Adding and removing tax
Adding tax to a net price
gross = net × (1 + rate ÷ 100)
At a 20% rate, a net price of 250 becomes 250 × 1.20 = 300, of which 50 is tax.
Removing tax from a gross price
net = gross ÷ (1 + rate ÷ 100)
This is the step people most often get wrong. A gross price of 300 at 20% VAT is not 300 − 20% = 240. It is 300 ÷ 1.20 = 250, because the 20% was charged on the smaller net figure. The tax portion is the 50 difference.
Rule of thumb: to add tax you multiply, to remove it you divide. Subtracting the percentage from the gross price always understates the net amount.
VAT versus sales tax
VAT is charged at every stage of production, with businesses reclaiming what they paid on inputs, and it is normally quoted inclusive of tax on consumer price tags. US sales tax is charged once at the point of final sale and is normally quoted exclusive, added at the till. The arithmetic is the same; what differs is whether the number you are looking at already contains the tax.
| Rate | Multiply by (to add) | Divide by (to remove) | Tax share of gross |
|---|---|---|---|
| 5% | 1.05 | 1.05 | 4.76% |
| 7.5% | 1.075 | 1.075 | 6.98% |
| 10% | 1.10 | 1.10 | 9.09% |
| 19% | 1.19 | 1.19 | 15.97% |
| 20% | 1.20 | 1.20 | 16.67% |
| 21% | 1.21 | 1.21 | 17.36% |
| 23% | 1.23 | 1.23 | 18.70% |
| 25% | 1.25 | 1.25 | 20.00% |
The last column explains a common surprise: at a 25% VAT rate, tax is 20% of what you actually hand over, not 25%.
Frequently Asked Questions
- How do I remove 20% VAT from a price?
- Divide by 1.20. A gross price of £120 has a net price of 120 ÷ 1.2 = £100 and £20 of VAT.
- Why can I not just subtract the VAT rate?
- Because the rate was applied to the net price, which is smaller than the gross. Subtracting 20% from the gross removes too much.
- What share of a gross price is tax at 21%?
- 21 ÷ 121 = 17.36% of the total you pay.