Reverse Percentage Calculator
Undoing a percentage means dividing, not subtracting.
Undoing a percentage means dividing, not subtracting. Find the amount a percentage was applied to.
Original amount
100
Before the 20% was added
Reversing a percentage means dividing, not subtracting. To undo a 20% increase you divide by 1.2; subtracting 20% instead lands 4% low, because the two percentages are taken from different bases. The fourth row shows exactly that error, and it is not a curiosity. It is how VAT gets miscalculated on inclusive prices, how discounts on marked-up figures come out wrong, and why a 10% pay cut followed by a 10% rise leaves you worse off than you started. The larger the percentage, the larger the gap. At 50% the naive reverse is 25% adrift, which is a difference nobody can afford to hand-wave.
How the Reverse Percentage Calculator works
Find the amount a percentage was applied to. It also shows what happens if you subtract the percentage instead of dividing by it — the mistake that costs 4% on a 20% markup and rather more on larger figures.
Also known as: price before discount · price before vat · work backwards from a percentage · original amount before increase
Where to go next
The Reverse Percentage question rarely arrives on its own. These are the ones that usually come with it:
- Odds Converter — Decimal, fractional, American and the probability behind all three.
- Digital Root Calculator — Sum the digits until one is left. It is always n mod 9.
- Number Base Converter — Validates the digits instead of silently truncating them.
- Percentage Calculator — Every common percentage question in one place.
Frequently asked questions
How do I find the original price before a discount?
Divide by one minus the discount as a decimal. A price of £80 after 20% off came from £100, because 80 divided by 0.8 is 100 — not from £96, which is what subtracting 20% from £80 gives.
Why doesn't adding 20% then subtracting 20% return the original?
Because the two percentages are taken from different bases. The 20% added is 20% of the original; the 20% subtracted is 20% of the larger figure. You land 4% below where you started.
How do I find the price before VAT?
Divide the inclusive price by one plus the VAT rate. At 20% VAT, divide by 1.2 — a £120 inclusive price is £100 plus £20 VAT. Taking 20% off £120 gives £96 and is wrong.
Does the error get worse with bigger percentages?
Substantially. At 20% the naive reverse is 4% adrift; at 50% it is 25% adrift. The gap grows with the square of the percentage, which is why the shortcut passes unnoticed on small figures and fails badly on large ones.
Is a 10% pay cut then a 10% rise break-even?
No. You end up 1% down. The cut is 10% of your original salary and the rise is 10% of the reduced one, so the rise is worth less in absolute terms than the cut took.
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