A reverse percentage calculation finds the original value before an increase. The key is to divide by the growth multiplier.
Select “Find original” in the calculator
Reverse percentage formula
Original value = New value ÷ (1 + Percentage increase ÷ 100)If a price is $138 after a 15% increase, the multiplier is 1.15.
$138 ÷ 1.15 = $120The original price was $120. You can check it: 15% of $120 is $18, and $120 + $18 is $138.
Why subtracting 15% is wrong
Subtracting 15% of $138 gives $117.30, not $120. The increase was calculated from the smaller original value. A percentage increase and an equal percentage decrease use different baselines.
This is why a 20% increase followed by a 20% decrease does not return to the starting value. Read the full explanation in why equal increases and decreases do not cancel.
Another example with attendance
An event reports 2,640 visitors after attendance increased by 10%.
Original attendance = 2,640 ÷ 1.10 = 2,400The increase was 240 visitors.
Special cases
A 0% increase means the original and new values are the same. A positive increase always produces a multiplier greater than 1. If the question involves a decrease, the reverse formula uses 1 − decrease rate instead.
For ordinary forward calculations, see how to calculate a price increase or a salary increase percentage.
Remember the multiplier
Convert the percentage to a multiplier, then divide the final value by that multiplier. Do not subtract the stated percentage from the final value.