Business studies
Adding and removing VAT
Add VAT to a net amount, or take it back out of a total that already includes it. One tap for the usual rates, and the answer with net, tax and gross kept apart.
Adding and removing are different operations
Adding VAT is straightforward: multiply the net amount by the rate and add the result, or in one step multiply by 1 plus the rate. At 20% a net amount of 100 becomes 120. No traps so far.
Removing VAT goes the other way, and that is where the error concentrates. The gross already contains the tax, so the VAT is not 20% of the gross but 20% of a net amount we do not yet know. The right move is to divide: net = gross / 1.20. Subtracting 20% from 120 instead produces 96 — plausible enough to slip through unnoticed, and wrong by four.
The third mode is for when a document shows only the net and the total and you need to work out which rate was applied. It is a common situation with receipts, expense claims and foreign invoices. The tax divided by the net, times a hundred, gives the rate.
Common mistakes
- Removing VAT by subtracting the percentage from the gross instead of dividing: it is by far the most widespread error and it grows with the rate. On 1,200 of net at 20% the gap is about 48.
- Applying the wrong rate: a single invoice can carry goods at different rates, and each line has to be worked out with its own.
- Rounding too early: VAT is rounded to the cent on the total tax, not line by line, or the cents will not add up.
Frequently asked questions
How do you remove VAT from a total?
Divide the total by 1 plus the rate as a decimal: at 20% divide by 1.20. The tax is the difference between the total and the net amount you get. You do not subtract the percentage from the gross.
How do you calculate VAT at 20%?
Multiply the net amount by 0.20 to get the tax, or by 1.20 to get the total directly. A hundred of net becomes 120.
How do you find the rate from the net and the total?
Divide the tax — the difference between total and net — by the net amount, and multiply by a hundred. From 100 and 120 you get (20/100)×100 = 20%.
Why is the VAT contained in a gross total not the same percentage?
Because the rate applies to the net amount, not to the total. At 20%, the tax is 16.67% of the gross, not 20%: it is the fraction rate/(1 + rate).
How this calculation works
Adding: VAT = net × rate; total = net × (1 + rate). Removing: net = total / (1 + rate); VAT = total − net. Equivalently the tax inside a gross figure is total × rate/(1 + rate): at 20% that is 16.6667% of the gross, not 20%. Rate from two amounts: rate = (total − net)/net × 100. Gross-to-net multiplier: 1 + rate. The figures carry no statutory rounding: the result is the exact arithmetic one.
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