About Percentages
A percentage is a way of expressing a number as a fraction of 100. The word comes from the Latin per centum, meaning "by the hundred". So 25% is simply another way to write 25/100 or 0.25, and 100% means "the whole thing". Percentages are used everywhere — from tax rates and discounts to interest rates, test scores, statistics and growth metrics — because they make comparisons between different-sized quantities easy.
Every percentage problem, no matter how it is phrased, reduces to one of four basic formulas. Learn which formula applies to which situation, and you will never be stuck on a percentage question again.
The four percentage formulas
| Question | Formula | Example |
|---|---|---|
| What is X% of Y? | (X ÷ 100) × Y | 25% of 200 = 0.25 × 200 = 50 |
| X is what % of Y? | (X ÷ Y) × 100 | 30 of 150 = (30 ÷ 150) × 100 = 20% |
| % change from X to Y | ((Y − X) ÷ X) × 100 | 50 → 75 = ((75 − 50) ÷ 50) × 100 = +50% |
| X is Y% of what? | X ÷ (Y ÷ 100) | 80 is 40% of 200 (since 80 ÷ 0.40 = 200) |
Percentage increase vs percentage decrease
Percentage change describes how much a value has moved relative to where it started. The sign tells you the direction:
- Positive % — the value increased. From 100 to 120 is a +20% change.
- Negative % — the value decreased. From 100 to 80 is a −20% change.
- Zero % — no change. The value stayed the same.
The denominator is always the original value, not the new one. This is why a 50% increase requires only a 33.3% decrease to undo it: 100 → 150 is +50%, but 150 → 100 is only −33.3%. This asymmetry is a common trap in financial and statistical analysis.
Percentages vs percentage points
A crucial distinction: when the underlying quantity is already a percentage, you cannot talk about "percentage change" without specifying whether you mean relative change or absolute change.
| Change | Meaning |
|---|---|
| Interest rate goes from 2% to 3% | +1 percentage point (absolute) = +50% relative change |
| Support rises from 40% to 50% | +10 percentage points = +25% relative change |
| Inflation drops from 4% to 3% | −1 percentage point = −25% relative change |
Journalists and advertisers frequently mix these up on purpose. "Interest rates rose 50%!" sounds alarming until you realise it means from 2% to 3% — a 1-point move.
Common percentage mental math
| Percentage | Trick |
|---|---|
| 10% | Move the decimal point one place left |
| 1% | Move the decimal point two places left |
| 5% | Half of 10% |
| 15% | 10% + 5% |
| 20% | 10% × 2, or divide by 5 |
| 25% | Divide by 4 |
| 50% | Divide by 2 |
| 200% | Multiply by 2 |
The commutative rule for percentages
X% of Y always equals Y% of X. So 8% of 50 = 50% of 8 = 4. This surprising identity comes straight from the formula (X ÷ 100) × Y = (Y ÷ 100) × X. It is often useful when one of the two is easier to work with mentally than the other. If someone asks you "what's 17% of 40?", it might be easier to think "what's 40% of 17?" — same answer, 6.8.
Common use cases
Discounts & Sales
Work out sale prices and savings from a percentage off.
Investment Returns
Calculate percentage gains or losses on investments.
Test Scores
Convert marks to percentages for exams and quizzes.
Taxes & Tips
Calculate sales tax, GST and tip amounts.
Statistics
Work out proportions, growth rates and survey results.
Fitness Tracking
Measure weight change and body composition shifts.
Privacy and accuracy
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