How to take sales tax or VAT out of a price

Adding tax

In the United States prices are usually shown before sales tax, and tax is added at the register. An $80 item at 7.25% (California's base state rate) costs $80 × 1.0725 = $85.80. In New York City, where the combined rate is 8.875%, a $1,299 laptop costs $1,414.29.

Taking it out: divide, do not subtract

In the UK, the EU and many other countries, prices already include VAT. A £120 price at the UK's 20% standard rate contains £120 ÷ 1.20 = £100 of price and £20 of VAT.

The common mistake is to take 20% off £120, which gives £96 and £24 of tax. That is wrong because the 20% was charged on the price before tax (£100), not on the total. The bigger the rate, the bigger the error: at 20% the shortcut is off by 4% of the price.

The rule: price before tax = total ÷ (1 + rate), and tax = total − price before tax. The sales tax calculator does it in either direction and also finds the rate from two prices.

Finding the rate from two prices

If a receipt shows $250 before tax and $270.63 after, the rate is 270.63 ÷ 250 − 1 = 8.25%. This is handy for checking a bill or working out the combined state and local rate where you shop.

Rounding and receipts

Stores round tax to the cent on each receipt, sometimes line by line, so a total worked out by hand can differ by a cent or two. Some items are taxed at a reduced rate or are exempt (food and medicines in many places), so one rate for a mixed basket is only an estimate. Businesses that claim VAT back need the exact VAT on each invoice, not a figure recomputed from the total.

A quick mental check

For a VAT-inclusive price at 20%, the VAT is one sixth of the total (because 20 ÷ 120 = 1/6). At 10% it is one eleventh, at 25% one fifth. If your answer is not close to that fraction, the calculation went wrong somewhere.

Sales tax and VAT are not the same tax

A US sales tax is charged once, at the final sale, by states and often by counties and cities as well, so the rate depends on where you buy. VAT, used in the UK, the EU and most other countries, is charged at every stage of production, with businesses reclaiming the VAT they paid on their own purchases; the consumer at the end bears the full rate. For a shopper the arithmetic is the same either way: one percentage on the price before tax.

Business use: invoices and reverse charge

A business registered for VAT shows the net price, the VAT rate and the VAT amount on each invoice and reclaims VAT on its costs. Cross-border sales between businesses often use the reverse charge, where the buyer accounts for the VAT instead of the seller, so an invoice can legitimately show 0%. Those rules vary by country; for a consumer price check, the divide-by-(1 + rate) rule above is all that is needed.

In short

Add tax by multiplying by (1 + rate). Remove it by dividing by (1 + rate), never by subtracting the rate from the total. Find the rate from two prices with after ÷ before − 1. Remember that rates differ by place and by product, and that receipts round to the cent, so a hand calculation can be a cent or two off. For a VAT-inclusive price, the tax is one sixth at 20%, one eleventh at 10% and one fifth at 25%, a quick check worth memorizing before you shop or travel abroad.