How to Work with Percentages

Percentages show up everywhere: discounts, tax rates, test scores, portfolio returns, nutritional labels. They all boil down to one idea -- a fraction of 100.

Three Common Questions

• "What is X% of Y?" -- Multiply Y by (X / 100). Example: 15% of 200 = 200 x 0.15 = 30.
• "X is what percent of Y?" -- Divide X by Y, then multiply by 100. Example: 45 out of 60 = (45 / 60) x 100 = 75%.
• "What is the percent change from X to Y?" -- Subtract X from Y, divide by X, multiply by 100. Example: from 80 to 100 = ((100 - 80) / 80) x 100 = 25% increase.

Common Percentage Conversions

Percentages, decimals, and fractions are interchangeable:

• 25% = 0.25 = 1/4
• 33.3% = 0.333 = 1/3
• 50% = 0.50 = 1/2
• 75% = 0.75 = 3/4

Percentage Change vs. Percentage Points

These are not the same thing. If an interest rate goes from 4% to 5%, that is a 1 percentage point increase but a 25% relative change. Financial news often conflates the two, so pay attention to which one is being used.