How to add or remove VAT, GST or sales tax from a price

Whether it is called VAT, GST or sales tax, the arithmetic is the same: a percentage added on top of a price. Adding it is easy. Taking it back out is where almost everyone gets it wrong the first time.

The words: net and gross

• Net is the price before tax.
• Gross is the price including tax — what the customer pays.
• The tax is the difference between them.

Adding tax

gross = net × (1 + rate)

At 20%, multiply by 1.2: a net price of 50 becomes 60. At 10%, multiply by 1.1: 50 becomes 55. The tax is the gross minus the net — 10 and 5 respectively.

Removing tax — the right way

net = gross ÷ (1 + rate)

At 20%, divide by 1.2: a gross price of 120 has a net price of 100 and contains 20 of tax.

The tempting shortcut — taking 20% off 120 — gives 96, which is wrong. The 20% was calculated on the net price of 100, not on the gross of 120, so subtracting 20% of the gross removes too much. Always divide. The Tax Calculator has a mode for each direction and always uses the division when extracting tax.

How much of a gross price is tax?

The tax share of a tax-inclusive price is rate ÷ (1 + rate). A few common cases:

That is why accountants in the UK talk about “the VAT fraction” of one sixth at the 20% rate, and why in Australia and New Zealand people speak of one eleventh for 10% GST.

VAT, GST and sales tax: what differs

For a single price, nothing in the arithmetic. The difference is in how the tax is collected:

• VAT and GST are charged at each stage of the supply chain, with each business reclaiming the tax it paid on its own purchases. Consumer prices are usually shown including tax.
• Sales tax, as in the United States, is charged once at the final sale. Prices are usually shown before tax, which is added at the till, and the rate depends on the state and often the city or county.

Rates differ widely between countries and often between kinds of goods. The UK's standard VAT rate is 20%, Germany's 19%, Australia's GST 10% and New Zealand's 15%; Canada combines a 5% federal GST with provincial taxes, or a single harmonised rate such as 13% in Ontario. Many countries apply reduced rates to food, books or energy. Always check the current rate for what you are pricing.

Discounts and tax together

Does it matter whether the discount or the tax is applied first? Not to the total. Both are multiplications, and multiplying in a different order gives the same answer: 100 with 10% off and 20% tax is 108 either way. Shops usually present the discount first. For stacked discounts, see the Discount Calculator.

On invoices: rounding

Take an invoice with three items at 0.99 each, before 20% tax. Rounded on each line, the tax is 0.198, which rounds to 0.20, three times: 0.60. Rounded once on the total, the tax is 2.97 × 0.2 = 0.594, which rounds to 0.59. When an invoice has many lines, tax can be rounded either way, and the two methods can differ by a cent or two. Both are legitimate; what matters is consistency and following any rule your tax authority sets. The Invoice Generator works in whole cents, so its lines, subtotal, tax and total always add up exactly.

A note on advice

This guide covers the arithmetic only. Whether you should charge tax, at what rate, and how to report it depends on your country, your business and what you sell — a question for your tax authority or an accountant.