To reverse a percentage, divide the final value by the multiplier that produced it. If a price after a 20% discount is 120, the multiplier was 1 − 0.20 = 0.8, so the original was 120 ÷ 0.8 = 150. After a 20% increase, divide by 1.2 instead.
Formula
original = final ÷ (1 ± % ÷ 100) Step by step
- Write the percentage as a multiplier: +20% is 1.2, −20% is 0.8.
- Divide the final value by the multiplier.
- Check: the original times the multiplier gives the final value back.
Examples
- A price including 20% tax is 96. Before tax: 96 ÷ 1.2 = 80 (the tax was 16).
- A jacket costs 63 after 30% off. Original price: 63 ÷ 0.7 = 90.
- A town has 13,200 people after growing 10%. Before: 13,200 ÷ 1.1 = 12,000.
Common mistakes
- Taking the percentage of the final value. 20% of 120 is 24, and 120 + 24 = 144, not the original 150.
- Subtracting the percentage after an increase: 180 − 20% = 144, not 150.
In Excel and Google Sheets
- Final value in A2, % in B2, after an increase
=A2/(1+B2) - After a decrease
=A2/(1-B2)
FAQ
How do I remove tax from a price?
Divide the price by 1 plus the tax rate. With a 20% rate: 96 ÷ 1.2 = 80, so the tax was 16.
How do I find the original price before a discount?
Divide the sale price by 1 minus the discount: 63 ÷ 0.7 = 90 for 30% off.
Why can’t I just take the percentage of the final value?
Because the percentage was applied to the original value, not the final one. The two bases are different.
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Updated October 2026