Percentage Calculator
Free online percentage calculator - Calculate percentages, percentage increase/decrease, discounts, tips, and solve all percentage problems instantly
Learn formulas, shortcuts, and real-world applications
Real-world examples explained
Learn essential formulas
Free comprehensive guide
What You'll Learn:
- ✓How to calculate percentages manually
- ✓Shopping discount strategies
- ✓Financial percentage applications
- ✓Common percentage mistakes to avoid
- ✓Advanced calculation techniques
- ✓Professional percentage tips
Understanding Percentages
A percentage represents a fraction of 100 and is one of the most practical mathematical concepts in daily life. Whether you're calculating discounts while shopping, determining test scores, analyzing business growth, or figuring out tips at restaurants, percentages simplify comparisons and help make informed decisions.
Quick Percentage Formulas
Example: 20% of 150 = (20 ÷ 100) × 150 = 30
Example: 40 is what % of 200? = (40 ÷ 200) × 100 = 20%
Example: From 50 to 75 = [(75-50) ÷ 50] × 100 = 50% increase
Real-World Percentage Applications
Shopping & Discounts
- • Calculate sale prices and savings
- • Compare product discounts
- • Determine final prices with tax
- • Calculate loyalty rewards
Finance & Business
- • Track investment returns
- • Calculate interest rates
- • Analyze profit margins
- • Measure sales growth
Education & Grading
- • Convert scores to percentages
- • Calculate grade averages
- • Determine test performance
- • Track academic progress
Data & Statistics
- • Analyze survey results
- • Calculate success rates
- • Compare performance metrics
- • Present research findings
Step-by-Step Examples
Example 1: Shopping Discount
Problem: A $80 jacket is on sale for 25% off. How much do you save and pay?
Step 1: Calculate discount: 25% of $80 = (25 ÷ 100) × 80 = $20
Step 2: Subtract from original: $80 - $20 = $60
Answer: You save $20 and pay $60
Example 2: Test Score
Problem: You got 42 out of 50 questions correct. What's your percentage?
Formula: (Correct ÷ Total) × 100
Calculation: (42 ÷ 50) × 100 = 84%
Answer: You scored 84%
Example 3: Salary Increase
Problem: Your salary increased from $50,000 to $55,000. What's the percentage increase?
Formula: [(New - Old) ÷ Old] × 100
Calculation: [(55,000 - 50,000) ÷ 50,000] × 100 = 10%
Answer: 10% salary increase
Mental Math Shortcuts
Move decimal point one place left
10% of 340 = 34.0
Half of 10%
5% of 200 = 10 (half of 20)
Divide by 4
25% of 80 = 20
Divide by 2
50% of 150 = 75
Common Percentage Mistakes to Avoid
A 10% increase followed by 10% decrease doesn't return to the original value because the base changes.
Example: $100 + 10% = $110, then $110 - 10% = $99 (not $100)
A change from 20% to 30% is a 10 percentage point increase, but a 50% relative increase.
Always divide by 100 when converting percentages to decimals for calculations.
15% = 0.15 (not 15)
Frequently Asked Questions
Use Reverse Calculations
If you know the final price after a discount, work backwards to find the original price. For example, if $80 is after a 20% discount, the original was $80 ÷ 0.80 = $100.
Chain Percentage Changes
For multiple successive percentage changes, multiply the factors. A 10% increase then 20% increase: 100 × 1.10 × 1.20 = 132 (total 32% increase, not 30%).
Verify Your Calculations
Always double-check by working backwards. If you calculated 25% of 200 = 50, verify: Is 50/200 = 0.25? Yes, so your answer is correct.
Decimal Precision Matters
For financial calculations, use at least 2 decimal places. For scientific calculations, you may need 4-6 decimal places for accuracy.
Common Fractions to %
Quick Conversions
Multiply by 100
0.85 = 85%
Divide by 100
45% = 0.45
Divide, then × 100
3/5 = 60%
Black Friday Sale
Item: $120 laptop
Discount: 35% off
Savings: $120 × 0.35 = $42
Pay: $78
Restaurant Tip
Bill: $85
Tip: 18%
Tip amount: $85 × 0.18 = $15.30
Total: $100.30
Final Exam Score
Correct: 47/60
Calculation: (47÷60) × 100
Score: 78.33%
Grade: C+
Sales Growth
Q1: $250K → Q2: $312K
Change: (312-250)/250 × 100
Growth: 24.8%
- 100% Free - No registration or payment required
- Instant Results - Real-time calculations as you type
- Mobile Friendly - Works on all devices
- Calculation History - Track your recent calculations
- Adjustable Precision - Choose decimal places
- Copy Results - One-click copy functionality
| % | Decimal | Fraction |
|---|---|---|
| 100% | 1.00 | 1/1 |
| 75% | 0.75 | 3/4 |
| 66.67% | 0.6667 | 2/3 |
| 50% | 0.50 | 1/2 |
| 33.33% | 0.3333 | 1/3 |
| 25% | 0.25 | 1/4 |
| 20% | 0.20 | 1/5 |
| 12.5% | 0.125 | 1/8 |
| 10% | 0.10 | 1/10 |
| 5% | 0.05 | 1/20 |