Percentage Calculator

Understanding Percentages: Formulas, Examples, and Tips

A percentage represents a fraction of 100. The word itself comes from the Latin per centum, meaning "by the hundred." Percentages are everywhere in daily life - from sales tax and discounts to grades, statistics, and financial growth rates.

The Three Core Percentage Formulas

Quick Mental Math Tricks

• 10% shortcut: Move the decimal one place left. 10% of 350 = 35.
• 5% shortcut: Find 10%, then halve it. 5% of 350 = 17.50.
• 15% (tips): Find 10% + half of that. 15% of $48 = $4.80 + $2.40 = $7.20.
• 25% shortcut: Divide by 4. 25% of 200 = 50.
• Flip trick: X% of Y equals Y% of X. So 8% of 50 = 50% of 8 = 4.

Percentage Difference vs. Percentage Change

Percentage change measures the increase or decrease from an original value - it has a direction (positive or negative). Percentage difference measures how far apart two values are relative to their average, regardless of direction. Use percentage change when there is a clear "before and after." Use percentage difference when comparing two independent values (e.g., the price of two products).

Common Mistakes to Avoid

• Adding percentages of different bases: A 50% increase followed by a 50% decrease does NOT return to the original. $100 → +50% = $150 → -50% = $75.
• Confusing percentage points with percentages: Going from 10% to 15% is a 5 percentage point increase, but a 50% relative increase.
• Forgetting the base: "20% off $80 then 10% off" is NOT 30% off $80. It is $80 × 0.80 × 0.90 = $57.60 (28% total discount).

Real-World Applications

Percentages are essential in finance (interest rates, returns on investment), retail (discounts, markup), academics (grades, test scores), science (concentration, growth rates), and health (body fat percentage, blood oxygen). Mastering percentage calculations helps you make better financial decisions, verify claims, and interpret data accurately. For quick restaurant tips, try our tip calculator.