To reverse a percentage increase, divide the new value by one plus the percentage expressed as a decimal. To reverse a percentage decrease, divide the reduced value by one minus the percentage expressed as a decimal. Reversing a change requires division, not simply applying the opposite percentage.
Enter an original value and a new value to calculate the percentage change, numerical difference, direction, and multiplier.
A value after a percentage change contains both the original amount and the applied multiplier.
Why Percentage Changes Must Be Reversed
A new value is created by multiplying the original value by a percentage multiplier.
To recover the original, divide by that multiplier.
The Percentage Change Calculator can verify the original and new values after the reversal.
Reverse a Percentage Increase
Convert the increase percentage to a decimal and add one.
Divide the final value by the resulting multiplier.
A 20 percent increase uses a multiplier of 1.20.
Worked Increase Example
Suppose a value is 120 after a 20 percent increase.
The increase multiplier is 1.20.
Dividing 120 by 1.20 recovers the original value of 100.
Reverse a Percentage Decrease
Convert the decrease percentage to a decimal and subtract it from one.
Divide the reduced value by the remaining multiplier.
A 20 percent decrease leaves a multiplier of 0.80.
Worked Decrease Example
Suppose a value is 80 after a 20 percent decrease.
The remaining multiplier is 0.80.
Dividing 80 by 0.80 gives the original value of 100.
Why Applying the Opposite Percentage Is Wrong
A 20 percent increase from 100 creates 120.
Reducing 120 by 20 percent removes 24 and leaves 96.
The opposite percentage uses the new base, so it does not restore the original.
Division by 1.20 reverses a 20% increase, while division by 0.80 reverses a 20% decrease.
Find a New Value After an Increase
Multiply the original value by one plus the increase percentage as a decimal.
An original value of 250 increased by 12 percent uses a multiplier of 1.12.
The new value is 250 multiplied by 1.12, which equals 280.
Find a New Value After a Decrease
Multiply the original value by one minus the decrease percentage as a decimal.
An original value of 250 decreased by 12 percent uses a multiplier of 0.88.
The reduced value is 220.
Reverse a Price Increase
Suppose a product now costs $138 after a 15 percent increase.
Divide 138 by 1.15.
The original price was $120.
Reverse a Discount
Suppose a sale price is $72 after a 20 percent discount.
The remaining multiplier is 0.80.
Dividing 72 by 0.80 gives an original price of $90.
Multiplier Reference Table
Percentage changes can be represented as multipliers.
| Change | Forward multiplier | Reverse operation |
|---|---|---|
| 10% increase | 1.10 | Divide by 1.10 |
| 25% increase | 1.25 | Divide by 1.25 |
| 10% decrease | 0.90 | Divide by 0.90 |
| 25% decrease | 0.75 | Divide by 0.75 |
Common Mistakes
Do not apply the same percentage in the opposite direction.
Do not divide by the percentage number itself.
Do not use the increase formula when reversing a decrease.
Conclusion
Reverse an increase by dividing by one plus the percentage decimal.
Reverse a decrease by dividing by one minus the percentage decimal.
Verify the recovered values with the Percentage Change Calculator.
FAQs
How do I reverse a percentage increase?
Divide the final value by one plus the percentage expressed as a decimal.
How do I reverse a percentage decrease?
Divide the reduced value by one minus the percentage expressed as a decimal.
Why not apply the opposite percentage?
The opposite change uses a different base and does not normally restore the original.
What was the original value if 120 is after a 20 percent increase?
Divide 120 by 1.20 to get 100.
What was the original price if $80 is after a 20 percent discount?
Divide 80 by 0.80 to get $100.