How to Calculate Percentages: Formulas, Examples & Common Mistakes

What Is a Percentage?

A percentage is a number expressed as a fraction of 100. The word comes from the Latin "per centum," meaning "by the hundred." When you see 25%, it means 25 out of 100, or 0.25 as a decimal, or 1/4 as a fraction.

Percentages are everywhere in daily life: shopping discounts, tax rates, tip calculations, exam scores, interest rates, and data analysis. Understanding how to calculate them quickly and accurately is a practical skill that saves time and money.

The Three Core Percentage Formulas

Formula 1: What is X% of Y?

This is the most common percentage calculation. Multiply the base number by the percentage divided by 100.

Formula: Result = Y × (X / 100)

Example: What is 20% of 150? → 150 × (20 / 100) = 150 × 0.20 = 30

Formula 2: X is what percent of Y?

This tells you the proportion of one number relative to another.

Formula: Percentage = (X / Y) × 100

Example: 42 is what percent of 50? → (42 / 50) × 100 = 84%

Formula 3: Percentage Change (Increase or Decrease)

This measures how much a value has changed relative to its original amount.

Formula: Change = ((New - Old) / Old) × 100

Example: Price went from $80 to $100 → ((100 - 80) / 80) × 100 = 25% increase

Real-World Percentage Calculations

Shopping Discounts

A store offers 30% off a $200 item. The discount is 200 × 0.30 = $60, so the sale price is $140.

Restaurant Tips

To tip 18% on a $75 meal: 75 × 0.18 = $13.50.

Exam Scores

You scored 38 out of 45 on a test: (38 / 45) × 100 = 84.4%.

Investment Returns

Your investment grew from $10,000 to $11,500: ((11,500 - 10,000) / 10,000) × 100 = 15% return.

Common Mistakes to Avoid

Confusing percentage points with percentages: If an interest rate goes from 2% to 3%, that is a 1 percentage point increase, but a 50% increase in the rate itself.

Calculating discounts on already-discounted items: Two successive 20% discounts are not the same as a single 40% discount. The first discount gives you 80% of the original, and the second gives you 80% of that, resulting in 64% of the original price (36% total discount).

Forgetting to convert: Always convert percentages to decimals before multiplying. 15% = 0.15, not 15.

Try Our Free Percentage Calculator

Our Percentage Calculator handles all three formula types through a simple dropdown selector. Enter your numbers and get instant results with the formula shown. It works on mobile and keeps your data in your browser.