— Everyday Math
Reverse Percentage Calculator
The undo button for percentages. You have the figure after a discount, a tax or a markup was applied, and you want the original — the pre-discount price, the pre-tax amount, the number before it grew. Pick which way the percentage went and this works backwards to the starting value.
Original before the decrease
100
- Amount removed
- 25
- Result → original
- 75 → 100
- Check (forward)
- 75
— How it works
After an increase: original = result ÷ (1 + rate ÷ 100). After a decrease: original = result ÷ (1 − rate ÷ 100). “Y is X% of what”: original = Y ÷ (X ÷ 100).
Working a percentage backwards
A reverse percentage problem starts where a normal one ends: you have the figure after a percentage was applied and you want the value it started from. The key is that applying a percentage is multiplication, so undoing it is division — you divide by the multiplier, you do not subtract the percentage. A 25% discount multiplies the price by 0.75, so to recover the original you divide the sale price by 0.75: a $75 item was $100 before the discount. A 10% markup multiplies by 1.10, so dividing the marked-up figure by 1.10 gives the original. And “45 is 30% of what number” divides 45 by 0.30 to get 150.
The most common mistake is to add the percentage back. Taking a $75 price and adding 25% gives $93.75, not $100 — because the 25% was originally taken off the larger number, not the smaller one. That asymmetry is exactly why a reverse-percentage tool is needed: you cannot simply reverse the sign. This calculator divides by the right multiplier for the direction you choose and shows a forward check so you can confirm the answer.
Worked examples: A jacket costs $75 in a 25% sale → original = 75 ÷ 0.75 = $100. An invoice totals $220 after a 10% markup → original = 220 ÷ 1.10 = $200. 45 is 30% of what number? → 45 ÷ 0.30 = 150.
Pre-discount, pre-tax and pre-markup
The same calculation answers a cluster of everyday questions. To find a pre-discount price, reverse a decrease: the sale price divided by one minus the discount gives the original ticket price — useful for checking whether a “50% off” deal really started from the regular price. To find a pre-tax amount, reverse an increase: a total that includes sales tax or VAT, divided by one plus the tax rate, gives the amount before tax — the figure you need to separate the tax out of a gross total. To find a cost before a markup, reverse the markup percentage the same way.
This is distinct from a forward discount or tax calculator, which starts from the original and applies the percentage. Here you start from the result and undo it. If you instead have the original and want the final figure, the increase, decrease or discount calculators are the ones to use; this page is purpose-built for going the other way.
Reversing stacked percentages
When several percentages were applied one after another, you reverse them by dividing by each multiplier in turn — and because multiplication is order-independent, you can divide them out in any order. A value that was raised 20% and then raised another 20% to reach 144 came from 144 ÷ 1.2 ÷ 1.2 = 100. The advanced option does this for you: enter the final figure and the sequence of changes, and it recovers the starting value. It is the honest way to back out an original from a string of markups, or to find a base price hidden behind stacked “extra % off” discounts.
Two cases have no answer. You cannot reverse a 100% decrease — it leaves nothing, so there is no information about what it started from — and you cannot solve “Y is 0% of what”, since zero percent of any number is zero. The calculator flags both rather than dividing by zero.
— Reader questions
How do I find the original price before a discount?
Divide the sale price by one minus the discount as a decimal. A $75 price after 25% off was 75 ÷ 0.75 = $100. Don’t add the percentage back — the discount was taken off the larger original, so adding it to the smaller sale price undershoots.
How do I work out the amount before tax?
Divide the tax-inclusive total by one plus the tax rate as a decimal. A $220 total that includes 10% tax was 220 ÷ 1.10 = $200 before tax, and the tax itself is the $20 difference. Use the “reverse an increase” mode.
Why can’t I just subtract the percentage to reverse it?
Because the percentage was applied to the original, not to the result. Adding 25% back to a $75 sale price gives $93.75, not the $100 it came from. You must divide by the multiplier (0.75 here), which this calculator does for you.
What does “Y is X% of what number” mean?
It is the reverse of taking a percentage: you know the part (Y) and the percentage (X), and you want the whole. Divide Y by X as a decimal — 45 is 30% of 45 ÷ 0.30 = 150. Choose the “Y is X% of what” mode for this.
Can I reverse more than one percentage at once?
Yes. If several percentages were applied in sequence, enter the final value and each change under the advanced options, and the calculator divides them out to recover the original. The order you list them in doesn’t matter.
Why does a 100% discount have no original?
Because a 100% reduction leaves zero, and zero carries no information about what it started from — any original would give the same result. The calculator flags this case rather than dividing by zero.