VAT arithmetic has one direction that is obvious and one that is not. Adding 20% to a net price is easy. Getting the net price back out of a gross one is where invoices, expense claims and quotes go wrong, because the intuitive move, taking 20% off, gives the wrong answer every time.
Adding VAT: multiply by 1.2
If a net price is £100, the VAT is £20 and the gross is £120. Multiply the net by 1.20 and you are done. At the reduced 5% rate, multiply by 1.05: £100 net becomes £105. Our VAT calculator does both and shows the three lines separately, which is what an invoice needs.
Removing VAT: divide by 1.2
Here is the trap. A gross price of £120 includes 20% VAT. Taking 20% off £120 gives £96, which is wrong: the net price was £100. The 20% was charged on the net, not the gross, so it is a smaller share of the gross. Divide instead: £120 / 1.2 = £100, and the VAT is the difference, £20.
The shortcut people reach for, "VAT is a sixth of the gross", is correct at 20% and only at 20%. At 5% the VAT is 1/21 of the gross. Dividing by 1 plus the rate works at every rate, which is why the calculator uses it.
Worked examples
| Gross (inc. VAT) | Rate | Net | VAT |
|---|---|---|---|
| £120.00 | 20% | £100.00 | £20.00 |
| £99.99 | 20% | £83.33 | £16.66 |
| £300.00 | 20% | £250.00 | £50.00 |
| £105.00 | 5% | £100.00 | £5.00 |
The £99.99 row shows the rounding rule: the net is rounded to the penny first and the VAT is whatever remains, so the three figures always add up. If you round the VAT and the net independently you can end up a penny out, which is enough to make an accounts package reject the invoice.
When each direction comes up
Quotes from a VAT-registered trader are often given as a round gross figure. If you can reclaim VAT, the number that matters to you is the net, so divide by 1.2 before comparing with a non-registered trader's quote.
Expense claims usually want the VAT shown separately even though the receipt only prints a total. Divide by 1.2 for standard-rated items; check the receipt, because food, books and children's clothing are zero-rated and some energy is at 5%.
Pricing your own work goes the other way. Decide what you need to keep, then multiply by 1.2 to get the price you quote. If you quote £500 and then remember VAT, you either eat £83.33 or have an awkward conversation.
Which rate applies
The calculator lets you pick 20%, 5% or 0% because the rate is a classification question, not a maths one. Most goods and services are standard-rated. Domestic fuel, children's car seats and some energy-saving installations are at 5%. Most food, books, newspapers and children's clothes are zero-rated, which is different from exempt: zero-rated sales still count towards the registration threshold and still let the seller reclaim input VAT. If you are unsure which rate a specific item carries, HMRC's rate lists are the authority; the calculator will only ever do the arithmetic on the rate you give it.
The same forward-and-reverse logic drives our Canadian GST/HST calculator and the US sales tax calculator; only the rate and the label change.