PercentSwift

Reverse percentage calculator

Enter the value after the change, choose whether it went up or down, and enter the percentage. The calculator divides by the right multiplier and checks the answer for you.

Find the original value before a percentage change

Settings
The change was
%

Original value

120

138 after a 15% increase means the original value was 120.

Change in units
+18
Multiplier that was applied
× 1.15

Formula

Original = Final ÷ (1 + Percentage ÷ 100)

Steps

  1. Write the change as a multiplier: 1 + 15 ÷ 100 = 1.15
  2. Divide the final value by it: 138 ÷ 1.15 = 120
  3. Check: 120 × 1.15 = 138
  • Don't subtract the percentage from the final value: that uses the wrong base and gives a different answer.

Exact decimal arithmetic, calculated in your browser.

Examples

Each one loads into the calculator above.

Why you can’t just subtract the percentage

Suppose a price went up 15% to $138. Taking 15% off $138 gives $117.30, but the real original price was $120. The 15% was calculated on $120, and 15% of $138 is a larger amount, so subtracting it removes too much.

The method

Turn the change into a multiplier: 1 + the percentage for an increase, 1 − the percentage for a decrease. Then divide the final value by it.

  • After a 15% increase: 138 ÷ 1.15 = 120
  • After a 30% decrease: 63 ÷ 0.70 = 90
  • After a 4% raise: 54,080 ÷ 1.04 = 52,000

Then check by multiplying: 120 × 1.15 = 138.

Common uses

You can use it to find a price before sales tax or VAT from a receipt total, the original price of a sale item, a salary before a raise, or last year’s figure from this year’s figure and its growth rate. For tax specifically, the tax calculator and the VAT calculator also show the tax amount and handle rounding to cents.

Limits

A decrease of 100% leaves zero, and every starting value gives zero after a 100% cut, so there’s no way back. The calculator refuses decreases of 100% or more and explains why.

The second tab answers a related but different question: if 18 is 40% of a total, what is the total? There’s no before-and-after change there, just a part and its share of a whole.

Questions people ask

Guides that use this calculator