“20% off, then another 10%”, “the VAT in this price including tax”, “the rent rose from 5 to 7%”: percentages are everywhere, and so are the mistakes. Most come from the same confusion: a percentage is always of a base, and that base changes from one calculation to another. This guide gives the formulas, checkable examples and the classic traps.
The three basic calculations
| Question | Formula | Example |
|---|---|---|
| X% of Y | Y × X ÷ 100 | 25% of 80 = 80 × 25 ÷ 100 = 20 |
| X is what % of Y | X ÷ Y × 100 | 20 is 25% of 80 |
| Change from A to B | (B − A) ÷ A × 100 | From 80 to 100: +25%. From 100 to 80: −20% |
The last example surprises: a 25% rise is offset by a 20% fall, not a 25% one, because the base is no longer the same. Percentage Calculator brings together six calculations (X% of Y, X is what percentage of Y, change between two values, increase or decrease an amount, find the total from a percentage, difference in percentage points). Each is pre-filled with an example: change the values and the result updates, with the formula applied to your numbers. Change is always measured against the starting value; a zero starting value is flagged instead of returning a meaningless result.
Percentage points or percent?
If a rate goes from 5% to 7%, it rises by 2 percentage points, but by 40% in relative terms (2 ÷ 5). The media often mix the two. When comparing two rates with each other, speak in points; when comparing two amounts, speak in percent.
Discounts: why 10% then 20% is not 30%
A 10% then 20% discount applies to an already reduced price: 100 becomes 90, then 72. The total discount is 28%, not 30%. The formula: 1 − (1 − 0.10) × (1 − 0.20) = 0.28.
VAT in both directions with VAT & Sales Tax Calculator
From excluding tax to including tax, you multiply: with a 20% tax, 100 excluding tax gives 120 including tax. The other way, you divide: 120 including tax ÷ 1.20 = 100 excluding tax. The classic mistake is to take 20% off 120 (giving 96) instead of dividing by 1.20, because the 20 of tax is 20% of the net price, not of the gross one.
- Say whether your amounts are excluding or including tax and enter the rate. It is free-form: no rate is imposed, and buttons offer common rates.
- Enter one or more lines. Each can have its own rate, handy for a multi-rate invoice; the breakdown by rate is shown.
- Choose the rounding: “per line” rounds each line then adds up, like an invoice; “on the total” adds each rate's base before rounding the tax.
- Read the net total, the tax and the gross total.
Rounding sometimes changes the result by a cent. Example: three items at 1.99 excluding tax with 20% tax. Per line, each tax is 0.398 rounded to 0.40, so 1.20 in total; on the total, 5.97 × 20% = 1.194 gives 1.19. Both methods are common: follow the one your country or invoicing software requires. Decimal quantities (2.5 kg) are accepted, with comma or dot.
Common mistakes
- Adding successive percentages instead of compounding them.
- Subtracting the VAT percentage instead of dividing by 1 plus the rate.
- Confusing percentage points and percent.
- Calculating a change from the wrong base: it is always the starting value.
- Applying an outdated VAT rate or one that does not match the product or country.
Honest limits
- VAT rates are not updated automatically: check the one that applies to your situation. The tools calculate, they do not give tax advice.
- Legal rounding rules vary by country and software.
- Calculations are exact in decimals (no 0.1 + 0.2 = 0.30000000000000004), but display is limited to the number of decimals chosen.
Frequently asked questions
How do I calculate 15% of 240?
240 × 15 ÷ 100 = 36.
How do I get the price excluding tax from the price including tax?
Divide the gross price by 1 plus the rate: at 20%, divide by 1.20. 120 including tax gives 100 excluding tax.
Why don't two 10% discounts make 20%?
The second applies to an already reduced price: 100 becomes 90, then 81, a total discount of 19%.
What is a percentage point?
It is the gap between two rates: from 5% to 7%, the gap is 2 points, a relative rise of 40%.
Are my amounts sent anywhere?
No. Calculations are done in your browser.