How Percentages Are Calculated
A percent is a number expressed as a fraction of 100, so 25% means 25 out of every 100. Every percentage problem is a variation of the same relationship between a part, a whole and a rate, and the calculator covers the three you are most likely to need:
- B% of A: multiply A by B and divide by 100. 20% of 250 = 250 × 20 / 100 = 50.
- A is what percent of B: divide A by B and multiply by 100. 50 out of 200 = 50 / 200 × 100 = 25%.
- Percent change: subtract the original value from the new value, divide by the original value and multiply by 100. From 100 to 120 = (120 − 100) / 100 × 100 = 20% increase.
Example: Discounts and Raises
A jacket priced at $80 is marked 25% off. 25% of 80 is 80 × 25 / 100 = $20, so you pay $60. If your rent goes from $1,500 to $1,620 a month, the percent change is (1,620 − 1,500) / 1,500 × 100 = an 8% increase.
Why an Increase and a Decrease Are Not Symmetric
Percent change is always measured against the starting value. Going from 50 to 65 is a 30% increase, but going back from 65 to 50 is only a 23.08% decrease because the base is now larger. The same reason explains why a 10% drop followed by a 10% gain leaves you slightly below where you started.
Frequently Asked Questions
How do I calculate a percentage of a number?
Multiply the number by the percentage and divide by 100. For example, 15% of 240 is 240 × 15 / 100 = 36. You can also convert the percentage to a decimal first: 240 × 0.15 = 36.
How do I find what percent one number is of another?
Divide the part by the whole and multiply by 100. If you answered 18 of 24 questions correctly, your score is 18 / 24 × 100 = 75%.
How do I calculate a percentage increase or decrease?
Use (new value − original value) / original value × 100. A positive result is an increase and a negative result is a decrease. A price that moves from $40 to $46 has risen by 15%.
What is the difference between percent and percentage points?
Percentage points describe the arithmetic gap between two percentages, while percent describes the relative change. If an interest rate rises from 4% to 5%, it went up by 1 percentage point, which is a 25% increase in the rate itself.