Percentage calculator
Pick what you need, enter two numbers, get the percent with the steps.
How do I calculate a percentage of a number?
Turn the percent into a decimal by dividing it by 100, then multiply. 15% of 80 is 0.15 × 80 = 12. A quick check: 10% is 8, so 15% is 8 plus half of 8.
How do I find what percent one number is of another?
Divide the part by the whole and multiply by 100. 30 out of 120 is 30 ÷ 120 = 0.25, which is 25%.
How do I calculate percent change?
Subtract the old value from the new one, divide by the old value and multiply by 100. From 50 to 65 is (65 − 50) ÷ 50 × 100 = 30% more; from 80 to 60 is (60 − 80) ÷ 80 × 100 = 25% less.
How do I find the whole when I know a part and its percent?
Divide the part by the percent as a decimal. If 12 is 15% of a number, the number is 12 ÷ 0.15 = 80.
What is the difference between percent change and percent difference?
Percent change measures from a starting value, so it has a direction. Percent difference compares two values with neither as the start: the gap divided by their average. For 40 and 60 it is 20 ÷ 50 = 40%, while the change from 40 to 60 is 50%.
Why does a 20% increase followed by a 20% decrease not return to the start?
Each percent applies to a different base. $200 up 20% is $240, and 20% of $240 is $48, so the decrease leaves $192, which is 4% below where you began. The same is true of two-step discounts.
What is the difference between percent and percentage points?
Percentage points subtract two percentages; percent change divides that gap by the starting percentage. A rate rising from 4% to 5% is up 1 percentage point, but up 25% in relative terms.
How the four calculations relate
Every percentage problem fits one relation: part = percent ÷ 100 × whole. Solve for the part (what is X% of Y), for the percent (part ÷ whole × 100), or for the whole (part ÷ (percent ÷ 100)). Percent change is a fourth form: (new − old) ÷ old × 100, using the absolute value of the old number as the base, so a change always has a sign. When the starting value is zero, percent change cannot be computed and the calculator says so.
Worked examples
18 is what percent of 250? 18 ÷ 250 × 100 = 7.2%, and checking backward, 7.2% of 250 is 0.072 × 250 = 18. If 45 is 12.5% of some number, the number is 45 ÷ 0.125 = 360. A price that goes from $80 to $100 rises 25%, but going back from $100 to $80 is a drop of 20%; the amounts are the same $20, but the base differs.
Common mistakes
Using the wrong base is the usual error: percent change is measured from the starting value, not the ending one, which is why +25% and −20% are inverses. Adding successive percents is another: two increases of 10% make 21%, not 20%, because the second 10% applies to a larger number. A third is moving the decimal point wrongly when converting (6% is 0.06, not 0.6). Check the answer for sense: 15% of a number should be a little more than a tenth of it.
Sources: OpenStax Prealgebra 2e, chapter 6 (Percents) for percent of, finding the percent and finding the whole; percent change and percentage points as defined in standard statistics and algebra texts. Related: discount calculator, percent error calculator, fraction to percent calculator and tip calculator.