Reverse Percentage Explained: Find the Original Value Before a % Change
Learn how to calculate the original value before a percentage increase or decrease. Covers the reverse percentage formula with worked examples in prices, discounts, and taxes.
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What Is Reverse Percentage?
Reverse percentage (also called "working backwards from a percentage") finds the original value when you know the final value and the percentage change that was applied.
The common mistake: If something costs $130 after a 30% increase, many people think the original was $130 − 30% = $91. That's wrong — 30% of $91 is $27.30, not $39.
The correct approach uses the reverse percentage formula.
Reverse Percentage Formulas
After a percentage increase: Original = Final Value ÷ (1 + Percentage/100)
After a percentage decrease: Original = Final Value ÷ (1 − Percentage/100)
Worked Examples
Example 1: Price after increase A jacket costs $130 after a 30% price increase. What was the original price? - Original = $130 ÷ (1 + 0.30) = $130 ÷ 1.30 = $100 - Check: $100 + 30% of $100 = $100 + $30 = $130 ✓
Example 2: Sale price after discount A TV costs $850 after a 15% discount. What was the original price? - Original = $850 ÷ (1 − 0.15) = $850 ÷ 0.85 = $1,000 - Check: $1,000 − 15% of $1,000 = $1,000 − $150 = $850 ✓
Example 3: Removing VAT (UK) A price including 20% VAT is £240. What is the pre-VAT price? - Original = £240 ÷ 1.20 = £200 - Check: £200 + 20% × £200 = £200 + £40 = £240 ✓
Example 4: Salary after raise Your salary is now $76,000 after a 7.5% raise. What was your previous salary? - Original = $76,000 ÷ 1.075 = $70,698 - Check: $70,698 × 1.075 = $76,000 ✓
Why the Simple Subtraction Method Fails
If you try to find the "original" price by just subtracting the percentage from the final value: - "The price is $130 after a 30% increase, so original = $130 × (1 − 0.30) = $91" - Error: $91 + 30% of $91 = $91 + $27.30 = $118.30 ≠ $130
The 30% was applied to the original, not the final value. Removing it requires dividing by the multiplier, not multiplying by its complement.
The Multiplier Approach
Every percentage change has a multiplier: - 20% increase → multiplier = 1.20 - 15% decrease → multiplier = 0.85 - 7.5% increase → multiplier = 1.075
Final = Original × Multiplier Original = Final ÷ Multiplier
This is the most reliable way to think about percentage changes in either direction.
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Frequently Asked Questions
- How do I find the original price before a percentage increase?
- Divide the final price by (1 + percentage/100). If a $150 item was sold after a 25% markup: Original = $150 ÷ 1.25 = $120. Never subtract the percentage from the final price — that gives the wrong answer because the percentage was applied to the original, not the final.
- How do I remove VAT from a price?
- Divide the VAT-inclusive price by (1 + VAT rate). For UK 20% VAT: Pre-VAT price = Total ÷ 1.20. For £360 including 20% VAT: £360 ÷ 1.20 = £300 pre-VAT price. This works for any tax rate — just replace 0.20 with the decimal form of your rate.
- What is the original price if the sale price is $75 after a 40% discount?
- Original = $75 ÷ (1 − 0.40) = $75 ÷ 0.60 = $125. Check: $125 × 0.40 = $50 discount; $125 − $50 = $75 ✓. The original price was $125.
- Can I use reverse percentage to find original salary?
- Yes — if you know your current salary and the raise percentage, divide current salary by (1 + raise%). If your salary is $85,000 after a 6% raise: Original = $85,000 ÷ 1.06 = $80,189. Your previous salary was approximately $80,189.
Last updated 7/28/2026