UK VAT at 20%, 5% and zero

What this works out

UK VAT, in both directions, at whichever of the three bands applies. Type a price that excludes the tax and it adds it; type one that includes it and it works the tax back out — which is a division rather than a subtraction, and is the arithmetic most people get wrong.

The table underneath shows the same amount in all three bands at once, with the VAT fraction for each. That is usually the next question: if this turns out to be reduced-rated rather than standard-rated, what does the invoice say instead?

The three bands

Standard, 20%. Since 4 January 2011, when it rose from 17.5%. It is the default for everything not placed in one of the other two bands, which is most goods and most services.

Reduced, 5%. Domestic fuel and power is the large one, along with children’s car seats, mobility aids for the elderly and a short published list besides. The 5% figure has an oddly specific history: domestic fuel was zero-rated from 1973 until 1994, when VAT at 8% was introduced on it, and the 1997 cut could go to 5% and no lower because EU VAT law as it then applied did not let a surrendered zero rate be reinstated.

Zero, 0%. Wider here than almost anywhere in Europe — most food, children’s clothes and shoes, books and newspapers, public transport, prescription medicines. Zero-rated is not the same as exempt, and the difference is not cosmetic: a zero-rated supply is taxable at nil, so the input tax on making it is recoverable, whereas an exempt supply is outside the charge and its input tax is not. Both print nothing on the invoice.

The method

Adding is a multiplication: the tax is the rate applied to the price before tax, and the total is the two added together.

Removing is a division. A price of £120 including 20% VAT is 120% of the price before tax, so the price before tax is £120 divided by 1.2. The shortcut HMRC publishes in VAT Notice 700 is the VAT fraction — the rate divided by 100 plus the rate. At 20% that is 20/120, one sixth. At 5% it is 5/105, one twenty-first. Those two are unusually tidy; 17.5% gives 7/47, which is what these fractions normally look like.

Only the VAT is rounded, and the third figure follows from the other two. A price of £12.03 including 20% VAT is exactly £10.025 before tax and £2.005 of tax. Round both independently and you get £10.03 and £2.01, which add to £12.04 — a penny more than the price on the receipt. Rounding the tax and subtracting cannot do that, so the three figures always reconcile.

The arithmetic is decimal, not binary floating point. 5% of £87.90 is exactly £4.395 and rounds to £4.40, but the nearest double sits fractionally below it, so a naive implementation reports £4.39. Which amounts trip that is not predictable from the shape of the sum — 5% of £24.90 is also a half-penny and happens to round correctly by luck — which is why the test file names a case that genuinely fails rather than one that merely looks like it should.

The rounding concession

HMRC lets a trader issuing VAT invoices round the tax down to a whole penny instead of to the nearest. The reasoning is that it is tax-neutral rather than generous: the supplier’s output tax and the customer’s input tax move together, so the Exchequer collects the same either way. The concession has existed since VAT was introduced here.

Two limits are worth knowing. It applies per line, not to the invoice total — VAT is worked out and rounded on each line, and the total is the sum of those. And it is written for traders invoicing at prices excluding tax, so a retailer computing VAT out of gross takings under a retail scheme rounds by that scheme’s own rules instead.

It is off by default here, because it is a concession rather than the rule. It is also the reason this tool has a rounding control at all and the other country tools do not: correct rounding is a rule of the authority you file with, so offering the same switch on a German or an Irish page would be handing them a British concession neither grants.

Before you read on

A VAT invoice line comes to £1.99 before tax. At 20% the VAT is £0.398. What may the trader charge?

• A£0.40 — round to the nearest penny.

  Allowed, and it is what this tool does by default. But it is not the only thing HMRC permits.

• B£0.39 — round it down.

  Yes. HMRC lets a trader issuing VAT invoices round the tax down to a whole penny.

• C£0.398 — an invoice can carry the third decimal.

  It cannot. The tax charged has to be an amount of money, so it lands on a penny either way.

Either £0.40 or £0.39, and the second is the one worth knowing about. HMRC lets an invoice trader round VAT down rather than to the nearest penny, and the reasoning is that it is tax-neutral rather than generous — the supplier's output tax and the customer's input tax move together, so the Exchequer collects the same. It applies per line, not to the invoice total. This tool leaves it off by default, because it is a concession rather than the rule, and it is the reason this page has a rounding control that no other country page here does.

A worked example

Adding. £100 before VAT at the standard rate:

VAT	£20.00
Price before VAT	£100.00
Price including VAT	£120.00
VAT fraction	1/6

Removing, at the reduced rate. A domestic energy bill of £126 that includes 5% VAT:

vat = 126 x 5 / 105
    = 126 / 21
    = 6.00

net = 126.00 - 6.00
    = 120.00

Taking 5% off £126 instead gives £119.70, which is 30p adrift — small on one bill, and not small across a year of them.

The concession. £179.99 including 20% VAT is £30.00 of tax rounded to the nearest penny and £29.99 rounded down, leaving £149.99 or £150.00 before tax. One penny, on every line it touches.

These are the same figures asserted in this tool’s test file, so the page and the formula cannot drift apart without the build going red.

What it does not do

It does not decide which band a supply falls in — that is a question about the supply, and HMRC publishes the lists. It holds no historic rates, so an invoice from before January 2011 needs the rate typing into “Another rate”. It does not handle the reverse charge, the flat rate scheme, margin schemes, partial exemption, import VAT or the construction industry domestic reverse charge, and it does not tell you whether to charge UK VAT at all on a cross-border sale.

For a rate no tool here holds, or a country without one of its own, a VAT calculator with no rate table is the right page. For the two other countries covered so far, there are Irish VAT and German VAT.

Adding VAT to a price that excludes it:
  vat   = round(net x rate / 100)
  gross = net + vat

Removing VAT from a price that includes it:
  vat = round(gross x rate / (100 + rate))
  net = gross - vat

UK bands and their VAT fractions:
  standard    20%   20/120 = 1/6
  reduced      5%    5/105 = 1/21
  zero         0%    no tax

round = to the nearest penny, or towards zero when the
        invoice trader's concession is chosen

Only the VAT is rounded. The third figure is derived from
the other two, so net + vat = gross to the penny, always.