Adding and removing VAT correctly
Why extracting VAT from a gross price is a division, how the rates differ across Europe, and what registration actually obliges you to do.
Last reviewed · 1,340 words
In short
- Removing VAT is a division, not a subtraction. A £120 gross price at 20% contains £20 of VAT, not £24.
- The UK standard rate is 20%; Ireland is 23%, Germany 19%, and Sweden and Denmark 25%.
- A registered business reclaims the VAT it pays, so VAT is a cost only to the final consumer.
- Zero-rated and exempt look the same on an invoice and are not the same. Zero-rated allows input VAT to be reclaimed; exempt does not.
- The UK registration threshold is £90,000 of taxable turnover in any rolling twelve months, not a financial year.
Value added tax is charged at each stage of production on the value added at that stage, with businesses reclaiming what they paid and the final consumer bearing the whole amount. The arithmetic has one genuinely counterintuitive step.
Adding VAT
Multiply the net amount by the rate and add it.
At 20% on £100: 100 × 0.20 = £20, so the gross price is £120.
Removing VAT — a division
Given a gross price that already includes VAT, the net is the gross divided by one plus the rate.
net = gross ÷ (1 + rate)
At 20% on £120: 120 ÷ 1.20 = £100, so the VAT is £20.
The instinct is to take 20% off £120, giving £24 of VAT and a net of £96. That is wrong by £4 on a single invoice, and it is wrong in the same direction every time.
The reason is that the 20% was charged on £100, not on £120. Reversing a percentage means finding the base, not applying the same percentage to a larger number.
Useful shortcuts: at 20%, the VAT in a gross price is the gross divided by 6. At 5%, divide by 21. At 23%, divide by 5.35.
The error grows with the rate:
| Rate | Gross | Correct VAT | Naive subtraction | Overstated by |
|---|---|---|---|---|
| 5% | £105 | £5.00 | £5.25 | £0.25 |
| 19% | £119 | £19.00 | £22.61 | £3.61 |
| 20% | £120 | £20.00 | £24.00 | £4.00 |
| 23% | £123 | £23.00 | £28.29 | £5.29 |
| 25% | £125 | £25.00 | £31.25 | £6.25 |
Rates across Europe and beyond
| Country | Standard | Reduced rates |
|---|---|---|
| Switzerland | 8.1% | 3.8%, 2.6% |
| Germany | 19% | 7% |
| United Kingdom | 20% | 5%, 0% |
| France | 20% | 10%, 5.5%, 2.1% |
| Spain | 21% | 10%, 4% |
| Netherlands | 21% | 9% |
| Belgium | 21% | 12%, 6% |
| Italy | 22% | 10%, 5%, 4% |
| Ireland | 23% | 13.5%, 9%, 4.8%, 0% |
| Poland | 23% | 8%, 5% |
| Sweden | 25% | 12%, 6% |
| Denmark | 25% | — |
| Norway | 25% | 15%, 12% |
Outside Europe the equivalent taxes are lower and usually called GST: Australia 10%, New Zealand 15%, Singapore 9%, the UAE 5%, and Canada 5% federally with provincial taxes on top.
EU rules require a standard rate of at least 15% and permit up to two reduced rates of at least 5%, with historical exceptions — France's 2.1% and Ireland's 4.8% among them.
Denmark is notable for having no reduced rate at all, which makes its system unusually simple and its food unusually expensive.
Zero-rated against exempt
Both show no VAT on the invoice and they are not the same thing.
Zero-rated supplies are taxable at 0%. The business charges no VAT and can reclaim the VAT on its own purchases. In the UK this covers most food, children's clothing, books, newspapers and public transport.
Exempt supplies are outside the VAT system. No VAT is charged and input VAT cannot be reclaimed. This covers insurance, most finance, postage, education and health services.
The difference is money. A zero-rated business — a bookshop, a bakery — reclaims VAT on rent, equipment and utilities while charging none, and frequently receives a refund from HMRC every quarter. An exempt business absorbs that VAT as a cost.
