Reverse Percentage Calculator UK

A reverse percentage (sometimes called an inverse or backwards percentage) works a percentage problem in the opposite direction. Instead of applying a change to find a new value, you start with the final value and recover the original.

Typical situations: finding a price before VAT was added, the original price before a sale discount or last year's figure when you only know this year's and the growth rate. It is also a core GCSE maths topic on every UK exam board.

The Method: Divide by the Multiplier

Every reverse percentage problem is solved the same way. Work out what the final value represents as a decimal of the original, then divide by it:

Original = final value ÷ multiplier

• After a decrease: a coat costs £68 after 15% off. The £68 is 85% of the original, so the multiplier is 0.85. Original price: 68 ÷ 0.85 = £80.
• After an increase: a football match draws 728 fans, 12% more than last week. The 728 is 112% of last week, multiplier 1.12. Last week: 728 ÷ 1.12 = 650 fans.

The critical rule: never just take the percentage off the final figure. Deducting 15% from £68 gives £57.80, which is wrong, because the 15% was originally calculated on the larger starting price, not the final one.

Removing VAT: Most Common Reverse Percentage

UK VAT at the standard 20% rate is the reverse percentage most people meet in real life. A VAT-inclusive price is 120% of the net price, so:

Net price = gross price ÷ 1.2

A £150 invoice including VAT breaks down as 150 ÷ 1.2 = £125 net plus £25 VAT. For the 5% reduced rate, divide by 1.05. Businesses reclaim input VAT and sole traders checking supplier invoices use this daily, and subtracting 20% instead of dividing by 1.2 is the classic bookkeeping error, understating the net figure every time. Use our dedicated VAT Calculator UK to check these values.

The Non-Calculator Method

GCSE papers often set reverse percentages without a calculator, and the trick is working through 1% or a convenient factor.

If 45% of a number is 36, then 1% is 36 ÷ 45 = 0.8, so 100% is 80. Or use bigger blocks: if 30% of a bill is £21, then 10% is £7 and the full bill is £70. Choose whichever factor divides cleanly.

Reverse Percentage Quick Reference

A related trap worth knowing: to undo an increase of X%, the required decrease is smaller than X. A 20% rise is reversed by a 16.7% cut (20 ÷ 120), not a 20% one, because the base has changed.

If you need to find relative changes, use the Percentage Calculator UK or the Percentage Decrease Calculator UK.