Add tax, or work backwards from the total
Add tax, or work backwards from the total
This is the straightforward direction. Multiply the price by the tax rate to get the tax, then add it:
Tax = Price × (Rate ÷ 100)
Total = Price + Tax
A $250 item at 8.25% tax carries $20.63 in tax for a total of $270.63.
Working backwards from a tax-inclusive total is where errors creep in. The instinct is to subtract 8.25% from the total. That is wrong, because the tax was calculated on the smaller pre-tax figure, not on the total.
Pre-tax = Total ÷ (1 + Rate ÷ 100)
On a $270.63 total at 8.25%: 270.63 ÷ 1.0825 = $250.00. Subtracting 8.25% from $270.63 would have given $248.30 — off by $1.70, and the error grows with the amount and the rate.
The same principle applies to any percentage worked backwards, which is why reverse percentage problems trip people up so consistently.
In the United States there is no national sales tax. Rates are set at state level and then added to by counties, cities, and special districts, so the rate that applies depends on the exact delivery or purchase location — sometimes differing between two sides of the same street.
Combined rates commonly range from zero in a handful of states to well over 10% in some localities. Several states exempt groceries, prescription medicine, or clothing, and a few apply reduced rates to specific categories.
This is why an online checkout total often differs from what you calculated: the rate is determined by your shipping address, not the seller's location.
Sales tax is charged once, at the final retail sale, and is normally shown separately from the price.
Value-added tax, used across Europe and much of the world, is collected at every stage of production with businesses reclaiming what they paid on inputs. The end consumer bears the same total either way, but the displayed price usually already includes it — which is why a European price tag is what you actually pay at the till, while a US price tag is not.
The reverse formula above is exactly what businesses use to extract the VAT component from an inclusive price for their returns.
Expense reports and bookkeeping. If you have a receipt showing only a total, the reverse calculation recovers the net and tax figures your accounting needs.
Comparing prices across regions. Stripping tax out puts a tax-inclusive European price and a tax-exclusive US price on the same footing.
Budgeting for a purchase. If you have a fixed total to spend, dividing by 1 plus the rate tells you the maximum ticket price you can choose.
Checking a receipt. Running the reverse calculation is a quick way to confirm the tax charged was correct.
Divide the total by 1 plus the rate as a decimal. For 8.25%, divide by 1.0825. Subtracting the percentage from the total gives the wrong answer, because the tax was calculated on the smaller pre-tax figure.
Sales tax is usually determined by your shipping address rather than the seller's location, and combined state, county, and city rates vary considerably even within short distances.
Sales tax is charged once at the final retail sale and shown separately. VAT is collected at each production stage and is normally already included in the displayed price.
It depends on the jurisdiction. Many US states exempt unprepared groceries or apply a reduced rate, while prepared food is usually taxed at the full rate. Prescription medicine is commonly exempt.