A business making both taxable and exempt supplies is partially exempt and can only reclaim the proportion of input VAT relating to its taxable activity, which is one of the more troublesome calculations in UK accounting.
Registration
In the UK, registration is compulsory once taxable turnover exceeds £90,000 in any rolling twelve-month period — not a financial year, which catches out businesses that check only at the year end. It is also compulsory if you expect to cross it in the next thirty days alone.
Voluntary registration below the threshold is often worth it. If your customers are VAT-registered businesses, the VAT costs them nothing because they reclaim it, while you gain the ability to reclaim your own. If you sell to consumers, registration adds 20% to your price with no offsetting benefit to them — which is why many small consumer-facing businesses deliberately stay below the threshold.
That bunching below £90,000 is a well-documented effect, and it is the clearest evidence that the threshold changes behaviour rather than merely measuring it.
Two simplification schemes exist for small businesses. The flat rate scheme, available under £150,000 of turnover, charges a fixed percentage of gross turnover instead of tracking every transaction, at the cost of losing most input VAT reclaims. Cash accounting, under £1.35 million, accounts for VAT when money moves rather than when invoices are issued, which helps businesses paid slowly.
Cross-border, briefly
Business to business within the EU uses the reverse charge: the seller invoices without VAT and the buyer accounts for it in their own country, reclaiming it at the same time.
Business to consumer is taxed where the customer is, for digital services always and for goods above the €10,000 distance-selling threshold. The One Stop Shop lets a seller file for all EU countries through a single registration.
UK to EU since 2021 is an import and an export. Goods entering the EU attract import VAT and any duty in the destination country, which is what produced the unexpected charges on parcels that followed Brexit.
Invoice requirements
A valid VAT invoice needs a unique sequential number, the supplier's name, address and VAT number, the customer's name and address, the supply date, a description, the net amount, the rate applied and the VAT amount.
Two habits prevent most problems. Round the total rather than every line, or the invoice will not reconcile with the return. And keep the purchase invoices, because input VAT cannot be reclaimed without them — a bank statement is not evidence of a VAT-bearing supply.
UK returns are quarterly and filed under Making Tax Digital, which requires compatible software and a digital link from the records to the return.
Common VAT mistakes
Subtracting the rate from a gross figure. The single most frequent error, and it overstates the VAT every time.
Reclaiming VAT with no valid invoice. A card statement, an order confirmation or a delivery note is not a VAT invoice. Without the supplier's VAT number and a stated VAT amount, the input tax is not reclaimable.
Reclaiming on things you cannot. Business entertainment and most cars are blocked outright, whatever they were used for. Fuel for mixed private and business use needs either detailed mileage records or the fuel scale charge.
Rounding each line. Round the invoice total, not every line, or the totals will not tie to the return.
Missing the rolling-twelve-month test. Turnover is checked continuously, not at the year end, and registration is backdated to the date the threshold was crossed — with the VAT owed on sales already made without it.
Treating exempt as zero-rated. They look identical on paper and differ entirely in whether input VAT is recoverable.
Why VAT is built this way
The design has a purpose that is worth understanding, because it explains most of the rules.
Under a simple sales tax charged at every stage, tax is charged on tax: the manufacturer's tax becomes part of the wholesaler's cost, which is taxed again. The final price carries far more than the headline rate, and the effect is worse the more stages a product passes through — which quietly penalises specialisation.
VAT removes that by letting each business reclaim what it paid, so the government collects the headline rate once, spread across the chain. That is also why compliance is self-policing: your reclaim is someone else's declared output, and the two are cross-checkable.
It is the same logic behind India's GST, introduced in 2017 for exactly the same reason, and behind the GST systems of Australia, New Zealand, Singapore and Canada.
What this calculator assumes
- The rate you select applies to the whole amount, with no mixed-rate lines.
- Amounts are net or gross as you indicate, with no reverse charge applied.
- Rates are the current standard and reduced rates for the countries listed and change from time to time.
- Rounding is applied to the final figures rather than line by line.
- It calculates the tax, not your obligations. Registration, scheme choice and cross-border treatment are questions for an accountant.