Reverse Percentage Calculator
Reverse percentage problems give you the amount after a change and ask for the amount before. The classic mistake is to take the percentage off the final value — this calculator shows why you divide instead.
Answer
70 + 20% = 84
Step by step
- After an increase of 20%, the value is 100% + 20% = 120% of the original.
- So 84 = 1.2 × original.
- Divide to undo it: 84 ÷ 1.2 = 70.
- Check: 70 × 1.2 = 84.
Answer: 70
Still stuck? Ask the tutor about these steps
How it works
final ÷ (1 + P ÷ 100)final ÷ (1 − P ÷ 100)Work out what percentage of the original you now have: after a 20% increase you have 120%; after a 20% decrease you have 80%.
Write that as a decimal multiplier (1.2 or 0.8) and divide the final amount by it.
Why not just subtract 20%? Because the 20% was 20% of the original, not of the final amount. 84 − 20% = 67.20, but 67.20 + 20% = 80.64, not 84.
Worked example
After a 20% price rise a ticket costs $84. What did it cost before?
- New price = 120% of old = 1.2 × old
- 84 ÷ 1.2 = 70
- The original price was $70.
Frequently asked questions
How do I reverse a percentage?
Divide the final amount by the multiplier that was applied: 1 + P/100 for an increase, 1 − P/100 for a decrease.
How do I find a price before tax?
Divide the price including tax by 1 plus the tax rate. With 8% tax on a $54 bill: 54 ÷ 1.08 = $50 before tax.