Work backwards to the original value. Available with Premium in The Percentage Calculator app.
A monthly plan or lifetime Premium purchase is required for this feature.
The iOS reverse percentage screen shows the amount after a deduction, the percentage deducted and the original value. Use Premium to work backwards with your own figures.
For a reduction, use the mode labelled “After % is deducted” in the iOS app.
The official screen shows 100 after a 50% deduction. Entering those values recovers an original amount of 200.
The displayed formula divides the final amount by the share remaining. The result control offers copy and save to history.
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After a reduction of p%, divide the final value by (1 − p/100). After an increase, divide by (1 + p/100).
Recovering a discounted price is different from adding the same percentage back. Adding 20% to 80 gives 96, not the original 100. A 100% reduction cannot be reversed from the final value alone.
A reverse percentage calculation starts with the final amount and a known rate of change. Your first step is to identify what percentage of the original remains. After a 20% decrease, the final amount is 80% of the original. After a 20% increase, it is 120%.
| Known change | Reverse formula | Worked example |
|---|---|---|
| Decrease of p% | original = final ÷ (1 − p/100) | 80 ÷ 0.80 = 100 |
| Increase of p% | original = final ÷ (1 + p/100) | 120 ÷ 1.20 = 100 |
The increase or decrease must describe the change applied to the original amount. A percentage describing a different base requires a different equation.
A sale price of 72 after a 10% discount came from 72 ÷ 0.90 = 80. Check it by reducing 80 by 10%, which subtracts 8 and leaves 72.
A salary of 2,100 after a 5% raise came from 2,100 ÷ 1.05 = 2,000. Subtracting 5% from 2,100 would give 1,995 because that subtraction uses the new salary as its base.
When several percentage changes were applied, reverse their combined multiplier. A value of 108 after a 20% increase followed by a 10% decrease came from 108 ÷ (1.20 × 0.90) = 100.
A 100% reduction leaves zero whatever the original positive amount was. You cannot recover a unique original from that final value alone. The reverse formula would require division by zero.
Rounding can also limit precision. If a displayed sale price or percentage has been rounded, the recovered original is an estimate consistent with those inputs.
If you know a part and the percentage it represents directly, use the free find the whole calculator. If both the starting and final amounts are known, use percentage change to find the rate.
Finding the whole starts with a part and the percentage it represents. Reverse percentages starts with an amount after a known increase or decrease.
Download the app and unlock Premium for reverse percentages. The examples here explain the method; the four core percentage modes are free online and in the app.
The original discount was taken from a larger base. After 20% off 100, the sale price is 80. Adding 20% of 80 gives only 96. Divide by the remaining share, 0.80, to recover 100.
Divide the final value by one plus the rate as a decimal. For a final value of 120 after a 20% increase, calculate 120 ÷ 1.20 = 100.
