To add tax, multiply by 1 + rate. To remove it, divide by 1 + rate.
Those two operations cover every sales tax, VAT and GST system in the world. Only the rate changes.
Adding is the easy direction
A 100 service at a 20% rate:
100 × 1.2 = 120The tax is 20, the total is 120. You can also calculate 20% separately and add it — same answer, one extra step.
Removing is where it goes wrong
You have a tax-inclusive total of 120 and want to know how much of it is tax.
The instinct is to take 20% off, because the rate is 20%. That gives 24. It is wrong.
The tax was never calculated on 120. It was calculated on 100. By the time you are looking at the total you are looking at 120% of the original, so taking 20% of it takes a slice of a number that is already inflated.
Divide instead:
120 ÷ 1.2 = 100 ← price before tax
120 − 100 = 20 ← the taxThe error is always in the same direction: subtracting the rate overstates the tax. Not by much on one invoice, but consistently, on every single one.
The reference
| Rate | Add tax | Find pre-tax price | Shortcut for the tax itself |
|---|---|---|---|
| 5% | × 1.05 | ÷ 1.05 | ÷ 21 |
| 8% | × 1.08 | ÷ 1.08 | ÷ 13.5 |
| 10% | × 1.1 | ÷ 1.1 | ÷ 11 |
| 15% | × 1.15 | ÷ 1.15 | ÷ 7.667 |
| 20% | × 1.2 | ÷ 1.2 | ÷ 6 |
| 25% | × 1.25 | ÷ 1.25 | ÷ 5 |
Those last-column shortcuts are worth knowing if you work with one rate all day. At 10% the tax is exactly one eleventh of the total; at 20% it is exactly one sixth. Both fall straight out of the algebra — at a rate of r, the tax is r ÷ (100 + r) of the total.
Tax-exclusive and tax-inclusive pricing
Which number gets advertised differs by country, and it is the source of a lot of confusion when comparing prices across borders.
- Tax-inclusive — the shelf price is what you pay. Common across Europe, the UK, Australia, New Zealand and Japan.
- Tax-exclusive — tax is added at the register. Standard in the United States and Canada, where the rate also varies by state, province and sometimes city.
So a US price tag understates what you will actually hand over, while a European one does not. When comparing quotes internationally, confirm which basis each is quoted on before assuming one is cheaper.
Business invoicing
If you are registered for tax, the amount you collect is not revenue — you are holding it on behalf of the tax authority.
The practical consequence is that your income should be recorded excluding tax. Booking tax-inclusive totals as revenue overstates your income by the full rate and produces a nasty surprise at filing time, when the money you thought you had earned turns out to be owed.
Rates, thresholds and exemptions vary by country, and plenty of categories are zero-rated or exempt. The arithmetic here is universal; what it applies to is not.