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 link carries your figures, so it reopens on exactly these numbers.

Why adding the percentage back never works

Your number, undone at different rates. The last column is what you would be out by if you simply added the percentage back on instead of dividing — it grows with the square of the rate, which is why the mistake survives at small percentages.

Percentage	Before a decrease	Amount taken off	Error if you just add the percentage back
10%The naive method is out by about 1%.	93.33	9.33	0.93
20%	105	21	4.2
30%	120	36	10.8
40%Now out by 16% — impossible to miss on an invoice.	140	56	22.4
50%Halving is undone by doubling, never by adding 50%.	168	84	42

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.