Percentage questions come up constantly in student life — what percentage you scored, how much a mark changed, what a percentage of a total is. This percentage calculator handles the three most common types instantly: X% of Y, X as a percentage of Y, and the percentage change from one value to another.
It is a pure browser calculator: type in the numbers, and the answer appears without any page reload.
A percentage of a number: 20% of 150 is 0.20 × 150 = 30. A number as a percentage of another: 30 out of 150 is (30 ÷ 150) × 100 = 20%. Percentage change between two numbers: from 150 to 180 is (180 − 150) ÷ 150 × 100 = 20%.
All three produce 20 in these examples and mean entirely different things, which is precisely why they get mixed up. Identify which question you are answering before reaching for a formula, because the arithmetic is trivial and the misidentification is not.
Percentage change always divides by the original value, not the new one. Marks rising from 60 to 75 is a 25% increase because the base is 60. Dividing by 75 gives 20%, which is the answer to a different question nobody asked.
The asymmetry follows from this and surprises people: a 50% fall followed by a 50% rise does not return you to the start. 100 falls to 50, then rises to 75, because each change applies to a different base. When reporting changes, state the base so a reader can follow.
A move from 40% to 45% is a rise of 5 percentage points and an increase of 12.5%. Both statements are correct and they describe different quantities, so writing "a 5% increase" when you mean percentage points is simply an error.
This matters wherever you report changes in proportions — pass rates, market share, response rates, unemployment. It is one of the most common mistakes in student results chapters and one of the easiest to avoid once you have noticed it exists.
If a price after a 20% discount is 80, the original was not 96. Divide rather than multiply: 80 ÷ 0.80 = 100. Adding 20% back to the reduced figure applies the percentage to the wrong base and undershoots every time.
The same logic recovers a pre-tax figure from a total, or an original mark from a scaled one. Whenever a percentage has already been applied and you want what came before it, division by (1 ± rate) is the operation you want.
(new − old) ÷ old × 100. The base is always the original value.
A move from 40% to 45% is 5 percentage points but a 12.5% increase. Use percentage points when comparing two percentages.
No. 100 falls to 50 and rises to 75, because each change is applied to a different base.
Divide rather than multiply. A price of 80 after a 20% discount was 80 ÷ 0.80 = 100.
Divide marks obtained by the total available and multiply by 100 — 68 out of 80 is 85%.