How to Calculate Percentages: A Complete Guide with Examples

Percentages are one of the most useful mathematical concepts in everyday life. Whether you are working out a tip at a restaurant, calculating a discount, or analysing data, understanding percentages is essential. This guide walks you through the core formula, five worked examples, and the most common mistakes people make.

What Is a Percentage?

A percentage is a way of expressing a number as a fraction of 100. The word itself comes from the Latin per centum, meaning “by the hundred”. When we say 45%, we mean 45 out of every 100, or equivalently, the fraction 45/100.

Percentages allow us to compare quantities on a common scale, making them invaluable in finance, science, statistics, and day-to-day arithmetic.

The Core Percentage Formula

The fundamental formula for calculating a percentage is:

This formula answers the question: “What percentage of the whole does the part represent?”

There are three common types of percentage problems:

1. Finding the percentage: What percentage is 15 of 60?
2. Finding the part: What is 25% of 200?
3. Finding the whole: 30 is 20% of what number?

Worked Example 1: Finding the Percentage

Problem: You scored 42 out of 60 on a test. What is your percentage score?

Your score is 70%.

Worked Example 2: Finding a Percentage of a Number

Problem: What is 15% of 240?

To find a percentage of a number, convert the percentage to a decimal and multiply:

So 15% of 240 is 36.

Worked Example 3: Percentage Increase

Problem: A product's price rose from $80 to $92. What is the percentage increase?

The price increased by 15%.

Worked Example 4: Percentage Decrease

Problem: A shirt was originally $50 and is now on sale for $35. What is the percentage decrease?

The price decreased by 30%.

Worked Example 5: Reverse Percentage (Finding the Whole)

Problem: After a 20% discount, a jacket costs $64. What was the original price?

If the discount is 20%, the sale price represents 80% of the original. So:

The original price was $80.

Worked Example 6: Tip Calculation

Problem: Your restaurant bill is $85. You want to leave a 18% tip. How much is the tip?

The tip is $15.30, making the total $100.30.

Common Mistakes to Avoid

1. Dividing by the wrong number. When calculating percentage increase, always divide the change by the original value, not the new value.
2. Confusing percentage points with percentages. If interest rises from 2% to 3%, that is a 1 percentage point increase, but a 50% relative increase.
3. Forgetting to multiply by 100. The formula gives a decimal (e.g. 0.7). Multiply by 100 to express it as a percentage (70%).
4. Applying successive percentages incorrectly. A 10% increase followed by a 10% decrease does not return you to the original value. 100 → 110 → 99.
5. Rounding too early. Keep extra decimal places during intermediate steps and only round at the final answer.

Quick Reference: Percentage Shortcuts

• 50% = divide by 2
• 25% = divide by 4
• 10% = move the decimal point one place left
• 1% = move the decimal point two places left
• To find 15%: find 10% + 5% (half of 10%)

Try It Yourself

Ready to practise? Use our free Percentage Calculator to check your answers instantly. It handles percentage of a number, percentage change, and reverse percentage calculations.