Reverse Percentage Calculator
Find the original value before a percentage increase or decrease — or what number a value is a percentage of.
Three common cases
Reverse a discount, reverse an increase (or remove tax), or solve 'X is P% of what'.
Divide, don't add back
Adding the percentage back to the reduced figure gives the wrong answer — you divide instead.
What is a reverse percentage?
From the result back to the start
A reverse percentage finds the original number when all you have is the value after a percentage change. If a coat costs 120 in a 20 %-off sale, what was the original price? The reverse percentage works backwards to the answer: 150. As school maths references such as BBC Bitesize explain, the trick is to treat the value you have as a percentage of the original, then divide.
Express the value you have as a percentage of the original, then divide by that as a decimal.
original = known value ÷ (1 − rate) for a decrease, or ÷ (1 + rate) for an increaseAfter a 20 % discount you paid 80 % of the original, so you divide by 0.80. After a 20 % increase you have 120 % of the original, so you divide by 1.20. For a 'percent of' problem, divide by the percentage as a decimal directly.
A jacket is 120 in a 20 %-off sale. What was the original price?
Find what percent you paid
A 20 % discount means you paid 100 − 20 = 80 % of the original.Write it as a decimal
80 % = 0.80.Divide the known value
120 ÷ 0.80 = 150.Check it
20 % of 150 is 30, and 150 − 30 = 120 — the sale price. Correct.
The single most common error is adding the percentage back to the reduced figure. It does not work because the percentage was taken from the original.
Wrong
120 + 20 % = 144 — this adds 20 % of 120, not 20 % of the original.
Right
120 ÷ 0.80 = 150 — the value is 80 % of the original.
Check
20 % of 150 = 30, and 150 − 30 = 120.
The same logic removes tax: a total that includes 20 % tax is 120 % of the net amount, so divide by 1.20 to find the pre-tax figure and the tax in between.
The original value is the number you started from before the percentage was applied, and the change amount is the difference between it and the value you entered. For a discount the original is larger than your known value; for an increase it is smaller. The method is unit-agnostic, so the same steps recover an original price, weight, population, or any quantity. The only impossible cases are a 100 % decrease or a −100 % increase, which would require dividing by zero.
The arithmetic is exact; the interpretation is on you.
Match the mode to the problem
The result is only correct if you pick the situation that matches your problem — reversing a discount, reversing an increase, or 'percent of'. Using the wrong mode gives a precise but wrong answer. For chained changes (a discount on top of another, or successive increases) reverse them one step at a time in the right order, because percentages do not simply add.