The Percentage Formula: How to Calculate Percentages with Worked Examples

A percentage expresses a number as a fraction of 100. Mathematically, the relation between the part, the whole, and the percentage is represented by: $$\text{Percentage} = \left(\frac{\text{Part}}{\text{Whole}}\right) \times 100$$ For example, if you answered 46 questions correctly on a 50-question examination: $$\text{Percentage} = \left(\frac{46}{50}\right) \times 100 = 0.92 \times 100 = 92\%$$

When you need to find X% of a number Y, rearrange the formula by dividing the percentage by 100 and multiplying by the total: $$\text{Part} = \left(\frac{X}{100}\right) \times Y$$ Example: To find 18% sales tax on a $250 purchase: $$\text{Tax} = 0.18 \times 250 = $45.00$$

To determine how much a quantity has increased or decreased relative to its starting point, use the percentage difference formula: $$\text{Percentage Change} = \left(\frac{\text{New Value} - \text{Old Value}}{\text{Old Value}}\right) \times 100$$ A positive result indicates an increase, while a negative result represents a decrease.