Reverse Percentage Calculator — Find the Original Number Before a Change
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Reverse percentage questions come in two forms: "the price after a 25% discount is $75 — what was the original price?" and "this number is 30% more than the original — what was the original?" Both require working backwards from a percentage change, not forwards.
Find Original Price Before a Discount
Formula: Original Price = Discounted Price ÷ (1 - Discount %)
| Sale Price | Discount % | Original Price | Calculation |
|---|---|---|---|
| $75 | 25% | $100 | $75 ÷ 0.75 |
| $42 | 30% | $60 | $42 ÷ 0.70 |
| $90 | 10% | $100 | $90 ÷ 0.90 |
| $24 | 40% | $40 | $24 ÷ 0.60 |
Using the Percentage Calculator: use "X is what % of Y?" — if the discounted price is 75% of original (after 25% off), enter X = discounted price, then: original = discounted price / (sale percentage as decimal).
Alternatively, in "% Change" mode: enter the original as Old Value and the discounted price as New Value to verify you get the right discount percentage.
Find Original Number After a Percentage Increase
Formula: Original = Current Value ÷ (1 + Increase %)
| Current Value | Increase Applied | Original Value | Calculation |
|---|---|---|---|
| 130 | 30% | 100 | 130 ÷ 1.30 |
| $126 | 5% | $120 | $126 ÷ 1.05 |
| $88 | 10% | $80 | $88 ÷ 1.10 |
| $180 | 20% | $150 | $180 ÷ 1.20 |
Tax-Inclusive Price to Pre-Tax Price
A common reverse percentage problem: the receipt shows $108 after 8% tax — what was the pre-tax price?
Formula: Pre-tax = Tax-Inclusive Price ÷ (1 + Tax Rate)
$108 ÷ 1.08 = $100 pre-tax
| Price with Tax | Tax Rate | Pre-Tax Price |
|---|---|---|
| $108.00 | 8% | $100.00 |
| $117.60 | 20% (UK VAT) | $98.00 |
| $53.50 | 7% | $50.00 |
This also works for removing GST, VAT, HST, or any other sales tax embedded in a final price.
Why You Can't Just Apply the Percentage in Reverse
Common mistake: a price is $75 after 25% off, so people subtract 25% from $75 to get $56.25 — wrong.
The 25% was applied to the original price, not the discounted one. Subtracting 25% from the discounted price gives you a different number because you're now taking a percentage of a smaller base.
Always divide by (1 - discount rate) to reverse a discount, never subtract the percentage from the discounted price.
Reverse Any Percentage Calculation
Use "X is what % of Y?" mode or % Change mode to work backwards from any percentage. Free, no signup, instant results.
Open Free Percentage CalculatorFrequently Asked Questions
How do I find the original price before a 20% discount?
Divide the discounted price by 0.80. Example: sale price is $64 → $64 ÷ 0.80 = $80 original price. The formula is: Original = Discounted Price ÷ (1 - Discount Rate).
How do I remove 10% VAT from a price?
Divide the VAT-inclusive price by 1.10. Example: $55 including 10% VAT → $55 ÷ 1.10 = $50 pre-VAT price.
A number increased by 15% is now 230. What was the original?
230 ÷ 1.15 = 200. The original was 200. Verify: 200 × 1.15 = 230. ✓