How to Use This Tool
Pick a direction, enter the amount and the rate. Going backwards from a tax-inclusive total is the case worth being careful about.
Why subtracting the rate is wrong
Tax is charged as a percentage of the net price, so it is a smaller percentage of the total that includes it. Undoing it therefore has to divide, not subtract.
- Add:
total = net × (1 + rate) - Remove:
net = total ÷ (1 + rate)
At 20% VAT on a 1,000 total: dividing gives 833.33 net and 166.67 VAT. Subtracting 20% gives 800, which is 33.33 too low — a 3.3% error on the invoice. At 8.25% sales tax on a 108.25 total, dividing gives exactly 100; subtracting gives 99.32, short by 0.68.
Notice that 20% of the net is 16.67% of the total. That second figure is the one to use if you ever need to pull the tax straight out of a gross number in your head: divide by 6 for 20% VAT.
Sales tax and VAT are not the same thing
They produce a similar number on a receipt and behave differently:
- US sales tax is charged once, at the final sale, and is normally quoted and displayed excluding tax. The advertised price is the net price and the tax appears at checkout.
- VAT and GST are charged at every stage, with businesses reclaiming what they paid, so only the final consumer bears it. Consumer prices are almost always quoted including it, which is why the reverse calculation comes up so often.
The practical consequence: if you are a business quoting a business, you usually quote net. If you are quoting a consumer in a VAT country, quoting net and adding at checkout tends to be unlawful as well as annoying.
Two taxes at once
Some places levy more than one tax on the same sale — a state and a city rate, or a federal and a provincial one. Two arrangements exist and they give different totals:
- Both on the net. 100 at 10% and 5% gives 115.00. Rates simply add.
- The second on the already-taxed price. 100 at 10% gives 110, then 5% of that gives 115.50. Fifty cents more, and the gap widens as rates rise.
Which applies is set by statute. Most US combined state-and-local sales tax is the first kind; some historical Canadian provincial arrangements were the second. If you are invoicing, check — do not infer it from the arithmetic.
Rates are not built in, deliberately
You have to type the rate, and that is not laziness. US sales tax is set at state, county, city and sometimes special-district level, runs to thousands of distinct combinations, and changes throughout the year. VAT and GST rates change by statute, and reduced rates apply to particular goods.
Any tool shipping a built-in rate table is shipping a table that is wrong somewhere, and you cannot tell which entry. Get the rate from the tax authority or your accounting system, then use this to do the arithmetic. This is information, not tax advice.
