How to Calculate Percentages (With Examples)

What Is a Percentage?

A percentage is a way of expressing a number as a fraction of 100. The word itself comes from Latin: 'per centum' means 'out of 100.' When you see 25%, it means 25 out of 100, or one-quarter.

Percentages are used everywhere in daily life—sales discounts, test scores, interest rates, tax calculations, and tip amounts. Understanding how to calculate them quickly and accurately saves time and prevents costly mistakes.

The key insight is that percentages are just proportions. Whether you're calculating 15% of a restaurant bill or finding how much a stock price changed, you're using the same fundamental math.

The Core Percentage Formula

All percentage calculations stem from one simple relationship: (Part / Whole) × 100 = Percentage. This formula is the foundation for every calculation you'll encounter.

You can rearrange it depending on what you're solving for. If you know the percentage and want to find the part, use: Part = (Percentage / 100) × Whole. If you know the part and the percentage and want the whole, use: Whole = Part / (Percentage / 100).

• Percentage = (Part / Whole) × 100
• Part = (Percentage / 100) × Whole
• Whole = Part / (Percentage / 100)

Calculating X% of Y

This is the most common percentage calculation: 'What is 20% of 150?' You're finding a part when you know the whole and the percentage.

The formula is straightforward: multiply the whole by the percentage, then divide by 100. Or convert the percentage to a decimal (20% = 0.20) and multiply directly.

Example: A store offers a 25% discount on a $80 jacket. What's the discount amount? Multiply 80 × 0.25 = $20. The new price is $80 − $20 = $60.

• Formula: (Percentage / 100) × Whole = Part
• Or: Percentage as decimal × Whole = Part
• 15% of 200 = 0.15 × 200 = 30
• 8% of 50 = 0.08 × 50 = 4

Finding What Percentage One Number Is of Another

Sometimes you know two numbers and need to find the percentage: 'What percentage is 45 out of 180?' This is useful for calculating test scores, sales performance, or completion rates.

Use the formula: (Part / Whole) × 100 = Percentage. Divide the smaller number by the larger one, then multiply by 100 to shift to a percentage scale.

Example: You scored 36 points on a 40-point quiz. Your percentage is (36 / 40) × 100 = 90%. If you earned $15,000 in commission on $300,000 in sales, your commission rate is (15,000 / 300,000) × 100 = 5%.

• Formula: (Part / Whole) × 100 = Percentage
• 28 out of 50 = (28 / 50) × 100 = 56%
• 150 out of 600 = (150 / 600) × 100 = 25%

Calculating Percentage Increase and Decrease

Percentage change measures how much a value has grown or shrunk as a proportion of its original value. This shows up in salary reviews, investment returns, price hikes, and population growth.

For percentage increase, subtract the original from the new value, divide by the original, and multiply by 100. For percentage decrease, use the same formula—a negative result shows a decrease.

Example: Your salary increased from $50,000 to $57,500. The increase is ((57,500 − 50,000) / 50,000) × 100 = 15%. If a stock dropped from $100 to $85, the change is ((85 − 100) / 100) × 100 = −15% (a 15% decrease).

• Percentage change = ((New − Original) / Original) × 100
• Percentage increase: result is positive
• Percentage decrease: result is negative
• Price went from $200 to $250: ((250 − 200) / 200) × 100 = 25% increase

Quick Mental Math Tips

While calculators are handy, knowing how to estimate percentages mentally is a practical skill. These shortcuts work well for rough estimates and quick checks.

To find 10% of any number, move the decimal point one place to the left. 10% of 250 = 25. To find 5%, calculate 10% and divide by 2. To find 1%, move the decimal two places left. Build larger percentages from these foundations: 20% = two times 10%, 25% = 10% + 15% (which is 10% + half of 10%).

• 10% of any number: move decimal left one place
• 5% of any number: find 10%, then divide by 2
• 1% of any number: move decimal left two places
• 25% of any number: divide by 4
• 50% of any number: divide by 2

Common Percentage Scenarios and Worked Examples

Here are real-world situations where percentage calculations matter. Work through these examples to solidify your understanding.

Restaurant Tip: Your bill is $85. You want to tip 18%. Calculate 0.18 × 85 = $15.30. Total: $85 + $15.30 = $100.30. Sales Tax: You buy items totaling $150 in a 9% tax area. Tax amount = 0.09 × 150 = $13.50. Final cost = $150 + $13.50 = $163.50. Test Score: You got 34 correct out of 40 questions. Your percentage = (34 / 40) × 100 = 85%. Investment Growth: Your $5,000 investment grew to $6,200. Percentage gain = ((6,200 − 5,000) / 5,000) × 100 = 24%.

• Discount: $120 item with 30% off = $120 × 0.70 = $84
• Markup: Cost $50, mark up 40% = $50 × 1.40 = $70 selling price
• Commission: $500,000 in sales at 3% = 0.03 × 500,000 = $15,000

When to Use a Percentage Calculator

While the formulas are simple, using an online calculator eliminates arithmetic errors and saves time, especially with complex numbers or multiple calculations. A good calculator lets you switch between the three main modes: finding X% of Y, finding what percentage one number is of another, and calculating percentage change.

Calculators are invaluable when you're working with decimals, large numbers, or need to run multiple scenarios quickly—like comparing discount offers or calculating compound percentage changes. They also help verify mental math estimates and build confidence in your understanding.

Frequently asked questions