Percentage Calculator
What is X% of Y, X is what % of Y, and percentage change.
About the percentage calculator
Four calculators covering nearly everything people mean by "work out the percentage": what is X% of Y, X is what percent of Y, the percentage change from one number to another, and adding or subtracting a percentage from a starting figure.
The change calculator also reports the difference in plain numbers, because that is usually the figure you actually wanted. All four update as you type.
The formulas, in case you need to show your working
- X% of Y β
Y Γ X Γ· 100. 15% of 200 = 200 Γ 15 Γ· 100 = 30. - X is what % of Y β
X Γ· Y Γ 100. 30 out of 200 = 30 Γ· 200 Γ 100 = 15%. - Percentage change β
(new β old) Γ· |old| Γ 100. From 200 to 250 = 50 Γ· 200 Γ 100 = +25%. - Add a percentage β
Y Γ (1 + X Γ· 100). 200 plus 15% = 230. - Remove a percentage β
Y Γ (1 β X Γ· 100). 200 less 15% = 170.
Percentage points are not percentages
A rate moving from 4% to 5% has risen by one percentage point, but by 25% in relative terms. Both are correct and they describe the same change, which is why the distinction gets abused in reporting. If a figure is already a percentage, say "percentage points" when you mean the arithmetic difference.
The other frequent trap: a 50% fall followed by a 50% rise does not return you to where you started. 100 β 50 β 75. Percentage changes compound against a moving base, so they never simply cancel out.
Frequently asked questions
How do I calculate a percentage of a number?
Multiply the number by the percentage and divide by 100. For 15% of 200: 200 Γ 15 Γ· 100 = 30. Use the first calculator above and it does it as you type.
How do I work out percentage increase?
Subtract the old value from the new one, divide by the old value, and multiply by 100. From 200 to 250: (250 β 200) Γ· 200 Γ 100 = 25% increase.
How do I calculate a discount?
Use the fourth calculator: enter the original price and the discount percentage, and the "minus" figure is what you pay. A 30% discount on Β£80 gives Β£56.
What is the difference between percent and percentage points?
Percentage points are the plain arithmetic difference between two percentages; percent describes relative change. Going from 4% to 5% is a rise of one percentage point, but a 25% relative increase.
Why doesn't a 50% decrease then a 50% increase get me back to the start?
Because each change applies to a different base. 100 less 50% is 50; 50 plus 50% is 75. To reverse a 50% fall you need a 100% rise.