How to Calculate Percentages: The Complete Guide

Percentages are everywhere - from calculating tips to understanding sale discounts and tracking investment returns. This guide breaks down the fundamental percentage formulas with real-world examples.

For quick answers, try our Percentage Calculator or use the Discount Calculator for shopping savings.

What Is a Percentage?

A percentage expresses a number as a fraction of 100. "Percent" comes from Latin "per centum" meaning "by the hundred." 25% means 25 out of 100, or 0.25 as a decimal.

The 3 Basic Percentage Formulas

Formula 1: What Is X% of Y?

Part = Whole × (Percentage ÷ 100)

Example: What is 15% of 80?

80 × 0.15 = 12

Formula 2: What Percent Is X of Y?

Percentage = (Part ÷ Whole) × 100

Example: What percent is 24 of 80?

(24 ÷ 80) × 100 = 30%

Formula 3: Y Is X% of What?

Whole = Part ÷ (Percentage ÷ 100)

Example: 45 is 25% of what?

45 ÷ 0.25 = 180

Percentage Increase and Decrease

% Change = ((New - Old) ÷ Old) × 100

Stock rises from $50 to $65:

((65 - 50) ÷ 50) × 100 = 30% increase

Real-World Examples

Calculating Tips (Bill: $68.50)

• 15% tip: $68.50 × 0.15 = $10.28
• 18% tip: $68.50 × 0.18 = $12.33
• 20% tip: $68.50 × 0.20 = $13.70

Sale Discounts ($120 jacket, 30% off)

$120 × (1 - 0.30) = $120 × 0.70 = $84

Mental Math Shortcuts

• 10%: Move decimal one place left
• 5%: Half of 10%
• 20%: Double 10%
• 25%: Divide by 4
• Flip Rule: X% of Y = Y% of X (8% of 50 = 50% of 8 = 4)

Frequently Asked Questions

What's the difference between percentage and percentage points?

Going from 10% to 15% is a 5 percentage point increase, but a 50% relative increase (5 is 50% of 10).

Why doesn't a 50% increase followed by 50% decrease return to the original?

Because the decrease applies to the increased value. $100 + 50% = $150. $150 - 50% = $75.