Percentage Calculator

What is a Percentage?

A percentage is a way of expressing a number as a fraction of 100. The word “percentage” comes from the Latin “per centum,” meaning “by the hundred.” Percentages are used to compare parts to a whole and make calculations easier to understand.

How Percentage Calculations Work

Basic Percentage Formulas

Percentage of a Number: Result = (Percentage ÷ 100) × Number

What Percentage is X of Y: Percentage = (X ÷ Y) × 100

Find the Whole from a Percentage: Whole = Part ÷ (Percentage ÷ 100)

Decimal to Percentage Conversion

Percentage = Decimal × 100

Example: 0.25 = 25%

Percentage to Decimal Conversion

Decimal = Percentage ÷ 100

Example: 75% = 0.75

How Our Calculator Works

Our percentage calculator handles multiple calculation types:

1. Input Analysis: Determines which type of calculation you want to perform
2. Formula Selection: Chooses the appropriate mathematical formula
3. Computation: Performs the calculation with high precision
4. Format Output: Displays results in the most useful format
5. Multiple Results: Shows related calculations (decimal equivalents, reverse calculations)

Common Percentage Calculations

Type 1: Find X% of a Number

• Question: What is 20% of 150?
• Formula: (20 ÷ 100) × 150 = 0.20 × 150 = 30
• Answer: 30

Type 2: What Percentage is X of Y?

• Question: What percentage is 30 of 150?
• Formula: (30 ÷ 150) × 100 = 0.20 × 100 = 20%
• Answer: 20%

Type 3: Find the Whole

• Question: 30 is 20% of what number?
• Formula: 30 ÷ (20 ÷ 100) = 30 ÷ 0.20 = 150
• Answer: 150

Real-World Applications

Business and Finance

• Profit margins: Calculate profit as a percentage of revenue
• Interest rates: Determine loan costs and investment returns
• Discounts: Calculate sale prices and savings
• Tax calculations: Determine tax amounts and after-tax values

Statistics and Data Analysis

• Survey results: Express responses as percentages
• Growth rates: Show changes over time
• Success rates: Compare performance metrics
• Market share: Show company position in industry

Everyday Use

• Tips: Calculate restaurant gratuities
• Grades: Convert scores to percentages
• Cooking: Scale recipes up or down
• Shopping: Compare prices and discounts

Mathematical Properties

Percentage Rules

1. 100% = the whole amount
2. 50% = half the amount
3. 25% = one quarter of the amount
4. Percentages are additive: 30% + 20% = 50% of the original amount

Common Fraction-Percentage Equivalents

• 1/2 = 50%
• 1/3 ≈ 33.33%
• 1/4 = 25%
• 1/5 = 20%
• 1/8 = 12.5%
• 1/10 = 10%

Advanced Percentage Concepts

Percentage Change

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

Percentage Point vs Percentage

• Percentage change: If interest rates go from 2% to 3%, that’s a 50% increase
• Percentage point change: The same change is a 1 percentage point increase

Compound Percentages

When applying multiple percentage changes:

• Sequential: Apply each percentage to the result of the previous calculation
• Not simply additive: 10% + 10% ≠ 20% when applied sequentially

Pro Tips

1. Check your work: Use inverse calculations to verify results
2. Round appropriately: Consider the precision needed for your use case
3. Understand context: Know whether you’re dealing with simple or compound percentages
4. Use estimation: 10% is easy to calculate mentally for quick approximations

Note: This calculator provides precise mathematical results. Always consider the context and appropriate level of precision for your specific application.

Frequently Asked Questions

How do I calculate a percentage of a number?

To calculate X% of a number, multiply the number by X and divide by 100. For example, 25% of 80 = (80 × 25) ÷ 100 = 20.

What’s the difference between percentage and percentage points?

A percentage point is the absolute difference between percentages. If something increases from 10% to 15%, that’s a 5 percentage point increase, but a 50% increase in the rate.

How do I convert a decimal to a percentage?

Multiply the decimal by 100. For example, 0.75 = 0.75 × 100 = 75%.

How do I find what percentage one number is of another?

Divide the first number by the second number, then multiply by 100. For example, 20 is what percentage of 80? (20 ÷ 80) × 100 = 25%.

Can percentages be more than 100%?

Yes! Percentages can exceed 100% when the part is larger than the whole. For example, if you have 150% of something, you have 1.5 times the original amount.

How do I calculate percentage increase or decrease?

Use the formula: ((New Value - Old Value) ÷ Old Value) × 100. A positive result means increase, negative means decrease.