Reverse Percentage Calculator
Work backwards from a result to find the original value before a percentage was added or removed. Useful for finding pre-tax prices, original values before a discount, or the starting number before any percentage change was applied.
How It Works
When you know the result of applying a percentage to a number but need to find the original number, you use a reverse percentage calculation. This is sometimes called "working backwards" from a percentage.
The Formula
Original = Final Value ÷ (1 + Percentage ÷ 100)
Original = Final Value ÷ (1 − Percentage ÷ 100)
Use the addition formula when a percentage was added (e.g. VAT or markup), and the subtraction formula when a percentage was removed (e.g. a discount). The calculator handles both cases automatically.
When to Use This
Common uses include finding the pre-VAT price from a VAT-inclusive total, finding the original price of an item before a sale discount, or finding the base salary before a percentage pay rise was applied.
Worked Examples
Example 1: Price is £120 including 20% VAT. Find the ex-VAT price
120 ÷ (1 + 20 ÷ 100) = 120 ÷ 1.20 = £100
Example 2: Sale price is £85 after a 15% discount. Find the original price
85 ÷ (1 − 15 ÷ 100) = 85 ÷ 0.85 = £100
Example 3: Final value is 330 after a 10% increase. Find the original
330 ÷ (1 + 10 ÷ 100) = 330 ÷ 1.10 = 300
Example 4: Score of 76 represents 95% of the total. Find the total marks
76 ÷ (95 ÷ 100) = 76 ÷ 0.95 = 80
Example 5: After a 25% markup, item costs £500. Find the cost price
500 ÷ (1 + 25 ÷ 100) = 500 ÷ 1.25 = £400
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