from a known result.
Using the Reverse Percentage Calculator
Our calculator offers two tabs: After Increase and After Decrease. Enter the new value and the percentage change, and it instantly shows the original value along with the amount that was added or subtracted. This eliminates the need to remember formulas and provides instant, accurate results for any reverse percentage calculation.
Frequently Asked Questions
A reverse percentage calculator helps you find the original value before a percentage increase or decrease was applied. For example, if you know a price was increased by 20% and the new price is $120, the reverse percentage calculator tells you the original price was $100.
Enter the discounted (final) price and the discount percentage into the "After Increase" tab. The calculator divides the final price by (1 + percentage/100) to find the original price. For example, $90 after a 12.5% increase means original = 90 / 1.125 = $80.
Yes. Use the "After Decrease" tab. Enter the decreased value and the percentage decrease. The formula is: Original = Decreased Value / (1 - percentage/100). For example, if a value decreased by 25% to $150, the original was $200.