Reverse Percentage Calculator
Find the original value before a percentage increase or decrease was applied. This is the reverse percentage method — essential for GCSE and A-level maths. Full step-by-step working shown.
Original value
100
How it works
Identify the multiplier for a 20% increase
A 20% increase uses the multiplier 1.2. The new value is the original multiplied by 1.2.
Result:1.2Divide the result by the multiplier
To reverse the percentage, divide the known result by the multiplier: 120 ÷ 1.2 = 100.
Result:100Verify
Check: 100 × 1.2 = 120. ✓
Result:120
The formula
Example substitution
If 120 is the result after a 20% increase, divide by 1.2 to find the original: 100.
Worked examples
After a 20% increase, a price is £120. What was the original price?
- 1Multiplier: 1 + 20/100 = 1.2
- 2Divide: 120 ÷ 1.2 = 100
After a 15% decrease, a value is 85. Find the original value.
- 1Multiplier: 1 − 15/100 = 0.85
- 2Divide: 85 ÷ 0.85 = 100
A price including 20% VAT is £180. What is the pre-VAT price?
- 1Multiplier: 1.2 (VAT added)
- 2Divide: 180 ÷ 1.2 = 150
Frequently asked questions
How do you find the original value after a percentage increase?+
Divide the new value by (1 + percentage/100). E.g., after a 20% increase the price is £120: original = 120 / 1.20 = £100.
How do you find the original value after a percentage decrease?+
Divide the new value by (1 − percentage/100). E.g., after 15% off the price is £85: original = 85 / 0.85 = £100.
Why do students get reverse percentages wrong?+
The common mistake is subtracting or adding the percentage directly. You must divide by the multiplier, not work backwards by adding/subtracting the percentage of the new value.
What is an example of a reverse percentage question?+
A jacket costs £68 after a 15% reduction. What was the original price? Answer: 68 / 0.85 = £80.