Quick Answer
To reverse a percentage, divide the final value by the multiplier: original = final ÷ (1 − %/100) after a decrease and final ÷ (1 + %/100) after an increase — a price of 80 after 20% off was 80 ÷ 0.80 = 100. For "X is P% of what number", divide the part by P/100: 18 is 30% of 18 ÷ 0.30 = 60.
Reverse Percentage Formula
A reverse percentage calculator answers the backwards question: you know the number after the percentage happened, and you want the number before it. All three versions of the problem reduce to one move — divide by the multiplier.
| Question | Formula | Example |
|---|---|---|
| Price is 80 after 20% off — original? | 80 ÷ (1 − 0.20) = 80 ÷ 0.80 | 100 |
| Total is 120 after adding 20% — original? | 120 ÷ (1 + 0.20) = 120 ÷ 1.20 | 100 |
| 18 is 30% of what number? | 18 ÷ 0.30 | 60 |
Reverse Percentage Chart (Divide by the Multiplier)
Find your discount or increase, divide the final value by the multiplier shown. The example column works a final value of 80 backwards in each row.
| What happened | Multiplier | Reverse it | 80 came from… |
|---|---|---|---|
| 10% off | 0.90 | ÷ 0.90 | 88.89 |
| 15% off | 0.85 | ÷ 0.85 | 94.12 |
| 20% off | 0.80 | ÷ 0.80 | 100 |
| 25% off | 0.75 | ÷ 0.75 | 106.67 |
| 30% off | 0.70 | ÷ 0.70 | 114.29 |
| 40% off | 0.60 | ÷ 0.60 | 133.33 |
| 50% off | 0.50 | ÷ 0.50 | 160 |
| 60% off | 0.40 | ÷ 0.40 | 200 |
| 75% off | 0.25 | ÷ 0.25 | 320 |
| +5% added | 1.05 | ÷ 1.05 | 76.19 |
| +10% added | 1.10 | ÷ 1.10 | 72.73 |
| +15% added | 1.15 | ÷ 1.15 | 69.57 |
| +20% added (UK VAT) | 1.20 | ÷ 1.20 | 66.67 |
| +25% added | 1.25 | ÷ 1.25 | 64 |
How to Use the Reverse Percentage Calculator
- Pick what you’re undoing.
% of what number for “18 is 30% of what” questions, Before a decrease for sale prices and losses, Before an increase for VAT, markups and raises.
- Enter the value you know.
The sale price on the tag, the total on the receipt, or the part — currency doesn’t matter, the math is identical for dollars, rupees or exam marks.
- Enter the percentage.
The discount, tax or share that was applied. Type 20 for 20%.
- Read the original — and the trap.
The panel shows the original value, the multiplier, the amount added or taken off, a check line (original × multiplier = your value) and the crossed-out wrong-way answer you’d get by just adding or subtracting the percentage.
Reverse Percentage Examples
Every row uses the calculator’s exact method — divide by the multiplier, then verify forwards.
| Scenario | Known value | Reverse step | Original |
|---|---|---|---|
| Jacket on a 40%-off rail | 45 | 45 ÷ 0.60 | 75 |
| Invoice total incl. 20% VAT | 240 | 240 ÷ 1.20 | 200 |
| “18 is 30% of what number?” (GCSE) | 18 | 18 ÷ 0.30 | 60 |
| Salary after a 5% raise | 42,000 | 42,000 ÷ 1.05 | 40,000 |
| Two successive 10% discounts | 81 | 81 ÷ 0.9 ÷ 0.9 | 100 — two 10% cuts are 19% off, not 20% |
Why You Can’t Just Add the Percentage Back
The most common reverse-percentage mistake is treating the percent as symmetric: “it went down 20%, so I’ll add 20%.” But the 20% you add is computed on the smaller final number, so it is a smaller amount than the 20% that was removed from the original. Start at 100, drop 20% to 80, add 20% of 80 and you land on 96 — four short. In general, down p% then up p% leaves you at (1 − p²/10,000) of the start, so the error grows with the square of the percentage:
| Down then up by | Where you land (start = 100) | Shortfall |
|---|---|---|
| 10% | 99 | −1% |
| 20% | 96 | −4% |
| 30% | 91 | −9% |
| 40% | 84 | −16% |
| 50% | 75 | −25% |
Reverse VAT and Sales Tax
Tax-inclusive prices are the everyday reverse-percentage-increase problem: the sticker already contains the tax, and the net price is gross ÷ (1 + rate). A UK receipt of £240 with 20% VAT contains a £200 net price and £40 of VAT — never £240 − 20% = £192, which double-counts the tax base. The same one-liner works for any rate: divide by 1.05 for a 5% sales tax, by 1.18 for an 18% GST. Splitting a purchase into monthly payments instead? The EMI calculator handles the interest-percentage side of the checkout.
