math calculator
Percentage Calculator
Handle common percentage math for discounts, salaries, tax, and comparisons.
Why this layout
Inputs, answers, and explainers are grouped for faster scanning on mobile and desktop.
Next step
Finish the calculation, then jump to a related tool without hunting through menus.
How to Use This Percentage Calculator
Our percentage calculator helps you solve various percentage problems quickly and accurately:
- Calculate Percentage: Enter the part and whole values to find what percentage one number is of another.
- Find Percentage Value: Input the percentage and total to calculate the actual value (e.g., 20% of 500).
- Percentage Increase/Decrease: Enter original and new values to calculate the percentage change.
- Reverse Calculation: Find the original value when you know the percentage and final value.
- Instant Results: All calculations update in real-time as you type.
Common Percentage Formulas
Basic Percentage Formula
Percentage = (Part / Whole) × 100
Example: What percentage is 30 of 150? → (30/150) × 100 = 20%
Percentage Increase
% Increase = [(New Value - Old Value) / Old Value] × 100
Example: Price increased from ₹100 to ₹125 → [(125-100)/100] × 100 = 25%
Percentage Decrease
% Decrease = [(Old Value - New Value) / Old Value] × 100
Example: Price dropped from ₹200 to ₹150 → [(200-150)/200] × 100 = 25%
Real-World Applications
Business & Finance
- • Calculate profit margins and markups
- • Determine sales tax and discounts
- • Analyze revenue growth rates
- • Track expense percentages
Education & Grades
- • Convert marks to percentages
- • Calculate grade point averages
- • Determine passing percentages
- • Track academic improvement
Shopping & Savings
- • Calculate discount percentages
- • Compare price changes
- • Determine savings amounts
- • Evaluate cashback offers
Health & Fitness
- • Track weight loss/gain percentages
- • Calculate body fat percentages
- • Monitor fitness improvements
- • Measure nutritional values
Detailed Real-World Examples
Shopping Discount
A shirt costs ₹1,200 with a 30% discount. How much do you save and pay?
Calculation:
Discount = 30% of ₹1,200
= (30/100) × 1,200 = ₹360
Final Price = ₹1,200 - ₹360 = ₹840
You save ₹360!
Salary Hike
Your salary increased from ₹40,000 to ₹48,000. What's the percentage increase?
Calculation:
Increase = ₹48,000 - ₹40,000 = ₹8,000
% Increase = (8,000/40,000) × 100
= 0.20 × 100 = 20%
20% salary hike!
Exam Score
You scored 432 marks out of 600. What's your percentage?
Calculation:
Percentage = (Marks Obtained / Total Marks) × 100
= (432/600) × 100
= 0.72 × 100 = 72%
You scored 72%!
Weight Loss
You lost weight from 80kg to 72kg. What's the percentage decrease?
Calculation:
Weight Lost = 80 - 72 = 8kg
% Decrease = (8/80) × 100
= 0.10 × 100 = 10%
10% weight loss!
Advanced Percentage Scenarios
Successive Discounts: 20% + 10% ≠ 30%
Problem: A product costs ₹1,000. First, a 20% discount is applied, then an additional 10% discount. What's the final price?
Step 1: Apply first discount (20%)
Price after 20% off = ₹1,000 - (20% of ₹1,000)
= ₹1,000 - ₹200 = ₹800
Step 2: Apply second discount (10% on ₹800)
Price after 10% off = ₹800 - (10% of ₹800)
= ₹800 - ₹80 = ₹720
Total Discount: ₹1,000 - ₹720 = ₹280 (28%, not 30%!)
Reverse Percentage: Finding Original Price
Problem: After a 25% discount, you paid ₹750. What was the original price?
Logic: If 25% discount, you paid 75% of original price
75% of Original Price = ₹750
(75/100) × Original Price = ₹750
Original Price = ₹750 × (100/75)
Original Price = ₹1,000
Verification: 25% of ₹1,000 = ₹250 discount → Final = ₹750 ✓
Business & Finance Applications
📊Profit Margin Calculation▼
Calculate profit margin to understand business profitability:
Example: Product cost = ₹600, Selling price = ₹900
Profit = ₹900 - ₹600 = ₹300
Profit Margin = (Profit / Selling Price) × 100
= (300/900) × 100 = 33.33%
33.33% profit margin is healthy for retail!
💳Credit Card Interest▼
Understanding credit card charges:
Scenario: Outstanding balance = ₹50,000, Monthly interest = 3%
Monthly Interest = 3% of ₹50,000
= (3/100) × 50,000 = ₹1,500
Annual Interest Rate = 3% × 12 = 36%
Always pay full balance to avoid high interest!
