How to Calculate a Percentage: The Complete Step-by-Step Guide

A percentage represents a portion of 100. The word comes from the Latin "per centum," which literally means "by the hundred." When you say that 25 out of 100 students scored an A, you can express this as 25%. Percentages standardize numbers of different sizes, making comparisons immediate and intuitive.

The fundamental formula to calculate what percentage one number is of another is: $$\text{Percentage} = \left(\frac{\text{Part}}{\text{Whole}}\right) \times 100$$ For instance, if a quiz has 40 total questions and you answer 34 correctly, your score is: $$(34 \div 40) \times 100 = 0.85 \times 100 = 85\%$$

To find a specific percentage of a known amount, follow two steps: 1. Convert the percentage to a decimal by dividing by 100 (e.g. 15% becomes 0.15). 2. Multiply the decimal by the total number. Example: To calculate a 15% tip on a $60 restaurant bill: $$0.15 \times 60 = $9.00$$

You don’t always need a pencil and paper for day-to-day calculations. You can combine foundational benchmark percentages: - **10%**: Move the decimal point one position to the left ($45.00 becomes $4.50). - **5%**: Cut the 10% value in half ($4.50 ÷ 2 = $2.25). - **20%**: Double the 10% value ($4.50 × 2 = $9.00). - **1%**: Move the decimal point two places to the left ($45.00 becomes $0.45).