Twelve examples, worked end to end
Every example below is produced by the same calculator that runs on the home page, from the same payload, at the moment this page was built. None of them is typed in by hand, so none of them can drift away from what the tool actually does.
All twelve are at the standard rate, because the arithmetic is what is being demonstrated and mixing rates would obscure it. What changes down the table is the amount and the direction — and the second of those is where the interesting behaviour is.
| Amount entered | Treated as | Before VAT | VAT | Including VAT |
|---|---|---|---|---|
| €9.99 | a price before VAT | €9.99 | €2.30 | €12.29 |
| €9.99 | a price including VAT | €8.12 | €1.87 | €9.99 |
| €49.50 | a price before VAT | €49.50 | €11.39 | €60.89 |
| €49.50 | a price including VAT | €40.24 | €9.26 | €49.50 |
| €250.00 | a price before VAT | €250.00 | €57.50 | €307.50 |
| €250.00 | a price including VAT | €203.25 | €46.75 | €250.00 |
| €1,250.00 | a price before VAT | €1,250.00 | €287.50 | €1,537.50 |
| €1,250.00 | a price including VAT | €1,016.26 | €233.74 | €1,250.00 |
| €4,999.99 | a price before VAT | €4,999.99 | €1,150.00 | €6,149.99 |
| €4,999.99 | a price including VAT | €4,065.03 | €934.96 | €4,999.99 |
| €12,500.00 | a price before VAT | €12,500.00 | €2,875.00 | €15,375.00 |
| €12,500.00 | a price including VAT | €10,162.60 | €2,337.40 | €12,500.00 |
Read the first row, then the second
€9.99 treated as a price before VAT and €9.99 treated as a price including VAT produce different VAT figures from the same input. That is not a quirk — it is the whole reason the direction control exists, and it is the single most common way a VAT calculation goes wrong: someone reverses a gross figure by adding VAT to it.
One of them, expanded
Here is the fifth pair’s reverse calculation with the working shown — the same lines the calculator on the home page renders, from the same engine call:
| Step | What happens | The sum | Result |
|---|---|---|---|
| 1 | Price including VAT | the amount you entered | €4,999.99 |
| 2 | VAT already in the price | €4,999.99 × 23⁄123 — the same answer as dividing by 123 and multiplying by 23 | €934.96 |
| 3 | Price before VAT | €4,999.99 − €934.96 | €4,065.03 |
The middle row is the one worth memorising. The VAT inside a standard-rated gross price is the gross multiplied by the rate over one hundred plus the rate — not the gross minus 23% of itself, which is a different and smaller number. The reverse page shows both methods side by side so the gap is visible.
Every one of these reconciles
Add the third and fourth columns of any row and you get the fifth, exactly, with no cent missing. That is a property of how this engine rounds: the amount you entered stays as you typed it, the VAT is the figure that gets rounded, and the third number is the sum or the difference. Rounding all three independently would give you rows that are individually plausible and collectively out by a cent — which is the state most spreadsheets are in.
The convention is a decision this site had to make rather than a rule it found, and the methodology page says so in as many words. It is frozen in a golden-master file of 229 cases, so it cannot change without somebody justifying the change.