Working out VAT: net, gross and rounding to the penny
Subtract 20% from a gross figure and you will not land on the net one. The exact formulas, UK rates, the VAT fraction and the penny-rounding traps.
£120 including VAT at 20%. The first thing most people do is punch 120 − 20% into a calculator, read £96 and write that figure into the “excluding VAT” box. The real net amount is £100. The error comes from the base: the 20% never applies to the VAT-inclusive price, it applies to the net price. On a £12,000 VAT-inclusive invoice the same slip makes £400 of net turnover vanish — £9,600 instead of £10,000 — and a VAT return that is simply wrong.
Two separate operations, never symmetrical
Adding VAT and taking it off are not the same operation run backwards with the same percentage. With t as the rate written as a decimal (20% → 0.20):
- Net to gross: gross = net × (1 + t). A multiplication.
- Gross to net: net = gross ÷ (1 + t). A division, not a percentage subtraction.
- The VAT itself: going gross → net, VAT = gross − net, worked out last; going net → gross, VAT = net × t, then gross = net + VAT.
HMRC has a name for the shortcut in the second direction: the VAT fraction, the number you multiply a VAT-inclusive price by to get the VAT it already contains. At the standard rate it is 1/6, small enough to keep in your head. The values worth knowing:
| Rate | Net → gross | Gross → net | VAT fraction |
|---|---|---|---|
| 20% | × 1.20 | ÷ 1.20 (× 0.833333) | 1/6 (× 0.166667) |
| 5% | × 1.05 | ÷ 1.05 (× 0.952381) | 1/21 (× 0.047619) |
| 19% | × 1.19 | ÷ 1.19 (× 0.840336) | 19/119 (× 0.159664) |
| 21% | × 1.21 | ÷ 1.21 (× 0.826446) | 21/121 (× 0.173554) |
| 23% | × 1.23 | ÷ 1.23 (× 0.813008) | 23/123 (× 0.186992) |
The gross-to-net multiplier is an unending decimal that has to be cut short: 1 ÷ 1.20 = 5/6 = 0.8333… Six decimal places hold the penny up to roughly £15,000; past that the accumulated drift passes half a penny — 3p on £100,000, 10p on £300,000. As soon as the amounts run into five figures, divide by 1.20 rather than multiply by a rounded factor. The VAT calculator divides by (1 + t), then rounds each line to the penny before deriving the next one, so the three amounts on screen always add up.
The rate follows what you sell, not a guess from the list
The UK runs three VAT rates, plus a fourth category that is not a rate at all:
- 20% — the standard rate, applied by default to anything not specifically relieved. That covers the great majority of services and manufactured goods.
- 5% — the reduced rate: domestic gas and electricity, children's car seats, mobility aids installed for people aged 60 and over, certain residential conversions.
- 0% — zero-rated: most food, books and newspapers, children's clothes and shoes, prescription medicines dispensed by a pharmacist, most public transport fares, new-build housing. It is still a taxable supply, so it counts towards your turnover and appears on your return.
- Exempt — insurance, postage stamps, most financial services, education from an eligible body, health care from registered practitioners. Not the same thing as 0%: exempt sales stay outside taxable turnover, and you cannot reclaim the VAT on what you bought in order to make them.
Across the Channel, standard rates sit between 19% and 23%: 23% in Portugal, 22% in Italy, 21% in Belgium and Spain, 19% in Germany — each with its own set of reduced rates. These schedules change: check the rate in force with the tax authority of the country concerned before issuing a cross-border invoice. The calculator carries the standard rates of those euro-area countries, plus a custom rate field that accepts any value between 0 and 100% — that is where the UK's 5% goes, along with any regional or historical rate.
Rounding to the penny, where totals drift apart
VAT is worked out to the penny. The trap is not the rounding itself but the order in which you apply it.
A worked example: £7.50 net at the 5% rate. The VAT is £0.375, rounded to £0.38, so the gross shown has to be £7.88 — that is 7.50 + 0.38. Multiplying straight through agrees here (7.50 × 1.05 = 7.875 → £7.88), because £7.50 is already a whole number of pence. It stops agreeing the moment the net is itself a computed figure: five units at £1.499 come to £7.495, which shows as £7.50 net with £0.38 of VAT and a £7.88 gross, whereas 7.495 × 1.05 = 7.86975 → £7.87. One penny apart, and only one of the two versions has three lines that add up. The safe rule: round the net, round the VAT, then get the gross by adding the two — never the other way round.
