Math

Reverse Percentage Calculator (Find the Original Value)

Enter the final amount and the percentage that was added or taken off.

By TheCalcTools Updated Formula checked and tested

Your numbers

%

Your results

Original amount
Original amount
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Amount of the change
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Check
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Reverse Percentage Calculator (Find the Original Value) by TheCalcTools

How the Reverse Percentage Calculator (Find the Original Value) works

A percentage change multiplies the original: after a 15% increase the final is 1.15 × original. To reverse it, divide by 1.15, not take 15% off the final.

For a discount of p%, the final is (1 − p/100) × original, so original = final ÷ (1 − p/100).

The formula

Original = final ÷ (1 ± p/100)

Worked example

Using the default values shown in the calculator:

Final amount (after the change)115
Percentage15 %
The percentage wasAdded (increase, tax, markup)
  1. 115 after a 15% increase: the original was 100.0000.
  2. 100 × 1.15 = 115.

Result:

Original amount100.0000
Amount of the change15.0000
Check100 × 1.15 = 115

Frequently asked questions

Why is taking 15% off 115 wrong?

15% of 115 is 17.25, giving 97.75, but 15% of the original 100 is only 15. The percentage applies to the original, not the final.

Sources and further reading

Percentage CalculatorChoose the question you want answered, enter two numbers, and get the percentage result… Percentage Change CalculatorFind the percentage change from an old value to a new value VAT CalculatorQuick VAT in either direction for invoices and quotes Discount CalculatorEnter a price and a percentage off to see what you pay Percent Error CalculatorEnter the measured value and the accepted value Percentage Difference CalculatorCompare two values when neither is the 'original'

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