Percentage Calculator
Calculate percentages and percentage changes
How to Use
- Select the type of percentage calculation
- Enter the required values
- Click calculate to see the result
- View step-by-step explanation
What are Percentages?
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." Percentages are used to describe proportions, changes, and relationships between numbers in a standardized way.
Key Formula
Percentage = (Part ÷ Whole) × 100
Types of Percentage Calculations
1. Percentage of a Number
Question: What is X% of Y?
Formula: (X ÷ 100) × Y
Example: What is 25% of 80? = (25 ÷ 100) × 80 = 20
2. Percentage Change
Question: What is the percentage change from X to Y?
Formula: ((New Value - Original Value) ÷ Original Value) × 100
Example: Change from 50 to 60 = ((60 - 50) ÷ 50) × 100 = 20%
3. Find the Percentage
Question: X is what percentage of Y?
Formula: (X ÷ Y) × 100
Example: 15 is what % of 60? = (15 ÷ 60) × 100 = 25%
Real-World Applications
Percentages are used extensively in everyday life and business:
Financial Applications
- Interest rates and loan calculations
- Tax calculations
- Investment returns
- Discounts and sales
- Commission calculations
Business & Analytics
- Market share analysis
- Performance metrics
- Growth rates
- Profit margins
- Statistical analysis
Daily Life
- Tips and gratuities
- Battery levels
- Grades and test scores
- Weather probability
- Recipe scaling
Science & Medicine
- Concentration levels
- Success rates
- Error margins
- Efficiency calculations
- Dosage calculations
Percentage Tips & Tricks
Quick Mental Math
- 10%: Move decimal point one place left (10% of 250 = 25)
- 1%: Move decimal point two places left (1% of 250 = 2.5)
- 50%: Divide by 2 (50% of 80 = 40)
- 25%: Divide by 4 (25% of 80 = 20)
- 20%: Divide by 5 (20% of 100 = 20)
Common Mistakes to Avoid
- Don't forget to multiply by 100 when converting decimals to percentages
- Be careful with percentage point vs percentage change
- Remember: X% of Y = Y% of X (commutative property)
- When calculating percentage change, use the original value as the denominator
Converting Between Forms
Decimal to Percentage: Multiply by 100 (0.25 = 25%)
Percentage to Decimal: Divide by 100 (25% = 0.25)
Fraction to Percentage: Divide and multiply by 100 (1/4 = 0.25 = 25%)
Frequently Asked Questions
- What's the difference between percentage change and percentage of a number?
- Percentage of a number answers questions like “What is 20% of 80?”, while percentage change compares the difference between two values relative to the original amount. Use the change tab whenever you are moving from a starting value to a new value.
- How do I convert between decimals, fractions, and percentages?
- Multiply a decimal by 100 to get a percentage (e.g., 0.375 → 37.5%). Divide a percentage by 100 to get a decimal, or place it over 100 and simplify to get a fraction.
- Why does the percentage change depend on the starting value?
- Percentage change measures growth relative to the original amount. A $10 increase on $20 is 50%, but the same $10 increase on $200 is only 5%, because the base amount is larger.
- Can a percentage be greater than 100%?
- Yes. Percentages over 100% mean the part is larger than the whole. For example, earning 150% of a target means you achieved one and a half times the goal.