how to calculate percentage

What Is a Percentage?

A percentage is a way to express a number as a fraction of 100. The word literally means “per hundred.” So if something is 25%, it means 25 out of every 100. Percentages help us compare values quickly, especially when totals are different.

Examples:

• Score of 90% on a test = 90 correct out of 100 possible points.
• 20% discount = you save $20 for every $100 of original price.
• 5% interest = you earn or pay $5 per $100 over a period.

The 3 Core Percentage Formulas

• Find X% of Y: (X ÷ 100) × Y
• Find what percent A is of B: (A ÷ B) × 100
• Find percent change: ((New − Old) ÷ Old) × 100

Method 1: How to Find a Percentage of a Number

Example: What is 30% of 250?

Use the formula (X ÷ 100) × Y:

• Convert 30% to decimal: 30 ÷ 100 = 0.30
• Multiply: 0.30 × 250 = 75

Answer: 30% of 250 is 75.

Shortcut Tip

To find 10%, move the decimal one place left. For 250, 10% is 25. Then multiply as needed:

• 20% = 50
• 30% = 75
• 5% = half of 10% = 12.5

Method 2: How to Find What Percent One Number Is of Another

Example: 18 is what percent of 60?

Use the formula (A ÷ B) × 100:

• 18 ÷ 60 = 0.3
• 0.3 × 100 = 30%

Answer: 18 is 30% of 60.

Common Use Cases

• Exam score percentage
• Budget category share (e.g., rent as % of income)
• Market share or conversion rate

Method 3: How to Calculate Percentage Increase or Decrease

Example: Price rises from $80 to $100

Use percent change formula: ((New − Old) ÷ Old) × 100

• Difference = 100 − 80 = 20
• 20 ÷ 80 = 0.25
• 0.25 × 100 = 25%

Answer: 25% increase.

Example: Traffic falls from 50,000 visits to 40,000

• Difference = 40,000 − 50,000 = −10,000
• −10,000 ÷ 50,000 = −0.2
• −0.2 × 100 = −20%

Answer: 20% decrease.

Percentage vs. Percentage Points

This is a common confusion.

• If interest rate goes from 5% to 7%, that is 2 percentage points.
• Relative increase is 40%, because (2 ÷ 5) × 100 = 40%.

Use percentage points for direct differences between percentages. Use percent change for relative change.

Real-Life Examples

1) Shopping Discounts

A jacket costs $120 and is 25% off:

• Discount amount = 25% of 120 = $30
• Final price = 120 − 30 = $90

2) Tips

Restaurant bill is $48. A 15% tip is:

• 0.15 × 48 = $7.20

3) Tax

Item is $200 with 8% sales tax:

• Tax = 0.08 × 200 = $16
• Total = $216

4) Savings Growth

You invest $1,000 and it grows to $1,080:

• Growth = $80
• Percent gain = (80 ÷ 1000) × 100 = 8%

Common Mistakes to Avoid

• Forgetting to divide by 100: 15% is 0.15, not 15.
• Switching part and whole: A ÷ B is not the same as B ÷ A.
• Using new value as base for change: percent change must divide by old value.
• Rounding too early: keep extra decimals until final step.

Mental Math Tricks for Percentages

• 1%: move decimal two places left.
• 10%: move decimal one place left.
• 5%: half of 10%.
• 15%: 10% + 5%.
• 20%: double 10%.
• 50%: half the number.

Quick Practice Problems

• What is 12% of 350?
• 72 is what percent of 90?
• A value moves from 64 to 80. What is the percent increase?
• Decrease 500 by 18%.

Try the calculator above, then solve manually to build confidence.

Final Thoughts

Learning how to calculate percentage is one of the most useful math skills you can have. It helps with money decisions, school, business metrics, and daily comparisons. Memorize the three core formulas, practice with real numbers, and use a calculator to check your work. Once you do this a few times, percentage math becomes fast and intuitive.