Backwards Percentage Calculator: Finding the Original Amount
A reverse percentage works out the number you started with when you only know the final figure and the percentage that was applied. It is the calculation behind 'what was the price before the discount' and 'what is the net amount before tax', and it is done by dividing rather than subtracting.
The rule: divide by the multiplier
- After a decrease: original = final ÷ (1 − rate/100). 80 after 20% off is 80 ÷ 0.8 = 100.
- After an increase: original = final ÷ (1 + rate/100). 120 after a 20% rise is 120 ÷ 1.2 = 100.
- Removing 20% VAT from 120 gives 100, not 96 — the tax was charged on the smaller net figure.
Why subtracting the percentage fails
A percentage is always a share of some base amount. When a discount is applied, the base is the original price, so taking the same percentage off the already-reduced price uses the wrong base and lands short every time. The larger the percentage, the larger the error: taking 50% off 50 gives 25, while the true original was 100.
Everyday reverse percentage problems
- Retail: recovering the ticket price from a sale price to check the discount claim.
- Tax: extracting net from gross for VAT, GST or sales tax returns.
- Salary: finding last year's pay from this year's figure and the raise percentage.
- Statistics: recovering a population total when you know a count and the percentage it represents.
Doing it on a plain calculator
Convert the percentage to a multiplier, then press divide. For 15% off, that is ÷ 0.85; for 7.5% tax added, ÷ 1.075. In a spreadsheet the same idea is =B2/(1-C2) with the rate stored as a percentage-formatted decimal.
Key takeaways — Reverse Percentage Calculator
- Divide by the multiplier — never subtract the percentage from the final amount.
- Decrease uses 1 − rate; increase uses 1 + rate.
- The error from subtracting instead of dividing grows with the size of the percentage.