The second trap is purely computational: spreadsheets and browsers work in binary floating point, where a decimal such as 1.035 has no exact representation. The VAT on £20.70 at 5% is exactly £1.035, but the nearest binary double is 1.03499999999999992 — a hair below the half penny. Round that stored value and you get £1.03 where £1.04 is correct. If you are building your own spreadsheet, force an explicit ROUND to two decimal places on every line rather than letting Excel or Google Sheets display two decimals while keeping the rest in memory: that is the classic reason a total reads £1,249.99 instead of £1,250.00.
An invoice with more than one rate
If a single invoice mixes 20% and 5%, you have to split it: add up the net amounts rate by rate, work out one VAT figure per rate, then total. Applying an “average rate” to the combined net gives a false answer — and a full VAT invoice has to show the rate applied and the net amount for each line anyway, so the breakdown has to exist on the document.
Discounts, currencies and the order of operations
A trade discount comes off the net amount, before VAT. On £1,000 net with 10% off, at the standard 20%: base £900, VAT £180, total £1,080. Arithmetically you reach the same total by discounting the gross, but the VAT line on your invoice is then wrong — it is the base that must appear reduced. To chain several discounts, or to work back to a discount rate from two prices, the percentage calculator keeps you clear of wrongly compounded “cascading” discounts: 10% twice is not 20% off but 19%.
For an invoice in a foreign currency the order matters too. Convert into sterling at the exchange rate you have chosen, then apply VAT to the converted figure. HMRC expects the VAT to appear in sterling on the invoice, using either the market selling rate at the time of supply or its own published rate for the period. A currency converter gives you the conversion; note the rate and its date, because you may be asked which one you used.
Finding a missing figure
The situations that come up most often need three formulas:
- You have the gross and the VAT: net = gross − VAT.
- You have the net and the gross but not the rate: rate = (gross ÷ net − 1) × 100. Handy for identifying the rate applied on a receipt whose header has faded.
- You have the net and the rate: VAT = net × rate ÷ 100, then gross = net + VAT.
The final check is one addition: net + VAT has to land exactly on the gross, to the penny. If the equality does not hold, you have a rounding or a base problem, not bad luck.
The cases where there is nothing to work out
Three common situations where the net equals the gross, and where charging VAT would be a mistake:
- Not registered for VAT: below the VAT registration threshold — check the figure in force on GOV.UK, it is revised from time to time — a business charges no VAT and shows no VAT number on its invoices. It cannot reclaim the VAT on its own purchases either.
- Reverse charge: general-rule services supplied to a business customer abroad fall outside the scope of UK VAT, so the invoice goes out with no VAT and states that the customer accounts for it under the reverse charge. Check an EU customer's number in the European Commission's VIES database, and a British one through the “Check a UK VAT number” service on GOV.UK.
- Exporting goods outside the UK: zero-rated, provided you keep the evidence that the goods actually left the country.
In all three cases, typing a 0% rate into a calculator comes to the same thing as not calculating at all: what counts is the wording on the document.
Checking an amount in ten seconds
Convertu's VAT calculator has two explicit modes — add VAT (net → gross) and remove VAT (gross → net) — precisely because confusing the two is error number one. The amount field takes either a full stop or a comma as its decimal mark and ignores thousands separators, so “1,250.50” goes in exactly as written, with no reformatting first. The rate comes from a short list of standard rates by country — the 20% filed under France is the same figure as the UK standard rate — or from the custom-rate field, which is where 5% belongs. One caveat before you paste: the result lines are formatted in euros, since the tool was built for the euro area — the arithmetic is identical, only the symbol changes. The calculation runs entirely in the browser: no amount is sent to a server.
If the job then drifts towards the paperwork — photographing receipts and assembling them into a single document for the books with the JPG to PDF tool, for instance — be aware that those jobs do go through the server: one free conversion a day with no sign-up, then a single subscription at €7 a year for unlimited use, cancellable in one click. The size limit per file is shown on the tool's own page, and files are deleted from the servers after an hour. The calculators themselves stay freely available.