ABC Tools

VAT and Sales Tax, Explained

After reading this you will be able to add a tax rate to a net price and, harder, pull the tax back out of a gross price without making the mistake almost everyone makes.

What the tool does and one example to fix the idea

Consumption taxes come in two shapes. Value added tax (VAT), used across Europe, is baked into the shelf price you see. Sales tax, common in the United States, is added at the register. Either way, two questions cover almost every real situation: how much is a price with tax, and how much tax is hiding inside a price you already paid.

Here is the hook. A receipt shows a gross total of 120 and says it includes 20% VAT. How much of that 120 is tax? The tempting answer is 20% of 120, which is 24. That is wrong. The correct answer is 20. The reason is that the 20% was applied to the net price of 100, not to the gross of 120. Getting this backwards is the single most common error with tax arithmetic, and the rest of this article makes sure you never make it.

When to use each direction

Use the add direction when you have a price before tax and want the final amount. A freelancer quoting a net fee of 500 at 20% VAT needs to invoice 600. A US shopper looking at a pre-tax price of 40 with 8.875% sales tax wants to know the checkout total.

Use the remove direction when the tax is already inside the number. You have a gross receipt and need the net figure for bookkeeping, or you want to know how much tax you actually paid. This is the calculation people get wrong, so it is worth slowing down for.

VAT and sales tax behave identically in this arithmetic. The percentage is applied to the net price in both systems. The only real difference is whether the tax is shown separately (US sales tax) or already folded into the sticker price (European VAT).

The formula and the intuition behind it

Let N be the net price, r the tax rate written as a decimal (20% is 0.20), and G the gross price. Adding tax is multiplication:

G = N \times (1 + r)

The 1 is the price itself and r is the tax stacked on top. At 20%, you pay 1 + 0.20 = 1.20 times the net price.

Removing tax is the same equation solved for N. Since gross equals net times (1 + r), net equals gross divided by (1 + r):

N = \frac{G}{1 + r}

The tax portion is then simply the difference:

T = G - N = G \times \frac{r}{1 + r}

That last fraction is the key. To extract 20% VAT you do not multiply the gross by 0.20. You multiply by \frac{0.20}{1.20}, which is 0.1667, about 16.67%. The tax is 20% of the smaller net figure, so it is a smaller share of the larger gross figure. That is why division, not subtraction, is the right move.

A worked example reproducing the demo

Adding 20% to a net price of 100

These are the tool's default values: mode add, amount 100, rate 20.

  1. Convert the rate to a decimal: r = 20 / 100 = 0.20.
  2. Compute the multiplier: 1 + r = 1.20.
  3. Multiply the net price: G = 100 \times 1.20 = 120.
  4. The tax added is 120 - 100 = 20.

So a net price of 100 becomes a gross price of 120, with 20 of tax.

Now reverse it: extracting the tax from 120

Switch to remove, keep amount 120 and rate 20. You should land back where you started.

  1. Multiplier is still 1 + 0.20 = 1.20.
  2. Net price: N = 120 / 1.20 = 100.
  3. Tax inside the gross: 120 - 100 = 20.

Twenty, not twenty-four. If you had wrongly taken 20% of 120 you would have reported 24 of tax and a net of 96, which does not add back up correctly: 96 \times 1.20 = 115.2, not 120.

Why the two directions are not symmetric

People expect adding and removing to be mirror images with the same percentage, and they are not. The chart below plots the tax fraction of the total price for each direction across a range of rates. The gap between the two curves is exactly the mistake to avoid.

The blue bars treat the rate as a share of the gross (the common error). The correct share, in the second series, is always smaller, and the gap widens as the rate rises.

At 27% (Hungary's rate, the highest standard VAT in the European Union), the tax is \frac{0.27}{1.27} = 0.2126, so it is 21.26% of the gross, not 27%. The higher the rate, the bigger the trap.

Explore the reverse calculation

Move the rate and watch the split of a fixed gross price of 120 into net and tax. Notice how the tax share never equals the rate itself.

With a gross price fixed at 120: at a 10% rate the net is 109.09 and the tax is 10.91; at 20% the net is 100.00 and the tax is 20.00; at 27% the net is 94.49 and the tax is 25.51. The tax always works out to gross times r/(1+r), which is less than the rate applied to the gross.

Reading and interpreting the result

The tool gives you three numbers: the net, the tax, and the gross. Always sanity-check that they reconcile. Net plus tax must equal gross, and net times (1 + r) must equal gross. If those two checks pass, your arithmetic is sound.

For invoicing, the net is your income and the tax is money you hold on behalf of the tax authority; it is not yours to keep. For expense claims, the net is usually the deductible business cost and the tax may be reclaimable depending on local rules. This tool computes the split. It does not tell you what you are legally allowed to reclaim.

Rounding can make the three figures disagree by one cent. If you round net and tax independently to two decimals, they may not sum to an exact gross. Decide which number is authoritative (usually the gross you actually paid) and derive the other two from it.

Common mistakes

Subtracting the rate from the gross
Taking 20% off 120 to get the net gives 96, but the true net is 100. Divide by 1.20 instead.
Using the wrong rate
Many goods sit at reduced rates. Food, books and medicine often carry 5% or 0% rather than the standard rate. Applying the standard 20% to a reduced-rate item overstates the tax.
Confusing tax-inclusive and tax-exclusive prices
European sticker prices already include VAT (use remove). US pre-tax prices do not (use add). Mixing these up doubles or omits the tax.
Compounding two taxes
If a jurisdiction has separate state and city sales taxes, add the rates first, then apply once. Applying one after the other multiplies the base twice and inflates the total.

Related tools

Tax is one adjustment to a price among several. To take money off instead of adding it, the Discount Calculator handles sale prices and stacked reductions. For a restaurant bill, the Tip Calculator covers the gratuity and the split. When comparing package sizes where tax is constant, the Unit Price Comparison tells you which is cheaper per unit. If your price is in another currency, convert it first with the Currency Converter, then apply tax. And to see what a tax-inclusive price was worth in an earlier year, the Inflation Calculator adjusts for changing prices over time.

Frequently asked questions

How do I remove 20% VAT from a price?

Divide the gross by 1.20. A gross of 120 gives a net of 100, so the VAT is 20. Do not multiply by 0.20, which would wrongly give 24.

Why is the tax not just 20% of the total?

The 20% is charged on the net price, which is smaller than the gross. As a share of the gross the tax is \frac{r}{1+r}, so 20% VAT is 16.67% of the gross total.

What is the difference between VAT and sales tax?

The arithmetic is the same. VAT is usually shown inside the displayed price and collected at each stage of production; US sales tax is added at the final register. For this calculator, treat them identically and just enter the rate.

Can I use this for a reduced or zero rate?

Yes. Enter whatever rate applies to the item, such as 5% for many books or 0% for exempt goods. At 0% the gross equals the net and the tax is zero.

How do I combine a state and a local sales tax?

Add the two percentages into a single rate and apply it once. A 6% state rate plus a 2.5% city rate is 8.5% total on the net price.

This is an educational estimate, not financial advice. Tax rules and reclaim rights vary by country and by product; check the current local rules or ask a qualified adviser before relying on the figures.

Try it yourself in the tool

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