A reverse percentage works backwards. Instead of applying a percentage to a number, you start with the result and work back to the original. It comes up constantly in real life — finding a pre-VAT price, working out what a salary was before a deduction, or checking what an item cost before a discount was applied.
What Is a Reverse Percentage?
In a standard percentage problem, you know the starting value and apply a percentage to it. In a reverse percentage, you know the end result (after a percentage has been added or removed) and you need to find the original value.
The key insight is this: if you add 20% to a number to get a result, you can't remove 20% from the result to get back to the original. The 20% was calculated on the original, not on the result. So you have to divide, not subtract.
The Formula
If a value has had a percentage added to it:
If a value has had a percentage removed from it:
Or, if you simply know that the result is X% of some unknown original:
Removing VAT: The Classic Reverse Percentage
This is probably the most common application. A price of £240 includes 20% VAT. What's the ex-VAT price?
VAT-inclusive price: £240
VAT rate: 20%
Original (ex-VAT): 240 ÷ 1.20 = £200
VAT amount: £240 − £200 = £40
Check: £200 × 0.20 = £40 ✓
Notice: you can't just do 240 − (240 × 0.20) = 240 − 48 = 192. That's wrong. 192 × 1.20 = 230.40, not 240. The subtraction method uses the wrong base for the 20%.
Finding the Original Price After a Discount
A coat is on sale for £119 after a 30% discount. What was the original price?
Sale price: £119 (after 30% off)
The sale price is 70% of the original (100% − 30% = 70%)
Original: 119 ÷ 0.70 = £170
Check: 170 × 0.30 = 51. £170 − £51 = £119 ✓
Finding an Original Salary Before a Deduction
After a 12% pension deduction, your net monthly contribution to your salary sacrifice scheme is £2,640. What was your gross monthly salary before the deduction?
Net amount: £2,640 (88% of the original)
Original: 2,640 ÷ 0.88 = £3,000
When the Result Represents X% of the Original
Sometimes the problem is stated differently: "150 is 75% of what number?" Here you're not reversing a change — you're finding the whole when you know a part.
240 is 60% of what number?
Whole: 240 ÷ 0.60 = 400
Check: 400 × 0.60 = 240 ✓
Why People Get This Wrong
The mistake is almost always the same: subtracting (or adding) the percentage instead of dividing. This is intuitive but incorrect, because the percentage was originally applied to the unknown number, not to the number you currently have.
The rule: when reversing a percentage addition, divide by (1 + rate). When reversing a percentage removal, divide by (1 − rate). Division is the reverse operation of multiplication, and multiplying by the inverse is always correct.
Use the free Reverse Percentage Calculator to find original values instantly — just enter the result and the percentage.
Reverse Percentage Calculator →Quick Reference
- Original (percentage added): Result ÷ (1 + rate/100)
- Original (percentage removed): Result ÷ (1 − rate/100)
- Whole from a part: Part ÷ (rate/100)
- Remove 20% VAT: Price ÷ 1.20
- Undo a 25% discount: Sale price ÷ 0.75
Examples use illustrative figures. Always verify reverse percentage calculations when used for financial, tax or accounting purposes.