Reverse Percentage Calculator
Find the original value before a percentage increase or decrease. Enter the final amount and the percentage change to calculate what the starting value was.
Find Original from Percentage Amount
If you know that a certain amount represents a specific percentage of something, find the original (100%) value. For example: “45 is 15% of what number?”
Remove VAT / Sales Tax
Calculate the price before VAT or sales tax was added. Common rates: UK VAT 20%, US varies by state.
Reverse percentage calculations help you work backwards to find an original value before a percentage change. Whether you need to find the price before a discount, calculate the pre-VAT cost, or determine what number a percentage came from, these calculators show you the answer with step-by-step working.
For standard percentage calculations, visit our percentage calculator. To find percentage increase or decrease, use the percentage increase calculator or percentage decrease calculator.
What is a Reverse Percentage?
A reverse percentage (also called inverse percentage) means working backwards from a result to find the original value. Instead of calculating “what is 20% of 100?” you are solving “if this is 120 after a 20% increase, what was the original?”
This is useful whenever you know the end result but need to find the starting point:
- Finding the original price before a sale discount
- Calculating the pre-VAT or pre-tax price
- Determining an original salary before a raise
- Working out the starting amount before interest was added
- Finding what number a percentage came from
Reverse Percentage Formulas
After a Percentage Increase
If a value increased by a percentage to reach the final amount:
The original price was $100
After a Percentage Decrease
If a value decreased by a percentage to reach the final amount:
The original price was $100
Finding Original from a Percentage Amount
If you know that a certain amount equals a specific percentage of the original:
45 is 15% of 300
Common Mistake to Avoid
A common error is to calculate 20% of $120 and subtract it. This gives $120 – $24 = $96, which is WRONG. The original was $100, not $96. The percentage must be calculated from the original, not the final value.
This mistake happens because people forget that the percentage was calculated on a different base. When you add 20% to $100, you get $120. But 20% of $120 is $24, not $20. The base changed, so you cannot simply reverse the operation.
Step-by-Step Method (Without Calculator)
If you need to solve reverse percentages mentally or on paper:
Method 1: The Division Method
- Determine the percentage the final value represents (100% + increase, or 100% – decrease)
- Divide the final value by this percentage to find 1%
- Multiply by 100 to find the original (100%)
Step 1: 230 represents 100% + 15% = 115%
Step 2: 1% = 230 / 115 = 2
Step 3: 100% = 2 x 100 = 200
The original value was 200
Method 2: The Decimal Multiplier
- Convert the percentage to a decimal multiplier (1.15 for 15% increase, 0.85 for 15% decrease)
- Divide the final value by this multiplier
Step 1: Multiplier = 1 – 0.25 = 0.75
Step 2: Original = 150 / 0.75 = 200
The original value was 200
Reverse Percentage Examples
Example 1: Sale Price to Original Price
Original price: $80. The discount saved $12.
Example 2: Remove VAT from Price
Price before VAT: $500. VAT amount: $100.
Example 3: Salary Before Raise
Previous salary: $50,000. Raise amount: $2,500.
Example 4: Finding Original from Part
Maximum score: 80 marks
Example 5: Property Value After Drop
Original value: $400,000. Lost value: $60,000.
Example 6: Restaurant Bill with Service Charge
Food cost: $60. Service charge: $6.
Quick Reference: Common Reverse Calculations
| % Change | Divide By | If Final is 100 |
|---|---|---|
| +5% (increase) | 1.05 | Original = 95.24 |
| +10% (increase) | 1.10 | Original = 90.91 |
| +15% (increase) | 1.15 | Original = 86.96 |
| +20% (VAT) | 1.20 | Original = 83.33 |
| +25% (increase) | 1.25 | Original = 80.00 |
| -10% (discount) | 0.90 | Original = 111.11 |
| -15% (discount) | 0.85 | Original = 117.65 |
| -20% (discount) | 0.80 | Original = 125.00 |
| -25% (discount) | 0.75 | Original = 133.33 |
| -50% (half price) | 0.50 | Original = 200.00 |
When to Use Reverse Percentages
| Scenario | What You Know | What You Find |
|---|---|---|
| Sale shopping | Sale price + discount % | Original price |
| VAT/Tax removal | Price inc. tax + tax rate | Pre-tax price |
| Salary history | Current salary + raise % | Previous salary |
| Investment value | Current value + gain/loss % | Original investment |
| Test scores | Marks earned + percentage | Total marks available |
| Population change | Current population + growth % | Previous population |
For 20% VAT: divide by 1.2 (or multiply by 5 and divide by 6). For 10% change: divide by 1.1 or 0.9. For 25% discount: the original was 4/3 of the sale price.
Frequently Asked Questions
A reverse percentage is when you work backwards from a final value to find the original value before a percentage change was applied. Instead of finding “what is 20% of 100” you are solving “what was the value before a 20% increase made it 120?”
Divide the sale price by (1 – discount/100). For a 30% discount with sale price of $70: Original = $70 / (1 – 0.30) = $70 / 0.70 = $100.
Divide the VAT-inclusive price by (1 + VAT rate/100). For UK 20% VAT on a $120 item: Pre-VAT = $120 / 1.20 = $100. The VAT amount is $20.
Because the percentage was calculated on the original value, not the final value. 20% of $100 is $20, but 20% of $120 is $24. Subtracting 20% of $120 gives the wrong answer because the base has changed.
Use the formula: Original = (Part / Percentage) x 100. If 45 is 15% of something: (45 / 15) x 100 = 300. So 45 is 15% of 300.
Divide your current salary by (1 + raise percentage/100). If you now earn $55,000 after a 10% raise: Previous = $55,000 / 1.10 = $50,000.
Divide by 1.5. If something is now 150 after a 50% increase, the original was 150 / 1.5 = 100. Note: a 50% increase requires only a 33.3% decrease to return to the original.
For multiple percentage changes, apply each reverse calculation in reverse order. If something increased 10% then 20%, first divide by 1.20, then divide by 1.10. The order matters!
Related Calculators
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