Adding tax vs extracting tax is a distinction about which number you start with. Both calculations use one rate, and they do not undo each other by a simple subtraction. Adding tax starts from a net amount, the price before tax, and builds a gross amount. Extracting tax starts from a gross amount, the price that already includes tax, and splits it into net and tax. Subtracting the rate from the gross answers neither question.
The rate here is a number you type. This article does not say what rate a country, state, or invoice should use, and it does not say whether a price is legally required to include tax. It only separates the two calculations.
Net is the amount before this tax. Gross is net plus the tax. If you know the net and the rate, you do not yet know the gross until you add the tax. If a receipt shows one figure that already includes tax, that figure is the gross. Treating it as the net and adding the rate again taxes the tax.
Write the rate as a percent. Tax is the net multiplied by that percent divided by 100. Gross is the net plus that tax.
tax = net × rate ÷ 100
gross = net + taxAt 10 percent, a net of 100.00 produces a tax of 10.00 and a gross of 110.00. The 10 is 10 percent of the net, not 10 percent of the 110.
The tax inside a gross amount is not the gross multiplied by the rate. The gross already contains the tax, so the base you want is smaller than the number in front of you. Divide the gross by 1 plus the rate as a fraction, or use the equivalent form below. Both isolate the same tax.
tax = gross × rate ÷ (100 + rate)
net = gross − taxAt 10 percent, a gross of 110.00 contains a tax of 10.00 and a net of 100.00. Check it the other way: 10 percent of 100.00 is 10.00, and 100.00 plus 10.00 is 110.00. The extract step recovered the amount the add step had built.
Take 10 percent of 110.00 and subtract it: 11.00 from 110.00 leaves 99.00. That is not the net. The 11.00 is 10 percent of a number that already includes tax, so it is larger than the tax that was added to 100.00. The gap is the whole point of the second formula. People often do this when a till shows one total and they want the pre-tax figure without changing the rate.
The same mistake appears in reverse. Someone sees 100.00 including tax and subtracts 10.00 because the rate is 10. The included tax on 100.00 at 10 percent is 100.00 × 10 ÷ 110, which is about 9.09, not 10.00. Ten subtracted from the gross only matches the included tax when the gross happens to be the net plus exactly that rate applied to the net, as in the 110.00 example. It is not a general rule.
Money is not left as a long decimal. The Sales Tax Calculator rounds the tax half away from zero to the cent, then sets the gross as net plus that rounded tax when you add, or the net as gross minus that rounded tax when you extract. After that rounding, the three displayed figures still agree: net plus tax equals gross. A rate can be entered to three decimal places. The page does not look up a jurisdiction, and it does not stack a second tax.
Use adding when the number you have is the price before this tax and you need the amount a buyer would pay after it. Use extracting when the number you have is already the tax-inclusive total and you need the tax and the pre-tax amount that sit inside it. If you are not sure which number you hold, the arithmetic cannot decide for you. Label the input before you pick a mode.
A discount is a different operation. Ten percent off a list price is not the same as removing a 10 percent tax from a gross price. One reduces a price by a share of itself. The other splits a price that was built as net plus a share of the net.
The calculator asks for one amount, one rate, and a mode: add or extract. It returns net, tax, and gross. It will not tell you whether a product should be taxed, which rate applies where you are, or how to file anything. Those are outside a single typed rate. Use it to check the arithmetic once you already know the rate and which of the two amounts you started with.
No. Subtracting 10 percent from 110 leaves 99. The tax inside 110 at 10 percent is 10, so the net is 100.
Net is the amount before this tax. Gross is the net plus the tax.
No. The rate is a number you already have. The article only separates the two formulas.
The Sales Tax Calculator adds tax to a net amount or extracts tax from a gross amount, and it rounds the tax to the cent.