About the Reverse Percentage Calculator
This reverse percentage calculator works a percentage backwards. If you know a price after tax, the sale price after a discount, a salary after a raise, or that a number is some percentage of an unknown total, it finds the original value you started from.
Shoppers use it to strip sales tax or VAT out of a receipt total, sellers use it to find the pre-markup cost, and students use it for “reverse percentage” exam questions. The key point is that you must divide by the multiplier — simply taking the same percentage off the final number gives the wrong answer.
Choose “increased” when the percentage was added (tax, tip, markup, growth), “decreased” when it was taken off (discount, depreciation, loss), or “is X% of” when the number you have is a portion of the total.
With the default inputs, the original value is 100. Change any value above to recalculate instantly.
How to use the reverse percentage calculator
- 1Enter the value you have now (after tax, discount or change).
- 2Enter the percentage that was applied.
- 3Choose whether it was added, taken off, or is a share of the total.
- 4Read the original value and the amount that was added or removed.
Formula and method
A percentage increase multiplies the original by (1 + p/100) and a decrease multiplies it by (1 − p/100). To undo the change you divide the final value by the same multiplier. For example, a price including 20% tax is 1.2 times the pre-tax price, so dividing by 1.2 recovers it.
Taking p% off the final value does not work, because the percentage was calculated on the smaller (or larger) original, not on the final figure. When the known number is a portion of the whole, divide by p/100 instead.
- Final
- The value after the percentage change (or the known part)
- p
- The percentage that was applied
- Original
- The value before the change (or the whole)
Worked examples
Remove 20% VAT from 120
The total is 1.20 × the net price, so 120 ÷ 1.2 = 100 before VAT and the VAT itself is 20. Taking 20% off 120 would wrongly give 96.
Sale price $68 after 15% off
A 15% discount leaves 85% of the price, so 68 ÷ 0.85 = $80 was the original price and the discount was $12.
Remove 8.25% sales tax from $59.99
59.99 ÷ 1.0825 = $55.42 before tax, so about $4.57 of the total was sales tax.
45 is 30% of what number?
If 45 is 30% of the whole, the whole is 45 ÷ 0.30 = 150, and the other 70% is 105.
Frequently asked questions
How do you calculate a reverse percentage?+
Divide the final value by the multiplier. After an increase of p%, divide by (1 + p/100); after a decrease of p%, divide by (1 − p/100). For $110 after a 10% increase: 110 ÷ 1.1 = $100.
Why can’t I just subtract the percentage from the final price?+
Because the percentage was applied to the original, not the final number. 20% of 120 is 24, but the tax added to the original 100 was only 20. Subtracting gives 96, which is too low.
How do I remove sales tax or VAT from a total?+
Divide the total by 1 plus the tax rate. With 20% VAT, divide by 1.2; with 8.25% sales tax, divide by 1.0825. The difference between the total and the result is the tax.
How do I find the original price before a discount?+
Divide the sale price by (1 − discount). A $45 item at 25% off came from 45 ÷ 0.75 = $60.
How do I find the whole when I know a percentage of it?+
Divide the part by the percentage as a decimal. If 18 students are 40% of a class, the class has 18 ÷ 0.4 = 45 students.