How sales tax works at the till
US sales tax is added at the till rather than shown in the shelf price, and the rate varies by state and often by city and county too. That's why the same item costs different amounts in different zip codes. Before you rely on a figure, check the local combined rate, which is the state rate plus whatever local add-ons apply where you're buying.
The reverse card trips people up. To pull tax out of a total, you divide by 1 plus the rate rather than subtracting the percentage, and dividing is the correct way. Subtracting takes a percentage of the total, but the tax was charged on the smaller pre-tax price, so subtraction always removes too much.
Worked example
With the defaults above: $49.99 at 8.25% adds $4.12 of tax for a $54.11 total; going the other way, a $100.00 receipt at 8.25% contains $92.38 of goods and $7.62 of tax.
Frequently asked questions
Why can't I just subtract 8.25% from the total?
Because the tax was charged as a percentage of the pre-tax price, which is smaller than the total. Subtracting 8.25% of the total takes off too much. Dividing the total by 1.0825 undoes the tax exactly, which is why the reverse card divides instead of subtracting.
Do all US states have sales tax?
No, a handful of states charge no state sales tax at all. Everywhere else the rate varies, and cities and counties often add their own percentage on top of the state rate, so the combined rate at the till depends on exactly where you're shopping.
Does this work for VAT?
Yes, it's the same maths. Enter the VAT rate and either card works. The practical difference is that VAT is usually already included in the shelf price, so the reverse card is the one you'll use most: it pulls the VAT out of a price you've already paid.