Reverse Percentage Calculator
Type the final value and the percentage change to recover the number you started with, such as the price before 20% VAT was added.
after a % change. What was it before?
The original value
45
Before a 20% change, the value was 45: 45 × 1.2 = 54.
How this works: Method, 1 source, Checked against 2 worked examples,
How this works
Method
If a value has already had a percentage added or taken off, divide by the multiplier to get back to the start. A 20% increase multiplies by 1.2, so a final value of 54 came from 54 ÷ 1.2 = 45. A 20% discount multiplies by 0.8, so a sale price of 54 came from 54 ÷ 0.8 = 67.50. Full method
Sources
How it’s tested
2 worked examples for this page are checked by automated tests before every release: given the inputs, the tool must show the expected answer.
Privacy
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Changes
- Added eight pages for common questions, from percent of a number to percent error and reverse percentages, each with its own method, examples and table.
- Added key facts with a worked example of each formula.
- Redesigned: type the numbers straight into a sentence, with bars on one scale that picture the answer.
- Results now update as you type, with no Calculate button.
- First published.
How to reverse a percentage
If a value has already had a percentage added or taken off, divide by the multiplier to get back to the start. A 20% increase multiplies by 1.2, so a final value of 54 came from 54 ÷ 1.2 = 45. A 20% discount multiplies by 0.8, so a sale price of 54 came from 54 ÷ 0.8 = 67.50.
The common mistake is to take the percentage of the final value and subtract it: 20% of 54 is 10.80, and 54 − 10.80 = 43.20, which is wrong, because the 20% was worked out on the original, smaller number.
This is how to remove sales tax or VAT from a price that includes it. With the UK’s 20% standard rate, a £54 price is £45 before VAT, and the VAT itself is £9, which is one sixth of the total, not a fifth.
original = final ÷ (1 + p ÷ 100)
- The UK’s standard VAT rate is 20%, with a reduced rate of 5% for some goods and services. Source: GOV.UK, VAT rates.
Removing a percentage from a total
For a final value of 120 after each change: the divisor, the original and the amount that was added or taken off.
| Change applied | Divide by | Original | Amount added (or taken off) |
|---|---|---|---|
| +5% | 1.05 | 114.29 | 5.71 |
| +7.5% | 1.075 | 111.63 | 8.37 |
| +10% | 1.1 | 109.09 | 10.91 |
| +12.5% | 1.125 | 106.67 | 13.33 |
| +15% | 1.15 | 104.35 | 15.65 |
| +20% | 1.2 | 100 | 20 |
| +25% | 1.25 | 96 | 24 |
| +50% | 1.5 | 80 | 40 |
| +100% | 2 | 60 | 60 |
| −10% | 0.9 | 133.33 | −13.33 |
Show all 13 rowsShow fewer
| −20% | 0.8 | 150 | −30 |
| −25% | 0.75 | 160 | −40 |
| −50% | 0.5 | 240 | −120 |
Frequently Asked Questions
How do I find the price before tax?
Divide the price including tax by 1 plus the tax rate. With 8% sales tax, a $54 total was 54 ÷ 1.08 = $50 before tax, so the tax was $4.
A shirt costs $36 after 25% off. What was the original price?
25% off leaves 75%, so divide by 0.75: 36 ÷ 0.75 = $48. Check: 25% of $48 is $12, and $48 − $12 = $36.
Why can’t I just subtract the percentage from the final price?
Because the percentage was taken from the original, not from the final value. Subtracting 20% of the final value undoes too much after an increase and too little after a decrease.