The six questions
What is X % of Y? The basic one. 19 % of 250 is 47.50.
X is what % of Y? A share. 47.50 out of 250 is 19 %.
Change from X to Y. Growth or decline between two numbers. From 200 to 250 is plus 25 %; from 250 to 200 is minus 20 %. The two are not symmetrical, which is the single most common mistake with percentages.
Plus Y % and minus Y % apply a markup or a discount to an amount.
Gross and net converts between prices with and without VAT.
Why a discount does not undo a markup
Add 20 % to 100 and you get 120. Take 20 % off 120 and you get 96, not 100. The percentage always refers to its own base, and after the first step the base changed.
To reverse a 20 % markup, divide by 1.2 instead of subtracting 20 %. This tool’s gross-to-net direction does exactly that.
VAT, from the other direction
The frequent real task is: a receipt says 119 euros including 19 % VAT, how much VAT is in there? Not 19 % of 119. The net amount is 119 divided by 1.19, which is 100, so the VAT is 19 euros.
Common rates: Germany 19 % standard and 7 % reduced, Austria 20 % and 10 %, Switzerland 8.1 % and 2.6 %.
Questions
What is the difference between percent and percentage points?
If an interest rate rises from 2 % to 3 %, that is one percentage point but a 50 % increase. Reports mix these two up constantly.
How do I calculate VAT backwards from a gross price?
Divide by 1 plus the rate. At 19 %, divide the gross amount by 1.19 to get the net amount. Use the gross-to-net direction above.
Why is minus 20 % not the opposite of plus 20 %?
Each percentage refers to its own base value, and the base changes after the first calculation. Divide by 1.2 to reverse a 20 % markup.
Does the calculator round?
Results are shown with up to four decimals. Nothing is rounded internally, so chained calculations stay accurate.