Percentage
calculator.
Answer every common percentage question in one place: a percent of a number, what percent one number is of another, the whole from a part, percentage change and difference, increases and decreases, and undoing a percentage.
Percent means
per hundred.
- P% of N = P ÷ 100 × N.
- A is (A ÷ B × 100)% of B; A is P% of A ÷ (P ÷ 100).
- Percentage change from A to B = (B − A) ÷ |A| × 100. It depends on direction.
- Percentage difference = |A − B| ÷ the average of |A| and |B| × 100. It is the same both ways.
- Undo a P% change by dividing by (1 ± P ÷ 100), never by applying the opposite percentage.
How do you calculate a percentage of a number?
Divide the percentage by 100 and multiply by the number. 15% of 80 is 15 ÷ 100 × 80 = 12. Percentages are reversible in a useful way: 15% of 80 equals 80% of 15.
What percent is one number of another?
Divide the part by the whole and multiply by 100. 18 out of 24 is 18 ÷ 24 × 100 = 75%. To find the whole from a part and a percentage, divide instead: if 20 is 25% of something, the whole is 20 ÷ 0.25 = 80.
Percentage change versus percentage difference
Percentage change has a direction: from 80 to 100 is +25%, but from 100 back to 80 is −20%, because each change is measured against its own starting value. Percentage difference compares two values with no before and after, such as two quotes of $40 and $60: their difference of 20 is 40% of their average of 50, whichever you list first.
Why adding the percentage back does not undo a discount
A 20% discount turns $120 into $96. Adding 20% back to $96 gives $115.20, not $120, because the second 20% is taken from a smaller number. Divide instead: $96 ÷ 0.80 = $120.
Percentage points
When a percentage itself changes, say an interest rate from 4% to 6%, the difference is 2 percentage points. In relative terms the rate rose by 50%. Reports that mix the two can make a change sound far larger or smaller than it is.
Worked examples.
What is 15% of 80?
A 15% tip on an $80 bill.
12. Divide 15 by 100 and multiply by 80.
Load this exampleWhat percent is 18 of 24?
You answered 18 of 24 questions correctly.
75%.
Load this example20 is 25% of what?
A $20 deposit is 25% of the price.
80: divide 20 by 0.25.
Load this examplePercentage change from 80 to 100
A price rises from $80 to $100.
+25%. Going back from 100 to 80 is −20%, not −25%.
Load this examplePercentage difference between 40 and 60
Two quotes for the same job: $40 and $60.
40% of their average of 50.
Load this exampleUndo a 20% discount
A jacket costs $96 after 20% off. What was the original price?
$120. Adding 20% back to $96 gives $115.20, which is wrong.
Load this exampleInterest rate from 4% to 6%
A rate rises from 4% to 6%.
2 percentage points, which is a 50% relative increase.
Load this exampleWhat this calculator
does not do.
- It works with plain numbers; it does not compound repeated percentage changes over time.
- Percentage change is undefined from a starting value of zero.
- Results are shown to up to 12 significant figures.
Common questions.
How do I calculate 20% of a number?
Multiply the number by 0.2. For example, 20% of 150 is 30.
Is a 50% increase undone by a 50% decrease?
No. 100 plus 50% is 150, and 150 minus 50% is 75. To return to 100 you need a decrease of one third (33.33%).
What is the difference between percent and percentage points?
Percentage points measure the gap between two percentages (4% to 6% is 2 points). Percent measures relative change (that same move is a 50% increase).
How do I find the original price before a discount?
Divide the sale price by (1 − discount ÷ 100). A $96 item after 20% off was $96 ÷ 0.8 = $120.
- Wikipedia, Percentage point — percentage points versus relative percent change
- Math is Fun, Percentage Difference — difference divided by the average of the two values
Legacy golden vectors carried over from the previous percentage engine plus 300 randomized round trips (percent of → whole, increase → reverse) that must recover the starting value.