How to Calculate Percentage: Complete Guide with Examples
Percentages are everywhere in our daily lives - from calculating tips and discounts to understanding test scores and financial returns. Mastering percentage calculations is an essential skill that will serve you well in academics, business, and personal finance.
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Use Percentage Calculator →What is a Percentage?
A percentage is a way of expressing a number as a fraction of 100. The word "percent" comes from the Latin "per centum," meaning "by the hundred." The symbol % represents "per 100" or "out of 100."
For example:
- 50% means 50 out of 100, or 50/100, or 0.5
- 25% means 25 out of 100, or 25/100, or 0.25
- 100% means 100 out of 100, or the whole amount
Basic Percentage Formulas
Find Percentage
(Part ÷ Whole) × 100 What percentage is 25 of 100?
Find the Part
(Percentage ÷ 100) × Whole What is 25% of 100?
Find the Whole
Part ÷ (Percentage ÷ 100) 25 is 25% of what number?
Step-by-Step Examples
Example 1: Finding a Percentage
Question: You scored 85 points out of 100 on a test. What percentage did you get?
Solution:
- Identify the part (85) and the whole (100)
- Apply the formula: (Part ÷ Whole) × 100
- Calculate: (85 ÷ 100) × 100 = 0.85 × 100
Answer: 85%
Example 2: Finding the Part
Question: A shirt costs $80. If there's a 25% discount, how much money will you save?
Solution:
- Identify the percentage (25%) and the whole ($80)
- Apply the formula: (Percentage ÷ 100) × Whole
- Calculate: (25 ÷ 100) × 80 = 0.25 × 80
Answer: $20 savings
Example 3: Finding the Whole
Question: You paid $15 in tax, which represents 8% of your purchase. What was the total purchase amount?
Solution:
- Identify the part ($15) and the percentage (8%)
- Apply the formula: Part ÷ (Percentage ÷ 100)
- Calculate: 15 ÷ (8 ÷ 100) = 15 ÷ 0.08
Answer: $187.50 total purchase
Percentage Increase and Decrease
Percentage Increase Formula
((New Value - Original Value) ÷ Original Value) × 100 Example: A stock price increased from $50 to $65. What's the percentage increase?
- New Value = $65, Original Value = $50
- Difference = $65 - $50 = $15
- Percentage = ($15 ÷ $50) × 100 = 30%
The stock increased by 30%
Percentage Decrease Formula
((Original Value - New Value) ÷ Original Value) × 100 Example: A laptop price dropped from $1,000 to $750. What's the percentage decrease?
- Original Value = $1,000, New Value = $750
- Difference = $1,000 - $750 = $250
- Percentage = ($250 ÷ $1,000) × 100 = 25%
The laptop price decreased by 25%
Common Percentage Applications
💰 Sales and Discounts
Calculate savings on sale items and determine final prices after discounts.
Example: 30% off $100 = $30 savings, $70 final price
🍽️ Tips and Gratuity
Calculate appropriate tips for restaurants, delivery, and services.
Example: 18% tip on $50 bill = $9 tip
📈 Investment Returns
Measure investment performance and compare different options.
Example: $1,000 to $1,200 = 20% return
🏦 Interest Rates
Understand loan costs and savings account earnings.
Example: 5% annual interest on $1,000 = $50 per year
Quick Mental Math Tricks
10% Rule
To find 10%, simply move the decimal point one place to the left. 10% of $45.60 = $4.56
5% Trick
5% is half of 10%. Find 10% first, then divide by 2. 5% of $60 = $6 ÷ 2 = $3
25% Shortcut
25% is the same as dividing by 4. 25% of $80 = $80 ÷ 4 = $20
50% Method
50% is simply half. 50% of any number = number ÷ 2
Converting Between Percentages, Decimals, and Fractions
| Percentage | Decimal | Fraction |
|---|---|---|
| 10% | 0.10 | 1/10 |
| 25% | 0.25 | 1/4 |
| 50% | 0.50 | 1/2 |
| 75% | 0.75 | 3/4 |
| 100% | 1.00 | 1/1 |
Related Math Calculators
Frequently Asked Questions
What's the difference between percentage and percentile?
A percentage is a proportion out of 100, while a percentile indicates the value below which a certain percentage of data falls. For example, scoring in the 90th percentile means you scored better than 90% of test-takers.
Can percentages be greater than 100%?
Yes! Percentages over 100% indicate values greater than the original whole. For example, if a stock doubles in value, that's a 100% increase, making the new value 200% of the original.
How do I calculate compound percentage changes?
For multiple percentage changes, multiply the factors: (1 + first change) × (1 + second change) - 1. For example, a 10% increase followed by a 20% increase: (1.10 × 1.20) - 1 = 0.32 or 32% total increase.
Conclusion
Mastering percentage calculations is a valuable skill that applies to countless real-world situations. Whether you're shopping for deals, calculating tips, analyzing investments, or working with data, understanding percentages will help you make better decisions and solve problems more efficiently.
Practice these formulas and mental math tricks regularly, and use our percentage calculator to verify your work. With time and practice, percentage calculations will become second nature, making you more confident in both academic and practical applications.