Reverse percentage: X is P% of what?
The third percentage direction: the original is unknown. Common UK use case — deducing the net price from a discounted total, or the pre-VAT price from gross.
Most calculators handle the first two percentage directions but skip the third. This is it. Defaults: 30 is 20% of 150. Type your own values; below are real UK use cases including reverse-VAT and 'what was it before the discount?'.
How it works. Original = part ÷ (percent ÷ 100). The same formula handles VAT-removal, pre-discount price, and 'what was the gross?' questions.
Worked examples
£30 is 20% of £150 — baseline example.
£480 is 80% of £600 — if a sale price is £480 and the discount was 20%, the original was £600.
£20 is 20% (VAT) of £100 net — given £20 of VAT charged, the net base was £100.
£18,000 is 60% of £30,000 — a £18k take-home keep-rate of 60% means the gross is £30k.
£30,000 is 4.5x rule of £6,667 — a £30k mortgage at 4.5× income means the borrower earns £6,667.
Sources:
HMRC VAT rates
· retrieved 2026-05-13.
Frequently asked questions
What is the reverse percentage formula?
Original = X ÷ (P ÷ 100). For 30 is 20% of what: 30 ÷ (20 ÷ 100) = 30 ÷ 0.2 = 150.
How do I remove VAT from a price?
If VAT is 20%, divide the gross price by 1.20 to get the net. £120 gross ÷ 1.20 = £100 net. The VAT amount is £20.
How is this different from percentage decrease?
Percentage decrease tells you how much something has fallen. Reverse percentage tells you the original whole given a known part and percentage. Different questions, different formulas.
Why does the reverse calc give a bigger number?
Because a percentage is by definition a part of a whole — the whole has to be at least as big as the part. If 30 is 20% of something, that something must be 150.