How to Calculate Percentages

Learn the percentage formulas for finding X% of Y, percent change, and reverse percentages with clear examples.

A percentage expresses a number as parts per hundred. Once you know the three core patterns—percent of a number, percent change, and reverse percentage—you can solve most everyday percent problems without a spreadsheet.

1. What is X% of Y?

Multiply the number by the percent, then divide by 100. Example: 20% of 150 = (150 × 20) ÷ 100 = 30. Decimal form is often faster: 150 × 0.20 = 30.

2. Percent change

Percent change = ((new − old) ÷ old) × 100. A price rising from $40 to $50 is a 25% increase. A drop from $50 to $40 is a 20% decrease—the base matters.

3. Reverse percentage

If you know the result and the percent, recover the original with (result × 100) ÷ percent. If 30 is 20% of a number, the original is (30 × 100) ÷ 20 = 150.

Practice tips

• Estimate first: 10% is one-tenth; 5% is half of that; 15% is 10% + 5%.
• Watch the base when comparing increases and decreases.
• For many specific questions, jump to the what is X% of Y hub or the percentage calculator.