Adding tax is simple: multiply by the rate and add it on. Taking tax back out of a price that already includes it catches out a surprising number of people, including in spreadsheets used for real invoices.
Adding tax
At a 20% rate, a net price of 100 carries 20 of tax, for a total of 120. The tax is 20% of the price before tax.
The mistake when removing it
Now start from the 120 and try to get back to 100. Taking 20% off 120 gives 96, not 100. That is because the 20% was calculated on 100, the smaller number, and you are now applying it to 120.
The same thing happens with any price. If a receipt says 100 including 20% VAT, the price before tax is not 80.
The right formula
Divide the tax-inclusive price by one plus the tax rate. At 20%, divide by 1.2. At 5%, divide by 1.05. At 8.25%, divide by 1.0825.
Price before tax
100 ÷ (1 + 20%)equals83.33
Tax included
100 − 83.33equals16.67
You can check the answer by adding the tax back: 83.33 × 1.2 is 100, give or take a rounding cent.
A sales tax example
US sales tax is usually added at the till rather than included in the shelf price, but the math is identical. At an 8.25% rate, a $250 purchase carries $20.63 of tax, for $270.63. Going back, $270.63 ÷ 1.0825 returns $250.00.
Where people slip up
- Subtracting the rate instead of dividing, as above.
- Rounding the tax on each line of an invoice and then again on the total, which can leave the two a cent apart.
- Using the wrong rate. Many countries have reduced rates for some goods, and US sales tax can differ by state and city.
Tip: Keep a quick check handy: the tax share of a tax-inclusive price is rate ÷ (1 + rate). At 20% that is 1/6, or 16.67%, of the total.