Reverse Percentage Calculator

Recover the original number when all you know is the value after a percentage was applied.

Reverse percentage

Undo a discount or an increase to find where the number started.

You paid a reduced price and want the original.

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Why reversing a percentage is not the same as applying one

The instinct is to apply the percentage again in the opposite direction, and that instinct is wrong every time. If a price rose 25% to reach 500, taking 25% off 500 gives 375 — but the true original was 400. The 25% was calculated on 400, not on 500, so the two percentages are slices of different-sized cakes.

The fix is division rather than subtraction. If a value has grown by 25%, it now represents 125% of the original, so dividing by 1.25 takes you back. The same logic applies to discounts: a price after 25% off is 75% of the original, so divide by 0.75.

How to use it

The first tab undoes a discount — useful when a receipt shows what you paid and the percentage saved but not the ticket price. The second tab undoes an increase, which is what you need for working back through a price rise, a salary increment or any figure that has grown by a known percentage.

The formulas

Before a discountOriginal = Paid ÷ (1 − Discount ÷ 100)
Before an increaseOriginal = Current ÷ (1 + Increase ÷ 100)

Worked examples

You paid 974.25 after 25% off

  1. After 25% off you pay 75% of the original
  2. Divide: 974.25 ÷ 0.75 = 1,299
  3. Check: 25% of 1,299 is 324.75, and 1,299 − 324.75 = 974.25 ✓

A figure of 1,416 after an 18% rise

  1. After an 18% rise the value is 118% of the original
  2. Divide: 1,416 ÷ 1.18 = 1,200
  3. Check: 18% of 1,200 is 216, and 1,200 + 216 = 1,416 ✓
Always check by going forwards Reverse percentages are easy to get wrong and easy to verify. Take your answer, apply the original percentage to it, and confirm you land back on the number you started with. The calculator includes that check in its working.

Where this comes up

More often than you would expect. Recovering a list price from a discounted invoice. Finding a pre-tax figure when only the gross is shown — although the tax calculator is more direct for that. Working out last year's rent from this year's figure and the percentage rise. Reconstructing a starting salary from a current one after a known increment.

Common mistakes

Subtracting instead of dividing. The single biggest error, and the reason this calculator exists as a separate page.

Reversing a discount of 100% or more. If everything was taken off, there is no information left to work back from. The calculator explains this rather than dividing by zero.

Using the wrong direction. Undoing a discount means dividing by a number smaller than 1, which makes the answer larger. Undoing an increase divides by a number larger than 1 and makes it smaller. If your answer moved the wrong way, you are on the wrong tab.

Frequently asked questions

How do I find the original price before a discount?
Divide the price you paid by one minus the discount as a decimal. After 30% off, divide by 0.7.
How do I reverse a percentage increase?
Divide the current value by one plus the increase as a decimal. After a 15% rise, divide by 1.15.
Why can't I just subtract the percentage to go backwards?
Because the percentage was calculated on the original value, not the final one. Subtracting it from the final value takes a slice from the wrong number and always gives the wrong answer.
Is this the same as removing tax from a total?
Mathematically yes — both divide by 1 plus the rate. The tax calculator presents the same arithmetic with net, tax and gross labelled the way an invoice does.
What if I don't know the exact percentage that was applied?
Then this calculation cannot be done, since the percentage is what links the two figures. If you know both the before and after values instead, use the percentage change calculator to find the percentage itself.

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