How Percentages Work: A Refresher You Can Actually Use

Percentages show up in tip calculations, sale discounts, exam scores, interest rates, and business reports — but the underlying math is the same handful of operations every time. Here are the three you'll use most.

1. Finding a percentage of a number

This answers: "What is X% of Y?"

result = (percentage ÷ 100) × number

Example: a 20% discount on a $150 jacket.

(20 ÷ 100) × 150 = 30

The discount is $30, making the sale price $120.

2. Finding what percentage one number is of another

This answers: "X is what percent of Y?" — useful for test scores, completion rates, or budget breakdowns.

percentage = (part ÷ whole) × 100

Example: you answered 42 questions correctly out of 50.

(42 ÷ 50) × 100 = 84%

3. Percentage change

This answers: "How much did this go up or down, in percentage terms?" — the calculation behind stock moves, salary raises, and year-over-year growth.

change = ((new value − old value) ÷ old value) × 100

Example: revenue grew from $80,000 to $100,000.

((100,000 − 80,000) ÷ 80,000) × 100 = 25%

A negative result means a decrease — if revenue had instead dropped to $60,000, the change would be −25%.

A common mistake worth avoiding

Percentage points and percentages are not interchangeable. If an interest rate moves from 5% to 7%, that's a change of 2 percentage points, but it's a 40% increase relative to the original 5% (2 ÷ 5 × 100). Financial headlines mix these up constantly, so it's worth checking which one is actually being reported.

Do the math instantly

All three calculations above are built into our percentage calculator — enter your numbers and every mode updates live, so you can sanity-check a discount, a grade, or a growth rate in seconds.