How do I find the original price before a discount?

Divide the price you paid by one minus the discount as a decimal. At 30% off, divide by 0.7; at 25% off, divide by 0.75. Never add the percentage back on — that answers a different question and always lands short.

How do I remove VAT or sales tax from a price?

Same arithmetic in the other direction: divide by one *plus* the rate. A £120 price including 20% VAT is £100 before tax. The sales tax page does this alongside adding tax on.

Why do the two answers differ so much?

Because a percentage is always a percentage *of something*, and the two questions start from different somethings. If 84 is after a 30% cut, the original was 120. If 84 is after a 30% rise, the original was 64.62. Same 84, same 30%, two different questions.

Math

Reverse Percentage Calculator

You have the number after the change. This finds the one before it.

The formula

before a decrease = number ÷ (1 − percent ÷ 100)

before an increase = number ÷ (1 + percent ÷ 100)

Worked example

A jacket costs $84 in a 30% off sale

84 ÷ (1 − 0.30) = 84 ÷ 0.70 = $120 before the sale
Adding 30% back to 84 would give $109.20 — nearly $11 short

Where this goes wrong

Adding the percentage back on to undo taking it off

A 30% reduction is not undone by a 30% increase, because the two percentages are of different numbers. $120 reduced by 30% is $84; $84 increased by 30% is $109.20, not $120. You have to divide by 0.70, not multiply by 1.30. The larger the percentage the worse it gets: at 50% off, adding half back recovers only three quarters of the original.

Questions

How do I find the original price before a discount?: Divide the price you paid by one minus the discount as a decimal. At 30% off, divide by 0.7; at 25% off, divide by 0.75. Never add the percentage back on — that answers a different question and always lands short.
How do I remove VAT or sales tax from a price?: Same arithmetic in the other direction: divide by one *plus* the rate. A £120 price including 20% VAT is £100 before tax. The sales tax page does this alongside adding tax on.
Why do the two answers differ so much?: Because a percentage is always a percentage *of something*, and the two questions start from different somethings. If 84 is after a 30% cut, the original was 120. If 84 is after a 30% rise, the original was 64.62. Same 84, same 30%, two different questions.