Whether you're trying to get back to the pre-tax price of an item as part of a word problem or calculating the sales tax backwards from a receipt in your hand, the math is the same. You'll need to know the total amount paid and either the amount of tax paid, which will let you calculate the tax rate, or the tax rate, in which case you can calculate the amount of tax paid.
Calculating the Tax Rate
This method assumes you know the total amount paid and the amount of tax paid, and you need to figure out the percentage tax rate that was assessed.
Subtract the Tax Paid From the Total
Subtract the amount of tax you paid from the total, post-tax price of the item. This gives you the pre-tax price of the item. So if you paid $26.75 in total for two books, and you know from looking at the receipt that $1.75 of that was tax, the books' pre-tax cost was:
$26.75 - $1.75 = $25
Divide the Tax Paid by the Pre-Tax Price
Divide the amount of tax you paid by the pre-tax price of the books. The result is the percentage tax rate you paid, expressed as a decimal. To continue the example, you have:
$1.75 ÷ $25 = .07
Convert the Tax Rate to a Percentage
Multiply the tax rate by 100 to convert it to a percentage. So if your tax rate is .07 in decimal form, here's the calculation to convert it into a percentage:
.07 × 100 = 7 percent is the tax rate you paid on the books.
Calculating Amount of Tax Paid
This method assumes that you know the total post-tax price for the item and the tax rate that was assessed, so you need to calculate backward to find out how much money actually went toward the sales tax.
Add 100 Percent to the Tax Rate
Add 100 percent to the sales tax rate. The 100 percent represents the whole, entire pre-tax price of the item in question; when you add it to the tax rate, you get a total percentage that represents the pre-tax price plus the tax. So if the sales tax in your area is 8 percent, you have:
100 + 8 = 108 percent
Convert the Total Percentage to Decimal Form
Divide the "tax paid" rate you just calculated by 100 to convert it from a percentage into a decimal. So if you had 108 percent as the tax paid rate, that becomes:
108 ÷ 100 = 1.08
Divide the Post-Tax Price by the Decimal
Divide the post-tax price of your item by the "tax paid" decimal you just calculated. The result will be the _pre-_tax cost of the item. So if you bought a stuffed animal that cost $42.50 after taxes, you'd have:
$42.50 ÷ 1.08 = $39.35
Subtract the Pre-Tax Price From Post-Tax Price
Now that you know how much the stuffed animal cost before and after taxes, you can subtract the pre-tax price from the post-tax price to find out how much tax you actually paid:
$42.50 - $39.35 = $3.15 is the amount of tax you paid.