What is X% of Y?
Formula: Result = (X ÷ 100) × Y
X is what % of Y?
Formula: Result = (X ÷ Y) × 100
Percentage Change
Formula: ((New − Old) ÷ Old) × 100
Increase a Value by %
Formula: Value × (1 + Percent ÷ 100)
Decrease a Value by %
Formula: Value × (1 − Percent ÷ 100)
Percentage Difference
Formula: |A − B| ÷ ((A + B) ÷ 2) × 100
How to Calculate Percentage?
Percentage is a way to express a number as a fraction of 100. The word "percent" comes from the Latin "per centum" meaning "by the hundred."
Basic Percentage Formula
Percentage = (Part ÷ Whole) × 100
Example: If 30 students passed out of 50, the pass percentage = (30 ÷ 50) × 100 = 60%.
Percentage Change Formula
To find how much a value has increased or decreased: % Change = ((New Value − Old Value) ÷ Old Value) × 100. A positive result = increase, negative = decrease.
Worked Examples
Example 1 — X% of Y: To find 15% of 800, calculate (15 ÷ 100) × 800 = 120.
Example 2 — X is what % of Y: If you scored 42 marks out of 60, the percentage is (42 ÷ 60) × 100 = 70%.
Example 3 — Percentage change: If a price rises from 500 to 575, the change is ((575 − 500) ÷ 500) × 100 = 15% increase.
Example 4 — Discount: A shirt costs 1,200 and has a 25% discount. The discount is 300, so you pay 900.
Percentage Increase vs Percentage Points
These two are often confused. If an interest rate moves from 5% to 7%, it has risen by 2 percentage points, but the percentage increase is (2 ÷ 5) × 100 = 40%. Always check which one a news report or offer is talking about.
Common Mistakes When Calculating Percentages
- Dividing by the new value instead of the original value when finding percentage change
- Adding a percentage increase and then subtracting the same percentage — a 20% rise followed by a 20% fall does not return to the starting value
- Forgetting to divide by 100 when converting a percentage into a decimal
- Mixing up percentage difference (between two values) and percentage change (from an old value)
Quick Mental Math Tricks
To find 10% of any number, move the decimal point one place to the left. 5% is half of that, and 1% is moving it two places. For 15%, add 10% and 5%. For 25%, divide by 4. These shortcuts are handy for checking discounts, tips and bills without a calculator.
Uses of Percentage in Daily Life
Percentages are used everywhere — in exam scores, discounts and offers, interest rates on loans, tax calculations, nutrition labels on food, and statistical data in news reports. Understanding percentage calculations is a fundamental life skill.