How to use the percentage calculator
- Pick the question you are asking from the five buttons: X% of Y, X is what % of Y, X is Y% of what, % change or Add or subtract %.
- Type your numbers in the two boxes, such as Percentage (X) and Of this number (Y). Commas, a dollar sign and a trailing % sign are ignored, so 1,250 and $1,250 both work.
- Read the answer under the boxes. It updates as you type, and the formula underneath shows your own numbers worked through.
- In Add or subtract %, choose Increase by or Decrease by. Press Reset to the examples to bring back the starting numbers.
How the percentage formulas work
A percent is a fraction of 100, so every mode is one of these. X% of Y is X ÷ 100 × Y. X is what % of Y is X ÷ Y × 100. X is Y% of what is X ÷ (Y ÷ 100). Percent change is (new - old) ÷ |old| × 100, the same method the U.S. Bureau of Labor Statistics uses for the Consumer Price Index. Add or subtract % multiplies the starting number by 1 + X ÷ 100 or 1 - X ÷ 100.
Worked example with the starting numbers
The first mode opens with 15 and 200, and the result reads 15% of 200 = 30, because 15 ÷ 100 = 0.15 and 0.15 × 200 = 30. The other modes open with their own examples: 42 is 84% of 50, 30 is 15% of 200, a change from 80 to 100 is a 25% increase, and 200 increased by 15% is 230.
Limits and edge cases
Percent change from zero has no answer, because there is nothing to divide by, so the tool asks for a non-zero old value. If the old value is negative the tool divides by its absolute value, so going from -50 to 25 is +150%. Dividing by a zero total or a 0% rate is refused with a message. Numbers beyond 1,000,000,000,000,000 are refused, and answers are rounded to six decimal places. Percent changes are not symmetrical, which the % change result spells out: after 80 to 100 it tells you a 20% drop gets you back. For discounts with tax use the discount calculator or the sales tax calculator, for a score as a percentage the grade calculator, and for a quick sum the scientific calculator.
Source: BLS, Calculating percent changes.
Percentage calculator FAQ
How do I calculate a percentage of a number?
Divide the percentage by 100 and multiply by the number. For example, 15% of 200 is 15 ÷ 100 × 200 = 30.
How do I calculate percent increase or decrease?
Subtract the old value from the new value, divide by the old value, then multiply by 100. Going from 80 to 100 is (100 - 80) ÷ 80 × 100 = 25%, a 25% increase. A negative result means a decrease.
Why does a 50% drop followed by a 50% rise not get me back to the start?
Each percent applies to a different base. 100 dropped by 50% is 50, and 50 raised by 50% is only 75. To undo a 50% drop you need a 100% rise. The % change mode shows the reverse percent for your own numbers.
What is the difference between percent and percentage points?
A percent change compares two values as a share of the starting value, while percentage points are the plain difference between two percentages. A rate that rises from 4% to 5% went up 1 percentage point, which is a 25% increase.
How do I find the original price before a percent increase?
Divide the final amount by 1 plus the rate. If a price is 230 after a 15% increase, the original is 230 ÷ 1.15 = 200. In the X is Y% of what mode, enter 230 and 115 to get the same answer.