Percentage Calculator

One calculator for four everyday percentage questions

"Per cent" means "out of a hundred", and almost every percentage question is one of four kinds. You know a rate and want the amount, such as 18 percent GST on a bill. You know two amounts and want the rate, such as 45 correct answers out of 60. You know an old and a new value and want the change, such as a fee that went up from 80 to 100. Or you have marks in several subjects and want one overall figure for a form. Pick the matching button above and the answer updates as you type, with the formula shown underneath so you can check it by hand.

How to use it

1. Choose the question type: X% of Y, X is what % of Y, % change or Marks %.
2. Type your numbers. Decimals and negative values work in the first three modes.
3. For marks, enter each subject's marks and its maximum. Use Add subject for more rows and the remove button to delete one.

The formulas

• X% of Y = X x Y / 100. Example: 18% of 2,450 = 441.
• X as a percentage of Y = X / Y x 100. Example: 45 out of 60 = 75%.
• Percentage change = (new - old) / old x 100. A positive answer is an increase, a negative one a decrease.
• Marks percentage = total marks obtained / total maximum marks x 100.

Worked examples

A fee rises from 80 to 100. The difference is 20, and 20 is a quarter of the old value, so the increase is 25%. Now reverse it: a fee falls from 100 to 80. The difference is still 20, but it is measured against the old value of 100, so the decrease is only 20%. This is why a 25% rise followed by a 20% cut brings you back to where you started, and why the order of "from" and "to" matters.

For marks, the default rows hold English 78, Mathematics 91, Science 84, Social Science 72 and Hindi 80, each out of 100. That is 405 out of 500, or 81%. When subjects have different maximums, the tool adds the marks and the maximums before dividing. With 45 out of 50 (90%) and 60 out of 100 (60%), the overall figure is 105 out of 150, which is 70%, not the 75% you would get by averaging the two percentages. Adding first is the usual method for an aggregate, because a paper worth 100 marks carries twice the weight of one worth 50.

Percent or percentage points?

When a percentage itself changes, say so carefully. If your score goes from 60% in the first test to 75% in the second, it rose by 15 percentage points, but by 25 percent of its earlier level. Use the % change mode with 60 and 75 to see the second figure, and simple subtraction for the first.

Limits worth knowing

• Dividing by zero has no answer, so "X is what % of 0" and a change measured from 0 cannot be worked out; the tool says so instead of showing a misleading number.
• For a negative starting value, the change is measured against its size, so going from -50 to -25 shows a 50% increase.
• Results are rounded to two decimal places for display. Some boards round or truncate differently, and some count only the best five subjects or exclude an additional subject, so follow the rule your board or admission form states.
• A marks row where the marks are above the maximum is left out and highlighted in a message, so one typing slip cannot inflate your total.