To add VAT, multiply the net by one plus the rate: 100 at 21 per cent becomes 121. To remove it, divide the gross by the same figure: 242 ÷ 1.21 is 200 net with 42 of VAT. Subtracting 21 per cent from 242 gives 191.18, which is wrong by 8.82 — because it removes tax on the tax.
Twenty-one per cent of 200 is 42. Twenty-one per cent of 242 is 50.82. The percentage was applied to the smaller number, so the reverse operation cannot be a subtraction from the larger one.
What are the multipliers and fractions?
One multiplier to add, one divisor to remove, and a VAT fraction that gives the tax directly from the gross.
| Rate | Add: × | Remove: ÷ | VAT fraction of gross |
|---|---|---|---|
| 5% | 1.05 | 1.05 | 1/21 |
| 19% | 1.19 | 1.19 | 19/119 |
| 20% | 1.20 | 1.20 | 1/6 |
| 21% | 1.21 | 1.21 | 21/121 |
| 23% | 1.23 | 1.23 | 23/123 |
| 25% | 1.25 | 1.25 | 1/5 |
The 20 per cent fraction of one sixth is the one worth memorising, because a great many invoices are at that rate and dividing by six is something anyone can do in their head. A 120 gross contains 20 of VAT.
Why does the mistake matter more than it looks?
Because it is systematic rather than random. Every line of an expense claim reconstructed by subtraction understates the net and overstates the reclaim in the same direction, so the errors add up instead of cancelling.
On a 21 per cent rate the subtraction method understates the net by 3.6 per cent of the gross on every line. Across a quarter of expenses that is a reconciliation that never balances and nobody can find.
Which price should be displayed?
The inclusive one, prominently, for consumers — that is a legal requirement across most of Europe rather than a convention. Business-to-business pricing is normally quoted excluding VAT, because the buyer reclaims it and the net figure is the real cost to them.
Rounding to a nice inclusive figure is where the net quietly changes. Deciding to display 59.95 rather than 59.90 lifts the net from 49.50 to 49.55 — trivial per unit, and it means the price list and the accounting figure disagree unless one of them is updated.
What does this do to a margin calculation?
It is the most common place a margin goes wrong. Margin has to use ex-VAT figures on both sides, and comparing a VAT-inclusive selling price against an ex-VAT cost inflates the apparent margin by the whole VAT rate.
A 59.90 shelf price at 21 per cent is 49.50 net. Against a 40 cost, the real margin is 19.2 per cent; against the same cost using the inclusive price it looks like 33.2 per cent. That gap has bankrupted businesses that thought they were profitable.
The rule is simple to state and easy to forget under pressure: strip VAT from both sides before any margin arithmetic, and never mix an inclusive figure with an exclusive one in the same sum. The markup and margin article covers what happens after that.
What about a mixed-rate invoice?
Each rate is calculated separately and the tax lines are shown separately, because the invoice has to state the taxable amount per rate and the VAT charged on each. There is no blended rate that produces the right answer on a mixed invoice.
That is why splitting a line item is sometimes necessary rather than pedantic. A delivered order of books at a reduced rate and stationery at the standard rate is two taxable amounts, and combining them into one line makes the invoice non-compliant as well as arithmetically wrong.
Which rate applies?
The one for what is being sold and where the customer is, not where you are. Selling digital services to consumers in another EU country means charging that country’s rate, which is what the One Stop Shop scheme exists to administer.
Rates also vary by product within a country. Reduced and zero rates apply to specific categories — food, books, children’s clothing and others, differently in each member state — and getting the category wrong is a more expensive error than getting the arithmetic wrong.
Questions people ask
Why can I not just subtract the percentage? Because the percentage was calculated on the net, and the gross is bigger. Subtracting from the gross removes a larger amount than was ever added.
What is the VAT fraction? The share of the gross that is tax. At 20 per cent it is one sixth, so 120 gross contains 20 of VAT and 100 of net — a single multiplication with no division needed.
Should I show prices with or without VAT? With, for consumers, as a legal requirement in most of Europe. Without, for business buyers, because they reclaim it.
Does the reverse charge change this? Yes — on cross-border business supplies the supplier charges no VAT and the customer accounts for it. The invoice must say so, and the arithmetic on it becomes a net figure with no tax line at all.
Is the flat-rate scheme different? Materially. A flat-rate business charges VAT normally and pays a fixed percentage of gross turnover to the authority instead of the difference between input and output tax, so its own arithmetic is a percentage of the gross rather than a fraction of it.
Multiply to add, divide to remove, and strip both sides before any margin. The VAT calculator works in both directions, the reverse VAT calculator starts from a gross figure, the VAT-inclusive and VAT-exclusive price calculators handle the display and accounting sides, and the sales tax calculator applies exactly the same arithmetic to a US combined rate.