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Percentages

Reverse Percentage Calculator

Work backwards from a percentage result to find the original value. Use this for finding the pre-discount price, the pre-VAT amount, or the original figure before any percentage increase or decrease was applied.

Reverse percentage calculator

The value you already know — e.g. the sale price, or the amount after tax.

is
%

The percentage applied to get the result. For a 20% discount, enter 80. For 20% VAT, enter 120.

of what?
Related Calculators
Percentage of a Number → Percentage Increase / Decrease → All 3 Types Together →

Step by step calculations

Enter values in the calculator to see the step by step calculations.

Reverse Percentage Calculator Explained

Core concepts, classroom applications, and plain-English explanations for all audiences.

When do you actually need this?

A coat is tagged £68 in a sale — 20% off. What did it cost before the sale? You can't just add 20% back, because 20% of £68 is different from 20% of the original price. Reverse percentage is the tool for finding that original figure.

Worked example

"A jacket costs £68 after a 15% discount. What was the original price?"

Sale price = 85% of original

£68 ÷ 0.85 = £80.00

Check: £80 × 0.85 = £68 ✓

The multiplier is always (100 − discount%) ÷ 100. Divide by it — never subtract the percentage.

Common mistake to avoid

  • ✗ Adding the percentage back: £68 + 20% = £81.60 — this is wrong because 20% of £68 ≠ 20% of the original.
  • → Correct method: divide by the multiplier. £68 ÷ 0.80 = £85.

VAT shortcut

To remove 20% VAT from an inclusive price: divide by 1.20. A £120 price inclusive of VAT → £120 ÷ 1.20 = £100 ex-VAT.

Good to know

How reverse percentages work

←
The key idea: divide, don't subtract
The most common mistake when working backwards is to simply add or subtract the percentage — but this gives the wrong answer. If something costs £80 after a 20% discount, the original is not £80 + 20% = £96. You must divide: £80 ÷ 0.80 = £100. The percentage tells you what fraction of the original you have, so you divide by that fraction.
After 20% discount, price = £80
£80 is 80% of original

Wrong: £80 + 20% = £96 ✗
Right: £80 ÷ 0.80 = £100 ✓

Check: £100 × 0.80 = £80 ✓
VAT
Real-world uses
Reverse percentages are essential for: finding a pre-VAT price from a VAT-inclusive total (divide by 1.20 for 20% VAT), finding an original price before a sale discount, calculating what a figure was before an interest rate was applied, or finding an original exam mark when you only know the percentage. In finance and accounting this is called "reversing out" a percentage.
Price inc. 20% VAT = £120
Original = £120 ÷ 1.20 = £100

Sale price after 35% off = £52
65% of original = £52
Original = £52 ÷ 0.65 = £80