4 min read · October 6, 2026
Reverse Percentages: How to Find the Original Price Before a Discount or Increase
To find the original amount before a percentage change, divide the final value by (1 + the percentage as a decimal) for an increase, or by (1 − the percentage as a decimal) for a decrease. A price that rose 10% to $220 started at $220 ÷ 1.10 = $200 — not $220 minus 10%, which is the mistake almost everyone makes on their first try.
Why you can't just subtract the percentage back off
The instinctive move — take a price that increased by 10% and subtract 10% off it — gives the wrong answer, and the gap grows with bigger percentages. $220 minus 10% is $198, not the $200 it actually started at. The error happens because 10% of $220 isn't the same amount as 10% of the original $200; the percentage was calculated on a smaller base than the one you're subtracting it from.
The fix is to think in terms of what the final value represents as a percentage of the original, not the other way around. A 10% increase means the final value is 110% of the original — so dividing by 1.10 undoes it exactly, while subtracting 10% never can.
The reverse percentage formula
For an increase: original = final value ÷ (1 + percentage/100). For a decrease: original = final value ÷ (1 − percentage/100). A jacket on sale for $75 after a 25% discount started at $75 ÷ 0.75 = $100. A salary that grew 8% to $70,200 started at $70,200 ÷ 1.08 = $65,000.
The same formula is what removing VAT or sales tax from a tax-inclusive price actually is — it's a reverse percentage problem wearing a different name. A UK price of £120 including 20% VAT has a pre-tax value of £120 ÷ 1.20 = £100, not £120 minus 20% (£96).
A worked example both directions
Forward (the easy direction): a $200 item with a 10% increase becomes $200 × 1.10 = $220. Reverse (the direction people actually get stuck on): given the $220 final price and the 10% increase, find the $200 original by dividing — $220 ÷ 1.10 = $200.
Once you have a candidate original value, it's worth checking it the easy way: does the original plus the stated percentage actually land back on the final number? $200 × 1.10 = $220 confirms the reverse calculation was done correctly.
Put it into practice
The fastest way to learn the math is to play with the numbers.
Open the Percentage Calculator