VAT added and removed

Value-added tax moves a price in two directions, and only one of them is obvious. Going up — from a net, tax-exclusive price to the gross price a customer pays — is a single multiplication. Coming back down — recovering the net hidden inside a VAT-inclusive total — is a division, and treating it as a subtraction is the mistake this page exists to head off. The engine behind the VAT calculator does both, reports the same three numbers each time, and every figure printed below was computed at build time by that engine on a labelled fictional rate — never a real jurisdiction's.

The three numbers the engine returns

Whichever direction you work in, the engine settles on the same trio: the net price (before tax), the gross price (including tax), and the VAT amount that separates them, which is always simply the gross minus the net. Adding VAT starts from the net and solves for the gross; removing VAT starts from the gross and solves for the net. The VAT amount falls out of the pair either way, which is why both modes can show all three — an invoice that must display net, tax, and total is reading straight off the same calculation.

Adding VAT is multiplication

The formula is gross = net × (1 + rate ÷ 100), and the VAT is whatever that adds: VAT = gross − net. Take a fictional net of 200 at an example rate of 18%. Multiplying by 1.18 gives a gross of 236, so the VAT portion is 36. Nothing here depends on the net being a round figure or the rate being a whole number: a net of 80 at a fictional 7.5% produces a gross of 86 and 6 of tax, the decimal rate handled exactly. A rate of zero is a legitimate input too — the gross then equals the net, 200, with 0 of VAT — because the engine treats the rate as a number you supply, not as a value it is entitled to assume.

Removing VAT is division, not subtraction

This is where a reasonable-looking shortcut goes wrong. To pull VAT out of a gross price the engine computes net = gross ÷ (1 + rate ÷ 100), then reports VAT = gross − net. It divides because the tax was charged on the net — the smaller figure — not on the gross total you are holding. Feed the gross of 236 back in at 18% and it divides by 1.18 to recover the net of 200 exactly, with 36 of VAT.

Now the tempting mistake: subtracting 18% of the gross. That removes 42.48 and leaves 193.52 — but the true net is 200, so the shortcut lands 6.48 too low. The reason is base confusion: 18% of the larger gross is a larger amount than the 18% that was originally added to the smaller net, so subtracting it overshoots. The gap is not a rounding quirk; it widens with the rate. At a higher fictional 30%, a net of 200 grosses up to 260; backing it out correctly returns 200, while subtracting 30% of the gross strips off 78 and leaves 182 — now 18 adrift. The larger the rate, the more the subtraction shortcut misprices the net.

The two operations round-trip

Because adding and removing VAT at one rate are exact inverses, running them in sequence returns the original price. The net 200 adds up to 236, and that gross removes back down to 200 — the same number you began with. That round-trip is a quick self-check: if adding then removing at a single rate does not return your starting figure, the two steps were not done at the same base.

Round numbers rarely survive the division, though, and that is expected. A gross of 100 at the fictional 18% rate backs out to a net of 84.75, carrying 15.25 of VAT — neither of them tidy. The engine keeps the full-precision value internally and only rounds for display, so the net and the VAT amount still add back to the original gross even when the printed digits look as though they might not. The methodology page sets out exactly how that displayed rounding relates to the internal precision.

What the rate is, and what the engine will not do with it

The rate is entirely yours. The engine carries no table of national or regional rates, no reduced or zero-rate categories, no notion of which goods fall where — it adds or removes whatever percentage you type and reports the arithmetic result. That is a deliberate boundary. VAT rates differ by place and category and change over time, and a generic calculator that pretended to know them would be wrong somewhere the moment it shipped. The only rules the engine enforces are arithmetic ones: the price must be greater than zero, and the rate cannot be negative. Decimals pass through untouched, and even a rate above 100% is computed without complaint, since the multiplication and division are well defined whether or not any real tax regime would use such a figure.

Where this sits among the tools

The interactive version of all of the above is the VAT calculator, with separate add and remove modes. Backing a number out of a grossed-up total is the same divide-by-the-factor move as recovering a price from before a percentage increase — the general form lives in the price change calculator. When discounts and VAT appear on the same invoice, the order they are applied in changes the result; the discount calculator covers that side. And whether a price still clears your costs once tax is set aside is a margin question for the profit margin calculator. The full set of explainers is indexed on the guides hub.

Frequently asked questions

The calculator implements the general mathematical definition of VAT — multiply to add, divide to remove — on the rate you supply. It knows nothing of your jurisdiction's rules, and your jurisdiction's or contract's conventions may differ, so for filings rely on official guidance and treat these figures as arithmetic rather than tax advice. How the numbers are computed, verified, and rounded is documented on the methodology page.