how do i calculate percentage

Percentage Basics: The Simple Formula

A percentage is just a way to express a number as a part of 100. The word literally means “per hundred.” So if something is 45%, that means 45 out of 100.

The core formula behind most percentage questions is:

Percentage = (Part ÷ Whole) × 100

Once you understand this one line, you can solve discounts, tips, tax, exam scores, investment gains, and almost every day-to-day percentage problem.

Three Common Percentage Questions (and How to Solve Each)

1) What is X% of Y?

Use this when finding discounts, tax amounts, commissions, or tips.

Formula: (X ÷ 100) × Y

• Example: What is 15% of 80?
• Step 1: 15 ÷ 100 = 0.15
• Step 2: 0.15 × 80 = 12
• Answer: 15% of 80 is 12

2) X is what percent of Y?

Use this when comparing one value to a total, like score percentages or completion rates.

Formula: (X ÷ Y) × 100

• Example: 30 is what percent of 120?
• Step 1: 30 ÷ 120 = 0.25
• Step 2: 0.25 × 100 = 25
• Answer: 30 is 25% of 120

3) What is the percentage increase or decrease from old to new?

Use this for price changes, salary growth, business metrics, weight change, or performance trends.

Formula: ((New - Old) ÷ Old) × 100

• Example: Old price = 50, New price = 65
• Step 1: 65 - 50 = 15
• Step 2: 15 ÷ 50 = 0.30
• Step 3: 0.30 × 100 = 30
• Answer: 30% increase

Fast Mental Math Tricks for Percentages

Start with 10%

10% is just moving the decimal one place left. For 240, 10% is 24.

Use 5% and 1%

• 5% is half of 10%
• 1% is moving decimal two places left

From these, you can combine percentages quickly. Example: 17% of 300 = 10% + 5% + 2% = 30 + 15 + 6 = 51.

Find 25% by dividing by 4

Because 25% = 1/4, 25% of 200 is 200 ÷ 4 = 50.

Real-Life Percentage Examples

Shopping Discount

If a $120 jacket is 30% off:

• Discount amount = 30% of 120 = 36
• Final price = 120 - 36 = 84

Restaurant Tip

For a $68 bill with an 18% tip:

• Tip = 0.18 × 68 = 12.24
• Total = 68 + 12.24 = 80.24

Exam Score

If you got 42 out of 50:

• (42 ÷ 50) × 100 = 84%

Salary Raise

If salary rises from $50,000 to $55,000:

• Increase = $5,000
• (5,000 ÷ 50,000) × 100 = 10%

Common Mistakes to Avoid

• Using the wrong base number: Always divide by the original whole when finding percentage.
• Forgetting to multiply by 100: If you stop at 0.24, that is not 0.24%, it is 24%.
• Confusing percentage points with percent change: Going from 10% to 12% is a 2 percentage-point increase, but a 20% relative increase.
• Dividing by zero: Percentage change from an old value of 0 is undefined in standard form.

Quick Practice Problems

• What is 12% of 250?
• 45 is what percent of 60?
• A price goes from 90 to 81. What is the percent change?

Answers: 30, 75%, and -10% (a 10% decrease).

Final Takeaway

If you can remember these three formulas, you can solve nearly every percentage question:

• Percent of a number: (Percent ÷ 100) × Number
• What percent one number is of another: (Part ÷ Whole) × 100
• Percent change: ((New - Old) ÷ Old) × 100

Use the calculator at the top whenever you want a quick result, then compare it with your own manual math to build confidence fast.