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.
In deal season the same base-shift arithmetic checks the sale tags: the Black Friday calculator (this calculator as a preset, pre-loaded for deal offers) works stacked discounts, BOGO and per-unit prices, the buy one get one calculator is the same idea aimed at one offer (what “buy one, get one half price” really works out to per item once the whole basket is counted), and the Black Friday hub asks whether the “was” price was ever real.
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.