How to Calculate Percentages: The Complete Guide with Examples

Percentages show up everywhere—discounts at the store, interest rates on loans, test scores, tax rates, tips at restaurants, and investment returns. Despite being one of the most practical math skills, many people feel unsure about how to calculate them. This guide covers every common percentage calculation with clear, step-by-step examples.

What Is a Percentage?

A percentage is simply a number expressed as a fraction of 100. The word itself 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.

How to Find the Percentage of a Number

Question: What is 15% of 200?

Method:Convert the percentage to a decimal (15% = 0.15), then multiply: 0.15 × 200 = 30. So 15% of 200 is 30.

This calculation is useful for figuring out tips, sales tax, and discounts. Our percentage calculator handles all of these scenarios instantly.

How to Find What Percentage One Number Is of Another

Question: 45 is what percent of 180?

Method:Divide the part by the whole, then multiply by 100: (45 ÷ 180) × 100 = 25%. So 45 is 25% of 180.

This comes up when you want to know what fraction of a budget you have spent, what proportion of questions you answered correctly on a test, or how much of a goal you have reached.

How to Calculate Percentage Change

Question:A product's price went from $80 to $100. What is the percentage increase?

Method:Subtract the old value from the new value, divide by the old value, and multiply by 100: ((100 − 80) ÷ 80) × 100 = 25% increase.

For a decrease, the formula is the same—you just get a negative result. A drop from $100 to $80 is a 20% decrease: ((80 − 100) ÷ 100) × 100 = −20%.

Practical Examples

Calculating a Tip

Your restaurant bill is $68 and you want to leave a 20% tip. Multiply $68 × 0.20 = $13.60. Your total comes to $81.60. Our tip calculator makes this even easier, especially when splitting the bill.

Figuring Out a Discount

A $120 jacket is 30% off. The discount is $120 × 0.30 = $36. The sale price is $120 − $36 = $84.

Understanding Interest Rates

If your savings account earns 4.5% annually on a $10,000 balance, you earn $10,000 × 0.045 = $450 in the first year (before compounding). To see how compounding affects this over multiple years, try the compound interest calculator.

Common Percentage Mistakes

• Confusing percentage points with percentages. A rate going from 5% to 7% is a 2 percentage point increase, but a 40% relative increase.
• Applying percentages in the wrong order.A 50% increase followed by a 50% decrease does not get you back to the original number—you end up 25% lower.
• Forgetting the base. 20% of $50 is very different from 20% of $500. Always double-check which number you are calculating the percentage of.

Quick Mental Math Tricks

• 10% shortcut: Move the decimal one place left. 10% of $75 is $7.50.
• 5% shortcut: Find 10%, then halve it. 5% of $75 is $3.75.
• 15% shortcut: Add 10% and 5% together. 15% of $75 is $7.50 + $3.75 = $11.25.
• Swap trick: 8% of 50 equals 50% of 8, which is 4. Find whichever direction is easier to calculate.

Key Takeaways

Percentages are one of the most practical math concepts you will use in daily life. Master the three core calculations—finding a percentage of a number, finding what percentage one number is of another, and calculating percentage change—and you will be equipped to handle discounts, tips, taxes, interest rates, and much more.