How to Calculate Percentage: A Complete Guide with Examples

Percentages are everywhere — sales tax, tips, discounts, interest rates, test scores, and statistics. Understanding how to calculate percentages is one of the most practical math skills you can learn. This guide covers every common percentage scenario with simple formulas and real-world examples.

What Is a Percentage?

"Per cent" comes from the Latin "per centum," meaning "by the hundred." A percentage is a way of expressing a number as a fraction of 100. For example, 45% means 45 per 100, or 45/100 = 0.45.

The Basic Percentage Formula

The fundamental relationship:

Part ÷ Whole = Percentage ÷ 100

This can be rearranged to solve for any unknown:

Three Core Scenarios:

1. Find X% of Y (Percentage of a Number)

Formula: Result = Y × (X ÷ 100)

Examples:

• What is 20% of $50? 50 × 0.20 = $10
• What is 15% of 200? 200 × 0.15 = 30
• What is 8% of 250? 250 × 0.08 = 20

Real-world uses:

• Sales tax: $45 item × 8% tax = $3.60
• Restaurant tip: $80 bill × 18% tip = $14.40
• Commission: $10,000 sale × 5% = $500

2. X Is What Percent of Y?

Formula: (X ÷ Y) × 100 = Percentage

Examples:

• 30 is what percent of 200? (30 ÷ 200) × 100 = 15%
• 42 out of 50 on a test: (42 ÷ 50) × 100 = 84%
• 15 sales out of 300 leads: (15 ÷ 300) × 100 = 5%

3. X Is Y% of What? (Find the Total)

Formula: Total = X ÷ (Y ÷ 100)

Examples:

• 30 is 15% of what? 30 ÷ 0.15 = 200
• 45 is 90% of what? 45 ÷ 0.90 = 50

Percentage Change (Increase/Decrease)

Formula: ((New − Old) ÷ Old) × 100

A positive result = increase. A negative result = decrease.

Examples:

• Stock from $50 to $60: ((60-50)/50) × 100 = 20% increase
• Population from 10,000 to 9,500: ((9500-10000)/10000) × 100 = −5% (5% decrease)

Why Percent Change Is Asymmetric

Going from 100 to 150 is a 50% increase. Going from 150 back to 100 is a 33.3% decrease. The absolute change is the same (50), but the reference point changes.

Percentage Difference (Symmetric)

Use when comparing two values with no "original" or "baseline."

Formula: |V1 − V2| ÷ ((|V1| + |V2|) ÷ 2) × 100

Example: Difference between 80 and 100:

(20 ÷ 90) × 100 = 22.2%

Percentage Points vs Percent Change

These are frequently confused:

Quick Mental Math Tricks

• 10%: Divide by 10 (e.g., 10% of 80 = 8)
• 5%: Divide by 20 or halve the 10% value (5% of 80 = 4)
• 1%: Divide by 100 (1% of 80 = 0.8)
• 15%: 10% + 5% (15% of 80 = 8 + 4 = 12)
• 50%: Divide by 2
• 25%: Divide by 4
• 20%: Divide by 5

FAQ: Percentage Calculations

Multiply the number by the percentage divided by 100. For 15% of 200: 200 × (15/100) = 200 × 0.15 = 30.

((New Value − Old Value) ÷ Old Value) × 100. For example, if a price goes from $50 to $65: ((65-50)/50) × 100 = 30% increase.

Use |V1 − V2| ÷ ((|V1| + |V2|) ÷ 2) × 100. This gives a symmetric comparison without a baseline.

Finding the original value before a percentage change. Original = Final ÷ (1 ± rate/100). For example, $75 after 25% discount: 75 ÷ 0.75 = $100.

Use benchmark percentages. For 15% of 80: calculate 10% (8) + 5% (4) = 12. For 7%: calculate 1% (0.8) × 7 = 5.6.

Yes. A change from 10% to 15% is 5 percentage points but a 50% percent increase.