PercentChangeFormula

Reverse Percentage Calculator

Work backwards from a final value to the number before a percentage was added or taken off.

Original = final ÷ (1 + % ÷ 100)  ·  Original = final ÷ (1 − % ÷ 100)
%
Original value: 75
  1. Multiplier = 1 + 20 ÷ 100 = 1.2
  2. Original = 90 ÷ 1.2 = 75
  3. Check: 75 × 1.2 = 90

How reverse percentages work

A percentage increase multiplies the original value by (1 + p ÷ 100); a decrease multiplies it by (1 − p ÷ 100). To undo it, divide by the same multiplier. Do not apply the percentage to the final value: it was calculated on the original.

Examples

SituationWorkingOriginal
Price after a 20% rise is 9090 ÷ 1.2075
Paid 60 after 25% off60 ÷ 0.7580
54 including 8% sales tax54 ÷ 1.0850
The common mistake: taking 20% off 90 gives 72. Check it: 72 × 1.2 = 86.40, not 90. The right answer, 75, checks out: 75 × 1.2 = 90.

Related

To find the percentage itself when you know both numbers, use the percent increase or percent decrease calculator.

Frequently asked questions

How do I find the original value before a percentage increase?

Divide the final value by (1 + percentage ÷ 100). If a price rose 20% to 90, the original was 90 ÷ 1.2 = 75.

How do I find the original price before a discount?

Divide the price you paid by (1 − discount ÷ 100). If you paid 60 after a 25% discount, the original price was 60 ÷ 0.75 = 80.

How do I remove tax from a price?

Divide the price including tax by (1 + tax rate ÷ 100). A total of 54 including 8% tax is 54 ÷ 1.08 = 50 before tax.

Why can't I just subtract the percentage?

Because the percentage was applied to the original value, not the final one. Taking 20% off 90 gives 72, but 72 increased by 20% is 86.40, not 90.