The three percentage questions
Almost every percentage problem is one of three questions in disguise. The first asks for a slice of a number — what is X% of Y. The second runs the other way, asking how big one number is relative to another — A is what percent of B. The third measures movement over time — how much a value rose or fell as a percentage of where it started. This calculator handles all three, and switching between them makes it easy to see how the same numbers answer different questions.
The three formulas
X% of Y = X ÷ 100 × Y
A is what % of B = A ÷ B × 100
% change = (B − A) ÷ A × 100
where A is the original or part value and B is the total or new value. In each case the result is undefined when the base you divide by — the total in the second formula, the original in the third — is zero.
Worked example
Take the calculator's default question — what is 15% of 200? Converting the percent to a decimal and multiplying answers it in one line:
| Step | Amount |
|---|---|
| Percentagedivide by 100 to get the decimal 0.15 | 15% |
| of value | 200 |
| = 15% × 200 ÷ 1000.15 of 200 — the same working the calculator shows | 30 |
Computed with this calculator's default settings — open the tool above and you'll see the same numbers, then switch modes to ask the other two percentage questions.
Percent versus percentage points
The most common percentage mistake is treating a percentage point as if it were a percent. If an interest rate moves from 4% to 6%, the gap is 2 percentage points, but as a relative change the rate has risen by 50%. Both statements are correct and they describe the same move, yet they are very different numbers. Whenever you are comparing two percentages, be clear about whether you mean the plain difference between them (percentage points) or the change relative to the starting figure (percent).
Percentage change always uses the original value as its base, which is why a rise and an equal-looking fall do not cancel out: each is measured against a different number. That same base rule is what powers related tools — to take a percentage off a price use thepercent-off calculator, and to combine sale prices and savings use thediscount calculator.
Frequently asked questions
How do I work out what X% of Y is?
Divide the percentage by 100 to turn it into a decimal, then multiply by the value. The formula is X% of Y = X ÷ 100 × Y. For example, 15% of 200 is 15 ÷ 100 × 200 = 30. The percentage is really just a fraction out of a hundred, so dividing by 100 first is what converts “per cent” into a number you can multiply with.
How do I find what percent one number is of another?
Divide the part by the whole and multiply by 100. The formula is A is what % of B = A ÷ B × 100. So 30 out of 200 is 30 ÷ 200 × 100 = 15%. The order matters: the number you are measuring goes on top and the total it is being compared against goes on the bottom.
How is percentage change calculated?
Subtract the original value from the new value, divide by the original, and multiply by 100. The formula is % change = (B − A) ÷ A × 100, where A is the starting figure and B is the ending figure. Going from 200 to 250 is (250 − 200) ÷ 200 × 100 = +25%. The original value is always the base you divide by.
What is the difference between a percent and a percentage point?
A percentage point is the plain arithmetic gap between two percentages, while a percent describes the relative change between them. If a rate rises from 4% to 6%, that is an increase of 2 percentage points but a 50% increase in the rate itself. Confusing the two is one of the most common percentage mistakes, so it is worth being explicit about which one you mean.
Why do increases and decreases of the same percent not cancel out?
Because each percentage is taken from a different base. A 50% rise followed by a 50% fall does not return you to where you started: 100 grows to 150, then 50% of 150 is 75, leaving you below the original 100. Percentage change always uses the value at that moment as its base, so the same percent applied to a larger or smaller number is a different absolute amount.
Disclaimer: This calculator is foreducation and illustration only. It performs standard arithmetic on the numbers you enter and does not constitute financial, tax, or other professional advice.