Reverse Percentage Calculator
You have a value after a percentage increase or decrease and you want the value before. Enter the number you have and the percent it changed by — the calculator divides it back out and shows why subtracting the same percent doesn’t get you there.
How reverse percentage works
A percentage change multiplies the original by a factor. To undo it you divide by that same factor:
original = final / (1 + percent / 100) (after an increase)
original = final / (1 − percent / 100) (after a decrease)
Why you can’t just subtract the percent back
The increase and the “undo” are percentages of different numbers. 100 increased by 20% is 120 — that added 20% of 100. Taking 20% off 120 removes 20% of 120, which is 24, landing on 96, not 100.
| Original | After +20% | Then −20% | Back to start? |
|---|---|---|---|
| 100 | 120 | 96 | No — 96 |
| 50 | 60 | 48 | No — 48 |
| 250 | 300 | 240 | No — 240 |
Worked examples
- Price is $120 after a 20% increase: 120 / 1.20 = $100.
- Sale price is $34 after 15% off: 34 / 0.85 ≈ $40.
- A total of $110 includes 10% tax: 110 / 1.10 = $100 before tax.
Reverse percentage table
The original value behind a few “after” amounts:
| Change | Divide by | $120 after → | $90 after → |
|---|---|---|---|
| +10% | 1.10 | $109.09 | $81.82 |
| +20% | 1.20 | $100 | $75 |
| +25% | 1.25 | $96 | $72 |
| −10% | 0.90 | $133.33 | $100 |
| −20% | 0.80 | $150 | $112.50 |
| −25% | 0.75 | $160 | $120 |
Frequently asked questions
How do I remove tax or VAT from a price?
Divide the total by 1 plus the tax rate as a decimal. A $110 total that includes 10% tax was 110 / 1.10 = $100 before tax.
Why isn't subtracting the percent the same as reversing it?
The increase is a percent of the smaller original; the reverse would be a percent of the larger final value. 20% of 100 is 20, but 20% of 120 is 24 — different amounts.
A price rose 20% then fell 20% — why isn't it back to the start?
Because the 20% fall is taken from the higher price. $100 rises to $120, then a 20% fall removes $24, leaving $96 — a net 4% loss.
Can every percentage change be reversed?
Almost. A decrease of 100% or more can't be — it sends every starting value to zero (or below), so there's nothing to recover.