Percentage calculator
Four small calculators on one page: a percent of a number, what percent one number is of another, the whole behind a part, and the percent change between two numbers. Fill in the boxes of the one you need.
What is a percent of a number?
What percent is one number of another?
What number is this a percent of?
How much did a number change, in percent?
How it works
The first box finds a part of a whole. It divides the percent by 100 and multiplies by the number, so 15 percent of 80 is 12.
The second box divides one number by the other and multiplies by 100, so 12 out of 80 is 15 percent. The third box works backward from a part and its percent. If 12 is 15 percent of a number, the number is 12 divided by 0.15, which is 80.
The last box measures a change as a share of where you started. From 80 to 100 is a rise of 25 percent. From 100 to 80 is a fall of 20 percent.
A worked example
A shirt costs $80 and is marked 15 percent off. The discount is $12, so you pay $68.
A price goes from $80 to $100. The rise is $20, which is 25 percent of $80. If it then falls back from $100 to $80, the fall is the same $20 but only 20 percent, because it is measured against $100.
Percent and percentage points
When a rate moves from 4 percent to 5 percent, it rises by one percentage point. As a percent change it is a rise of 25 percent, since the one point is a quarter of the 4 that you started with.
The two are easy to mix up, and they are not the same. The fourth box gives the percent change. The difference between the two rates is the number of points.
Where the answer stops
Every answer is shown with up to four decimals, so one third is 33.3333 percent. The boxes take numbers from 0 up, with no minus sign, and they do not divide by 0: a percent of 0, or a change from 0, has no answer.
Questions
How do I find a percent of a number?
Divide the percent by 100 and multiply by the number. 15% of 80 is 0.15 times 80, which is 12.
How do I calculate percent change?
Subtract the old number from the new one, divide by the old number and multiply by 100. From 80 to 100 the change is 20 divided by 80, which is a rise of 25%. From 100 to 80 it is a fall of 20%.
Why does a 25% rise not cancel a 25% fall?
Each change is a percent of a different number. A 25% rise takes 100 to 125, and a 25% fall from 125 takes it to 93.75, which is 6.25% below where you began.
What is the difference between percent and percentage points?
A rate that goes from 4% to 5% rose by 1 percentage point. As a percent change it rose 25%, because 1 is a quarter of 4.
How do I find the original number before a percent increase?
Divide the new number by 1 plus the percent as a decimal. After a 20% increase to 120, the original is 120 divided by 1.2, which is 100. In the third calculator, 120 is 120% of 100.
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