📈Investment Returns▼
Calculate returns on your investments:
Example: Invested ₹1,00,000, Current value = ₹1,35,000
Gain = ₹1,35,000 - ₹1,00,000 = ₹35,000
Return % = (Gain / Investment) × 100
= (35,000/1,00,000) × 100 = 35%
35% return is excellent!
💡 Quick Percentage Tricks
⚡ Mental Math Shortcuts
- • 10%: Divide by 10 (move decimal left)
- • 5%: Half of 10%
- • 1%: Divide by 100
- • 25%: Divide by 4 (quarter)
- • 50%: Divide by 2 (half)
- • 75%: 50% + 25%
✓ Quick Examples
- • 10% of ₹850 = ₹85
- • 5% of ₹850 = ₹42.50
- • 25% of ₹800 = ₹200
- • 50% of ₹1,200 = ₹600
- • 75% of ₹400 = ₹300
- • 15% = 10% + 5%
🔄 Percentage Symmetry
- • 20% of 50 = 50% of 20 = 10
- • 8% of 25 = 25% of 8 = 2
- • 16% of 50 = 50% of 16 = 8
- • Flip numbers for easier calculation!
📐 Fraction Equivalents
- • 50% = 1/2
- • 25% = 1/4
- • 33.33% = 1/3
- • 20% = 1/5
- • 10% = 1/10
- • Use fractions for quick mental math!
Frequently Asked Questions
How do I calculate percentage increase?▼
To calculate percentage increase, subtract the original value from the new value, divide by the original value, and multiply by 100. Formula: [(New Value - Original Value) / Original Value] × 100. For example, if a price increases from ₹100 to ₹120, the percentage increase is [(120-100)/100] × 100 = 20%.
What is the difference between percentage and percentile?▼
Percentage represents a portion out of 100 (e.g., 75% means 75 out of 100). Percentile indicates the position of a value in a dataset relative to others (e.g., 75th percentile means the value is greater than 75% of the data). Percentage is a ratio, while percentile is a rank or position.
How do I find what percentage one number is of another?▼
Divide the first number by the second number and multiply by 100. Formula: (Part / Whole) × 100. For example, to find what percentage 25 is of 200: (25/200) × 100 = 12.5%. This is useful for calculating discounts, completion rates, and proportions.
Why do successive discounts not add up?▼
Successive discounts are applied sequentially, not additively. The second discount is calculated on the already-reduced price, not the original price. For example, 20% + 10% discount on ₹100: First discount = ₹20 (price becomes ₹80), Second discount = 10% of ₹80 = ₹8 (final price ₹72). Total discount = ₹28 (28%), not ₹30 (30%).
How do I calculate the original price after a discount?▼
If you know the discounted price and discount percentage, use: Original Price = Discounted Price / (1 - Discount%/100). Example: Paid ₹800 after 20% discount. Original = 800 / (1 - 0.20) = 800 / 0.80 = ₹1,000. Alternatively: If 20% off, you paid 80%, so Original = (800 × 100) / 80 = ₹1,000.
What's the difference between markup and margin?▼
Markup is profit as a percentage of cost. Margin is profit as a percentage of selling price. Example: Cost = ₹100, Selling Price = ₹150, Profit = ₹50. Markup = (50/100) × 100 = 50%. Margin = (50/150) × 100 = 33.33%. Markup is always higher than margin for the same transaction.
How do I calculate percentage change between two numbers?▼
Use the formula: [(New Value - Old Value) / Old Value] × 100. If the result is positive, it's an increase. If negative, it's a decrease. Example: Sales changed from ₹50,000 to ₹45,000. Change = [(45,000 - 50,000) / 50,000] × 100 = -10%. This means a 10% decrease in sales.
Can percentages exceed 100%?▼
Yes! Percentages can exceed 100% in growth scenarios. If a stock price increases from ₹100 to ₹300, the percentage increase is [(300-100)/100] × 100 = 200%. This means the price tripled (increased by 200% of the original value). However, percentage decrease cannot exceed 100% (you can't lose more than everything).
How do I convert percentage to decimal and vice versa?▼
To convert percentage to decimal: Divide by 100 (or move decimal point two places left). Example: 45% = 45/100 = 0.45. To convert decimal to percentage: Multiply by 100 (or move decimal point two places right). Example: 0.75 = 0.75 × 100 = 75%. This is useful for calculations and formulas.
What's the easiest way to calculate 15% tip at a restaurant?▼
Quick method: Find 10% (move decimal left), then add half of that for 5%. Example: Bill = ₹850. 10% = ₹85. 5% = ₹42.50. Total 15% tip = ₹85 + ₹42.50 = ₹127.50. Even quicker: 15% ≈ 1/7 of the bill (slightly less). For ₹850, 1/7 ≈ ₹121. Round up to ₹130 for convenience!