How do I find the original price before a discount?

Divide by 1 minus the discount as a decimal. If 30% off gave you 700, the original was 700/0.7 = 1,000. Adding 30% back to 700 gives 910, which is the mistake this page exists to prevent.

How do I remove tax from a total?

Divide by 1 plus the tax rate. A total of 118 including 18% tax has a base of 118/1.18 = 100, so the tax is 18. Taking 18% off 118 gives 96.76 and understates the base.

Math & Statisticspercentage

Reverse Percentage Calculator

Work backwards from a value that has already had a percentage applied. Division, not subtraction. Taking 12% off 1120 gives 985.60, but the original was 1000.

Also called: work out original price before discount, reverse percent.

Original value

1,000

Before the 12% increase, the value was 1,000. Subtracting 12% from 1,120 would have given 985.6, which is the common mistake.

What subtracting instead would give

985.6

How far wrong that is

14.4

How this is calculated

Method and background

How this is calculated

If a value was multiplied by (1 + p), recovering it means dividing by (1 + p), not subtracting p. The two differ by p² of the original, which is why the error grows with the percentage: at 12% the mistake is 1.4%, at 50% it is 25%.

original = final / (1 + percent/100) for an increase

V_2: The final value

Worked examples

Each of these is asserted on every build. If a change to the engine ever moved one of these answers, the build would fail before the page could print it.

1120 after a 12% increase was 1000

Final value: 1,120
Percentage that was applied: 12
It was: An increase

Original value1,000

arithmetic identity: 1120/1.12

Open this example

880 after a 12% decrease was 1000

Final value: 880
Percentage that was applied: 12
It was: A decrease

Original value1,000

arithmetic identity: 880/0.88

Open this example

a 100% decrease cannot be reversed

Final value: 0
Percentage that was applied: 100
It was: A decrease

Original value0

degenerate case: dividing by zero is guarded

Open this example

Frequently asked questions

How do I find the original price before a discount?: Divide by 1 minus the discount as a decimal. If 30% off gave you 700, the original was 700/0.7 = 1,000. Adding 30% back to 700 gives 910, which is the mistake this page exists to prevent.
How do I remove tax from a total?: Divide by 1 plus the tax rate. A total of 118 including 18% tax has a base of 118/1.18 = 100, so the tax is 18. Taking 18% off 118 gives 96.76 and understates the base.