How to Calculate Percentages
Percentages appear everywhere — from sales tax and tip calculations to test scores and statistics. This guide walks you through the essential formulas with clear, worked examples.
What Is a Percentage?
A percentage is a way of expressing a number as a fraction of 100. The word itself comes from the Latin per centum, meaning “by the hundred.” When you see 45%, it simply means 45 out of every 100.
Percentages are used in everyday life to describe discounts, interest rates, tax rates, grades, probabilities, and much more.
How to Find a Percentage of a Number
Use the formula: Part = Whole × Percentage ÷ 100
Example: What is 15% of 200?
200 × 15 ÷ 100 = 30
So 15% of 200 is 30.
Example: What is 8% of 50?
50 × 8 ÷ 100 = 4
So 8% of 50 is 4.
How to Find What Percentage One Number Is of Another
Use the formula: Percentage = (Part ÷ Whole) × 100
Example: 12 out of 48 is what percent?
(12 ÷ 48) × 100 = 0.25 × 100 = 25%
So 12 is 25% of 48.
Percentage Increase and Decrease
To find how much something has changed in percentage terms, use:
Percentage Change = ((New Value − Old Value) ÷ Old Value) × 100
A positive result means an increase; a negative result means a decrease.
Example: A price went from $80 to $100. What is the percentage increase?
((100 − 80) ÷ 80) × 100 = (20 ÷ 80) × 100 = 25%
The price increased by 25%.
Example: A stock dropped from $60 to $45. What is the percentage decrease?
((45 − 60) ÷ 60) × 100 = (−15 ÷ 60) × 100 = −25%
The stock decreased by 25%.
Common Percentage Conversions
These fraction-to-percentage conversions come up often. Memorizing them can save time on tests and in everyday math.
| Fraction | Percentage |
|---|---|
1/10 | 10% |
1/5 | 20% |
1/4 | 25% |
1/3 | ≈33.3% |
1/2 | 50% |
2/3 | ≈66.7% |
3/4 | 75% |
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