How to Calculate a Percentage of a Total
A percentage is a way of expressing a part as if the whole were 100. If 18 of 40 students passed, the pass rate is 45 per cent: 18 divided by 40 is 0.45, and 0.45 times 100 is 45. The arithmetic is simple. The mistakes usually come from choosing the wrong whole or from adding percentages that do not share a base.
The Percentage Calculator does the division and shows the result. This guide explains which number goes where.
Quick answer
Divide the part by the whole, then multiply by 100. The whole is the group or amount you are comparing against, not the part itself. If the answer is greater than 100, the “part” is larger than the whole you chose, which usually means the whole is wrong. Check the units and the base before you use the result.
Identify the part and the whole
In “18 of 40 students”, 18 is the part and 40 is the whole. In “a 20 per cent discount”, the whole is the original price, not the sale price. In “35 per cent of the budget”, the whole is the total budget, not the amount already spent. Naming the whole in words is the step that prevents most errors.
If the part and the whole are in different units, convert one before dividing. A part measured in grams and a whole measured in kilograms will produce a meaningless percentage. The same applies to currencies, hours, and percentages of percentages.
Do the division in the right order
Divide first, then multiply by 100. Dividing 18 by 40 gives 0.45. Multiplying by 100 moves the decimal two places, giving 45. If you multiply first, you get 1,800 divided by 40, which is also 45, but the intermediate number is larger and easier to mistype.
To find the part when you know the percentage, reverse the operation: multiply the whole by the percentage and divide by 100. To find the whole when you know the part and the percentage, divide the part by the percentage and multiply by 100. The Percentage Calculator supports all three directions, but write down which one you are doing.
Percentages of percentages
A 10 per cent increase followed by a 10 per cent decrease does not return to the original number. Start with 100: a 10 per cent increase gives 110; a 10 per cent decrease takes 10 per cent of 110, which is 11, leaving 99. The second percentage applies to a different whole. This is why “we raised prices by 10 per cent, then gave a 10 per cent discount” does not restore the old price.
The same trap appears with tax and discounts. A discount is usually calculated on the pre-tax price, while tax is calculated on the discounted price, depending on the jurisdiction and the wording. Check the order before combining the two.
Check the answer
Use a rough estimate. If 18 of 40 is 45 per cent, then 50 per cent would be 20, so 45 per cent is slightly less than half. That is plausible. If the calculator says 4.5 per cent or 450 per cent, the decimal point or the whole is wrong.
Check that the percentage is between 0 and 100 when the part is inside the whole. A result above 100 can be valid when the part is larger than the comparison base, such as a 120 per cent increase, but it should be explained rather than assumed. For the difference between a percentage change and a percentage-point change, read Percentage Increase, Decrease, and Difference Explained. For discounts and tax, see How to Calculate Discounts, Tax, and Tips.
Common questions
How do I calculate what percentage one number is of another?
Divide the part by the whole and multiply by 100. If 18 of 40 students passed, 18 divided by 40 is 0.45, so the pass rate is 45 per cent. The whole is the group you are comparing against, not the part itself.
Why can a percentage be more than 100?
A percentage above 100 means the part is larger than the whole you chose. That can be valid for an increase, such as a 120 per cent rise, or it can mean the wrong base was used. Check which number is the whole before treating the result as an error.
Is the Percentage Calculator private?
The Percentage Calculator runs in your browser, so the numbers you enter are not uploaded by the tool. It does not store your calculation history. Avoid entering confidential financial details on any shared device, because the screen may be visible to others.