How to Work Out VAT Backwards
Adding VAT is easy. Taking it off again is where almost everyone goes wrong, because the obvious move — subtracting the VAT rate — quietly gives the wrong number every single time.
In short
- To remove VAT you divide by 1 + the rate, not subtract the rate.
- Subtracting 21% from a gross price undercounts the net price by roughly 4.3%.
- The error grows with the rate: it is about 1.0% at 10% VAT and about 4.0% at 25%.
- The VAT element is the gross price minus the net price — never the rate applied to the gross.
The mistake almost everyone makes
You have an invoice for 121.00 including 21% VAT and you need the net figure for your books. The instinct is to take 21% off: 121.00 − 25.41 = 95.59. That number is wrong, and it is wrong by more than a rounding error.
The correct net price is 100.00. The gap of 4.41 is not a rounding difference — it is a structural mistake that will misstate every line in your accounts in the same direction.
Why subtracting fails
The reason is that the VAT percentage is applied to the net price, not to the gross price. Those are two different bases, and a percentage means nothing without knowing what it is a percentage of.
When you add VAT you calculate 21% of 100.00 and get 21.00. When you subtract 21% from 121.00 you are calculating 21% of 121.00, which is 25.41 — a percentage of the wrong number. You have quietly changed the base halfway through the sum.
This is the same trap as a discount followed by an equal-sized increase. Take 20% off 100 and you have 80; add 20% back to 80 and you have 96, not 100. Percentages are not reversible by simply flipping the sign.
The rule that works
Because gross = net × (1 + rate), reversing it means dividing rather than subtracting:
net = gross ÷ (1 + rate)
At 21%, that is gross ÷ 1.21. So 121.00 ÷ 1.21 = 100.00 exactly. The VAT element is then simply the difference: 121.00 − 100.00 = 21.00.
Never calculate the VAT element by applying the rate to the gross price. Work out the net figure first, then subtract it from the gross. That ordering is what keeps the two numbers consistent with each other.
The divisors for common rates
The divisor is always 1 plus the rate expressed as a decimal. These are the rates you are most likely to meet in Europe:
| VAT rate | To add VAT, multiply by | To remove VAT, divide by | Net share of gross |
|---|---|---|---|
| 5% | 1.05 | 1.05 | 95.24% |
| 7% | 1.07 | 1.07 | 93.46% |
| 10% | 1.10 | 1.10 | 90.91% |
| 19% | 1.19 | 1.19 | 84.03% |
| 20% | 1.20 | 1.20 | 83.33% |
| 21% | 1.21 | 1.21 | 82.64% |
| 23% | 1.23 | 1.23 | 81.30% |
| 25% | 1.25 | 1.25 | 80.00% |
How big is the error, really?
Large enough to matter, and it always runs the same way — subtracting always understates the net price and overstates the VAT you have paid. The size of the error depends on the rate:
| Rate | Gross | Correct net | Net if you subtract the rate | Understated by |
|---|---|---|---|---|
| 10% | 110.00 | 100.00 | 99.00 | 1.00 (1.0%) |
| 19% | 119.00 | 100.00 | 96.39 | 3.61 (3.6%) |
| 21% | 121.00 | 100.00 | 95.59 | 4.41 (4.4%) |
| 25% | 125.00 | 100.00 | 93.75 | 6.25 (6.3%) |
On a single coffee that is pennies. Across a year of purchase invoices it is a systematic bias in one direction, which is exactly the kind of error a bookkeeper or a tax inspector notices, because it never cancels out.
A sanity check you can do in your head
The net price must always be a bit more than "gross minus the rate" suggests. If you have subtracted and got 95.59, the true answer is above that, not below.
A quicker check: at 21% VAT, the net price is always about 82.6% of the gross. Anything close to 80–85% of the gross is plausible; anything below that means you have subtracted when you should have divided.
If you want the VAT element alone as a fraction of the gross price, it is rate ÷ (1 + rate). At 21% that is 0.21 ÷ 1.21 = 17.36% of the gross. Multiply the gross by 0.1736 and you get the VAT directly — 121.00 × 0.1736 = 21.00.
Where this bites in practice
Three situations produce the error most often. The first is expense claims, where someone has a receipt showing only the total and needs to split it. The second is pricing: a shop decides on a shelf price of 24.99 including VAT and needs to know what it actually earns. The third is reconciling a payment processor statement, where fees and VAT are often reported on different bases.
In all three the fix is the same. Identify which figure you have — net or gross — before touching a calculator, because the arithmetic runs in opposite directions depending on the answer.
Frequently Asked Questions
How do I remove 21% VAT from a price?
Divide the gross price by 1.21. For a gross price of 121.00 that gives a net price of 100.00, and the VAT element is the difference, 21.00. Do not subtract 21% from the gross price — that gives 95.59, which is wrong by 4.41.
Why can I not just subtract the VAT percentage?
Because VAT is charged as a percentage of the net price, not of the gross price. Subtracting the rate applies it to the gross figure instead, which is a larger number, so you remove too much. The two bases are different, and a percentage is meaningless without knowing its base.
What is the VAT element of a gross price?
It is the gross price minus the net price. Equivalently, it is the gross multiplied by rate ÷ (1 + rate) — at 21% that is 17.36% of the gross. Never apply the VAT rate directly to a gross figure.
Does this work the same for sales tax in the US?
The arithmetic is identical for any tax added on top of a net price, so dividing by 1 + the rate recovers the pre-tax figure. The practical difference is that US prices are usually advertised before tax, so you far more often need to add it than remove it.
What if a price includes two different VAT rates?
You cannot reverse a mixed-rate total with a single divisor. Split the invoice into the lines at each rate first, reverse each group separately with its own divisor, and then add the results. Any total that combines rates has to be broken apart before the arithmetic works.