Percentage calculator
Three common percentage questions, each with its own answer. Type your numbers and the result updates as you go.
What is X per cent of a number?
For example a discount on a price, or the tax on an amount.
What per cent is one number of another?
For example how much of a budget one item takes.
How large is the change in per cent?
For example a price increase between two years.
How it works
Per cent means hundredths. Working out 15% of 80 is therefore the same as taking 15 hundredths of 80, which is 12.
To find what share something is, divide the part by the whole and multiply by 100. 12 out of 80 is 0.15, or 15%.
Percentage change is always measured against the starting value. Going from 200 to 250 is a 25% increase, while going back from 250 to 200 is a 20% decrease. The same difference in money gives different percentages depending on where you start.
A 50% increase followed by a 50% decrease does not cancel out. You end up at 75% of where you began.
How the tool calculates
Each of the three boxes uses its own formula: P% of X is P / 100 × X, the share is part / whole × 100, and the change is (to − from) / |from| × 100. Taking the size of the starting value keeps the direction right when it is negative: from −100 to −50 is an increase of 50%. The answer is shown to at most ten significant figures, so 20 out of 120 comes out as 16.66666667%. If the whole or the starting value is zero there is no percentage, because it would mean dividing by zero, and the tool says so instead of answering. From 0 to 0 counts as no change.
Spaces in the fields are ignored. Commas that separate thousands in the usual way, as in 1,250 or 12,500,000, are read as such, and 1,250.5 works too; any other single comma is a decimal point, so 2,5 is two and a half. The per cent sign is not typed into the fields; it already sits after the percentage box.
Per cent or percentage points
The third box always gives the relative change: the difference divided by the starting value. When the two numbers are themselves percentages, such as interest rates, that is rarely what people mean. In August 2024 the Bank of England reduced Bank Rate by 0.25 percentage points, from 5.25% to 5%. Enter 5.25 and 5 and the tool answers “A decrease of 4.761904762%”.
Both descriptions are right, but they answer different questions. The Office for National Statistics defines a percentage point as the difference between percentages: 10% falling by 1 percentage point becomes 9%, while a fall of 1% would leave 9.9%.
Example: VAT in a price
The standard rate of VAT in the UK is 20%. Something that costs £100 before VAT carries 20% of 100, or £20, and costs £120 with VAT. Put 20 as the part and 120 as the whole in the second box and the answer is 16.66666667%.
VAT is therefore 20% of the net price but only a sixth of the gross price. In general, a rate of p added on top makes up p / (100 + p) of the new total. That is why taking 20% off a price that includes VAT does not give the price without it: £120 less 20% is £96, not £100.