VAT calculator

What is a VAT calculator?

VAT is a percentage added to the price of most goods and services. A VAT calculator does two small sums: adding the tax to a net price to get the gross one, and working backwards from a gross price to find the net and the tax it contains. The second is the one people get wrong by hand, because you divide by one plus the rate rather than subtracting the rate.

At 20%, a net price of 100 becomes 120. Going the other way, a gross price of 120 contains 100 of goods and 20 of tax, but a gross price of 100 contains 83.33 and 16.67, not 80 and 20. Subtracting 20% from the gross is the classic mistake and it is wrong by a fifth of the tax.

This calculator does all of it in exact integer arithmetic on whole cents. Nothing passes through a floating point number on the way, which matters when the output is a figure someone will reconcile against a bank statement.

How to use it

1. Choose what you need. Add VAT takes a price before tax and gives you the tax and the total. Remove VAT takes a price that already includes tax and splits it. Compare an invoice takes several amounts and shows the discrepancy explained below.
2. Set the rate. Type any percentage, or use the quick row for the eight rates in common use across Europe. Fractional rates work, so 8.25 is fine, and the field accepts a comma as the decimal separator.
3. Read every row, not just the one you came for. In add and remove modes you get the net, the tax and the gross together, so the figure you were not looking for is there when someone queries it. In compare mode you get both totals and the gap between them.

Why an invoice can show two different VAT totals

Charge 20% on three lines of 10.33, 20.67 and 5.99 and there are two defensible ways to work out the tax. You can compute the VAT on each line, round each to the cent, and add those up. Or you can add the lines first and compute the VAT once on the total. These give different answers, and the reason is simply that rounding three numbers and adding them is not the same as adding three numbers and rounding once.

We measured how often it matters, over 100,000 randomly generated invoices of two to twelve lines at the common European rates. The two methods disagree on 52% of them, by up to four cents. That is not an edge case hiding in unusual data; it is half of all invoices, and a bookkeeper reconciling to the cent meets it constantly.

Neither answer is a mistake. Both are correct arithmetic answering slightly different questions, which is exactly why tax authorities have had to write down which one an invoice must use rather than leaving it to the software. That varies by country, so the tool shows you both figures and the gap rather than picking one and hiding the other. Check what your own authority requires before deciding which column to put on a document.

The practical advice that follows is duller than it sounds: be consistent. A supplier computing per line and a customer checking on the total will disagree by pennies forever, and the time spent finding out why costs more than the pennies.

The rounding worry that turns out to be unfounded

The obvious fear about a tool like this is drift. Every step rounds to the cent, so adding VAT to a net price and then removing it again ought to land somewhere slightly different from where it started, and doing that repeatedly ought to wander.

It does not. We swept it exhaustively rather than sampling: every net amount from one cent to 200,000 cents, at each of the eight common rates, which is 1.6 million cases. The round trip returned the original amount every single time. Widening it to all 5,000 rates between 0.01% and 50% at probe values found no failures either. With half-up rounding at both ends, adding VAT and removing it is exact.

This is worth saying plainly because the intuition is so strong, and because it points at where the real problem is. Rounding does bite in this domain, but it bites when several rounded figures are added together, not when one figure is rounded twice. That is the invoice comparison above, and it is the thing to check.

Honest limits

This is arithmetic, not tax advice, and it knows nothing about your situation. It does not know which rate applies to what you are selling, whether your customer is in another country, whether the reverse charge applies, or whether the transaction is exempt or zero-rated, which are different things with different consequences. Those questions decide the rate, and the rate is something you type in.

Rounding here is half away from zero, matching the ROUND function in every spreadsheet, which is what most people are checking against. Some jurisdictions and some accounting systems round half to even instead, and the two differ only when a value lands on an exact half. If your accounts round differently, expect an occasional one-cent disagreement with this tool and know where it comes from.

The tool works to two decimal places, which is right for the euro, the pound and most currencies that charge VAT. Currencies with no minor unit or with three of them exist, and this page does not offer them.

Finally, the comparison mode assumes one rate across every line. Real invoices often mix rates, with a reduced rate on some items and a standard rate on others, and the same discrepancy then arises within each rate group separately.

Why is it free?

Because it is integer arithmetic and there is nothing to run. No server is involved: everything happens in your browser, and no amount you type is uploaded, logged or stored. Prices and invoice lines are commercially sensitive more often than people think, which is a good reason for them not to travel.

So there is no account, no sign-up and nothing held back. The engine and the 59 checks that verify it sit in the repository beside the page, including the exhaustive round-trip sweep and the invoice comparison behind the figure quoted above.