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Please enter the final value.
The number you have after the percentage was applied
%
Please enter a percentage.
Enter as a positive number — e.g. 20 for 20%
Was the original value increased or decreased to reach the final?
Original Value (Before % Change)
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Sources & Methodology
Calculations use standard percentage algebra verified against mathematics curriculum references from Khan Academy and NCTM.
Khan Academy — Percent Problems: Finding the Whole
Mathematical foundation for working backwards from a percentage to find the original value
National Council of Teachers of Mathematics (NCTM)
Percentage and proportional reasoning standards used as curriculum reference for formula verification
Methodology: For a percentage increase: Original = Final ÷ (1 + %/100). For a percentage decrease: Original = Final ÷ (1 − %/100). The percentage change amount = Final − Original. Verification: applying the percentage to the original value should return the final value exactly.
⏱ Last reviewed: March 2026
How to Calculate Reverse Percentage
A reverse percentage calculation (also called "working backwards from a percentage") finds the original number when you know the result after a percentage was applied. This is useful for finding pre-discount prices, pre-tax amounts, pre-VAT prices, and original values before any markup or markdown.
The Formulas
After an INCREASE: Original = Final Value ÷ (1 + Percentage ÷ 100)
Example: Price is $120 after a 20% increase → Original = $120 ÷ 1.20 = $100
Check: $100 + 20% = $100 + $20 = $120 ✓
Check: $100 + 20% = $100 + $20 = $120 ✓
After a DECREASE: Original = Final Value ÷ (1 − Percentage ÷ 100)
Example: Sale price is $80 after a 20% discount → Original = $80 ÷ 0.80 = $100
Check: $100 − 20% = $100 − $20 = $80 ✓
Check: $100 − 20% = $100 − $20 = $80 ✓
Common Real-World Uses
| Scenario | Final Value | % | Type | Original |
|---|---|---|---|---|
| Sale price with 25% off | $75 | 25% | Decrease | $100 |
| Price after 10% markup | $110 | 10% | Increase | $100 |
| Price incl. 20% VAT | $60 | 20% | Increase | $50 |
| Price after 15% raise | $57,500 | 15% | Increase | $50,000 |
| Sale price after 30% off | $350 | 30% | Decrease | $500 |
| Price after 5% increase | $210 | 5% | Increase | $200 |
The Most Common Mistake
Many people try to "undo" a 20% increase by subtracting 20% from the final number — but this gives the wrong answer. If a price went up 20% to reach $120, subtracting 20% from $120 gives $96, not $100. The correct method divides by 1.20 because the percentage was applied to the original, not the final value.
💡 Pro Tip: Always verify your reverse percentage answer by applying the percentage forward. If you calculated the original as $100 and the increase was 20%, check: $100 × 1.20 = $120. If that matches the final value you started with, your reverse calculation is correct.
Frequently Asked Questions
Divide the final price by (1 + percentage/100). For example, if a price is now $130 after a 30% increase: Original = $130 ÷ 1.30 = $100. The key is to divide by the multiplier, not subtract the percentage from the final price — that common mistake gives the wrong answer.
Divide the final value by (1 − percentage/100). For a 15% discount that resulted in a $85 price: Original = $85 ÷ 0.85 = $100. You're essentially reversing the multiplication that created the discount by dividing instead.
Divide the VAT-inclusive price by (1 + VAT rate/100). For 20% VAT: Pre-VAT = Final ÷ 1.20. For 10% GST: Pre-GST = Final ÷ 1.10. For example, a £120 price including 20% VAT has a pre-VAT price of £120 ÷ 1.20 = £100, meaning £20 is the tax component.
Because the percentage was applied to the original value, not the final value. If you subtract 20% from $120, you get $96 — but that's wrong because 20% of $120 ($24) is different from 20% of $100 ($20). The original was $100, and $120 − $100 = $20 (which is 20% of $100, the original). Always divide by the multiplier to reverse a percentage correctly.
Reverse percentage is used constantly in everyday finance: finding the pre-tax price from a receipt, calculating the original retail price before a store discount, finding pre-VAT or pre-GST amounts, working out what a salary was before a raise, or determining the wholesale cost of a marked-up item. Anytime you have the "after" number and the percentage, reverse percentage finds the "before."
Apply the percentage forward to your calculated original value. If original × (1 + %/100) equals your final value (for an increase), or original × (1 − %/100) equals your final value (for a decrease), your answer is correct. For example: original $100, 20% increase → $100 × 1.20 = $120 ✓.
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