How to Calculate Percentages: The Complete Guide with Real Examples

Percentages are everywhere. A 20% tip. A 15% discount. A 7% tax. A 92% on your exam. Your portfolio is up 8.3% this year.

Most people can handle simple percentages but get confused when the question is phrased differently. Here's a complete guide to calculating any type of percentage problem.

The Three Basic Percentage Problems

Every percentage calculation is one of three types:

Type 1: What is X% of Y?

Formula: Result = (X ÷ 100) × Y

Example: What is 15% of $80?

= (15 ÷ 100) × 80 = 0.15 × 80 = $12

Type 2: X is what percent of Y?

Formula: Percentage = (X ÷ Y) × 100

Example: 45 is what percent of 180?

= (45 ÷ 180) × 100 = 0.25 × 100 = 25%

Type 3: X is Y% of what number?

Formula: Whole = X ÷ (Y ÷ 100)

Example: 30 is 20% of what number?

= 30 ÷ 0.20 = 150

Percentage Increase and Decrease

Percentage increase:

= ((New Value - Old Value) ÷ Old Value) × 100

Example: Price went from $50 to $65.

= ((65 - 50) ÷ 50) × 100 = (15 ÷ 50) × 100 = 30% increase

Percentage decrease:

= ((Old Value - New Value) ÷ Old Value) × 100

Example: Price went from $80 to $60.

= ((80 - 60) ÷ 80) × 100 = (20 ÷ 80) × 100 = 25% decrease

Quick Mental Math Tricks

10% of any number: Move the decimal one place left. 10% of 350 = 35. 10% of 4,200 = 420.

5%: Find 10% then halve it. 5% of 80: 10% = 8, halve = 4.

15%: Find 10% + 5%. 15% of 60: 10% = 6, 5% = 3, total = 9.

20%: Find 10% then double it. 20% of 45: 10% = 4.5, double = 9.

25%: Divide by 4. 25% of 120 = 30.

50%: Divide by 2. 50% of 86 = 43.

Percentages in Real Life

Restaurant tip (20%): Move decimal left (10%), double it. Bill $47: 10% = $4.70, × 2 = $9.40 tip.

Sales discount: Original price × (1 - discount%). $120 item, 30% off: $120 × 0.70 = $84.

Tax added to price: Original price × (1 + tax%). $50 item, 8% tax: $50 × 1.08 = $54.

Grade percentage: Points earned ÷ Total points × 100. 43 out of 50: (43÷50) × 100 = 86%.

Calculate any percentage instantly with our Percentage Calculator.