Tax arithmetic
Add tax to a price, or take it back out of one
One rate or two, additive or compound, on any rate you type. It shows its working and it does not guess which rate applies to you.
How do you add VAT to a price, and how do you take it out again?
Adding tax is a multiplication: multiply the net price by the rate and add the result, so a net price of 100 at 20 per cent becomes 120. Taking tax back out of a gross price is not a subtraction, and this is where most spreadsheets go wrong. Subtracting 20 per cent from 120 gives 96, which is not the net price. You divide instead: the net is the gross divided by one plus the rate, so 120 divided by 1.2 is 100, and the tax is the 20 left over. This calculator does both directions, handles a second rate either added alongside the first or charged on top of it, and shows every line so you can check it against an invoice.
Your result
Fill in the fields above and the answer appears here.
How this is worked out
One rate or two, additive or compound, on any rate you type. It shows its working and it does not guess which rate applies to you.
- Tax equals the net price multiplied by the rate, rounded to the nearest minor unit. The gross is the net plus the tax.
- The net equals the gross divided by one plus the rate, rounded to the nearest minor unit. The tax is then whatever is left over, gross minus net, so the two always add back up to exactly the amount you typed.
- With two additive rates each is charged on the original net price and the two tax lines are rounded separately and then added. With compound selected, the second rate is charged on the net plus the first tax instead.
A worked example
Take 100 at a rate of 20 per cent. Adding tax gives 20 of tax and 120 to pay. Now start from 120 and take the tax back out: divide by 1.2 and you are at 100, with 20 of tax. Subtracting 20 per cent from 120 would have given 96, which is four short. That round trip is the one an invoice has to survive.
What this assumes
- The rate is the one you type. This calculator never decides which rate applies to a sale, never works it out from where you or your customer are, and gives no tax advice. Which rate applies is a question for your accountant or your tax authority.
- Each tax line is rounded to the nearest minor unit on its own and the lines are then added, which is the rule most invoices follow. Rounding the total instead can differ by one minor unit, and that is exactly the difference an accountant queries.
- When taking tax out, the net is rounded and the tax is the remainder, so the two always sum to the gross you entered.
- The preset chips are standard rates only. Reduced, zero and exempt rates exist and none of them are offered here, because offering them would mean choosing one for you.
- Where the tax is owed is a separate question from what the arithmetic is. Distance-selling thresholds, digital-services rules and economic nexus all decide which authority you owe, and none of them are computed here.
Questions about this calculator
Short answers, and none of them hedge. If yours is not here, ask us on the contact page.
Why can I not just subtract the rate to get the price before tax?
Because the tax was charged on the smaller number, not the bigger one. Twenty per cent of 100 is 20, so the gross is 120, but twenty per cent of 120 is 24. Subtracting takes off 24 and leaves 96, which is four short. You have to divide by one plus the rate, and that is what this does.
What is the difference between the two rates being additive and compound?
Additive means both rates are charged on the original price and the two amounts are added. Compound means the second rate is charged on the price plus the first tax, so you pay a little tax on the tax. Additive is the default because it is what most places with two rates do.
Does this tell me which rate to charge?
No, and it never will. It does arithmetic on a rate you supply. The preset chips are common standard rates offered as a convenience and dated, and typing over them is expected. Which rate applies to a particular sale depends on what you sold, to whom and where, and that is a question for your accountant or your tax authority.
Can I use this for sales tax rather than VAT?
Yes. The arithmetic is identical, which is why the same page answers at both addresses. The two-rate option covers a state rate plus a local rate, and the compound toggle covers the places that charge one on top of the other.
Why does the tax sometimes end a cent away from what I expected?
Rounding. Each line is rounded to the nearest minor unit separately and then added, which is what most invoices do. Rounding the total instead gives a slightly different answer, and neither is wrong, but they disagree by a cent and it is worth knowing which one you are looking at.
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