Calculate Percentage Marks
1. What is Percentage?
A percentage is a way to express a number as a fraction of 100. The word "percent" means "per hundred" or "out of 100".
The symbol used for percentage is %
2. Basic Percentage Formula
Main Formula
\[\text{Percentage} = \frac{\text{Obtained Value}}{\text{Total Value}} \times 100\]
3. How to Calculate Percentage of Marks
Formula for Marks Percentage
\[\text{Percentage of Marks} = \frac{\text{Marks Obtained}}{\text{Total Marks}} \times 100\]Components:
- Marks Obtained: The actual marks/score you received
- Total Marks: The maximum possible marks
- Result: Your percentage score
4. Interactive Percentage Calculator
📊 Calculate Your Percentage
5. Step-by-Step Calculation Method
Steps to Calculate Percentage
- Write down the marks obtained
- Write down the total marks
- Divide marks obtained by total marks
- Multiply the result by 100
- Add the % symbol to your answer
6. Worked Examples
Example 1: Simple Percentage Calculation
Question: A student scored 85 marks out of 100. What is the percentage?
Solution:
Given:
- Marks Obtained = 85
- Total Marks = 100
Using the formula:
\[\text{Percentage} = \frac{85}{100} \times 100\] \[\text{Percentage} = 0.85 \times 100\] \[\text{Percentage} = 85\%\]
Answer: The student scored 85%
Example 2: Multiple Subjects
Question: A student scored the following marks. Calculate the overall percentage.
| Subject | Marks Obtained | Total Marks |
|---|---|---|
| Mathematics | 78 | 100 |
| Science | 85 | 100 |
| English | 72 | 100 |
| Social Studies | 88 | 100 |
| Computer | 92 | 100 |
Solution:
Step 1: Calculate total marks obtained
\[\text{Total Marks Obtained} = 78 + 85 + 72 + 88 + 92 = 415\]Step 2: Calculate total maximum marks
\[\text{Total Maximum Marks} = 100 \times 5 = 500\]Step 3: Calculate percentage
\[\text{Percentage} = \frac{415}{500} \times 100 = 83\%\]
Answer: The overall percentage is 83%
Example 3: Different Total Marks
Question: Calculate percentage when subjects have different maximum marks.
| Subject | Marks Obtained | Total Marks |
|---|---|---|
| Theory | 65 | 80 |
| Practical | 38 | 50 |
| Project | 55 | 70 |
Solution:
\[\text{Total Obtained} = 65 + 38 + 55 = 158\]
\[\text{Total Maximum} = 80 + 50 + 70 = 200\]
\[\text{Percentage} = \frac{158}{200} \times 100 = 79\%\]
Answer: The percentage is 79%
7. Common Grading Systems
Standard Percentage to Grade Conversion
| Percentage Range | Grade | Description |
|---|---|---|
| 90% - 100% | A+ | Outstanding |
| 80% - 89% | A | Excellent |
| 70% - 79% | B+ | Very Good |
| 60% - 69% | B | Good |
| 50% - 59% | C | Average |
| 40% - 49% | D | Pass |
| Below 40% | F | Fail |
8. Reverse Calculation: Finding Marks from Percentage
Formula to Find Marks
\[\text{Marks Obtained} = \frac{\text{Percentage} \times \text{Total Marks}}{100}\]
Example: If a student scored 75% out of 500 marks, what are the actual marks?
\[\text{Marks} = \frac{75 \times 500}{100} = \frac{37500}{100} = 375\]
Answer: 375 marks
9. Important Formulas Summary
| What to Find | Formula |
|---|---|
| Percentage | \(\frac{\text{Obtained}}{\text{Total}} \times 100\) |
| Marks from Percentage | \(\frac{\text{Percentage} \times \text{Total}}{100}\) |
| Total Marks | \(\frac{\text{Obtained} \times 100}{\text{Percentage}}\) |
| Percentage Increase | \(\frac{\text{Increase}}{\text{Original}} \times 100\) |
| Percentage Decrease | \(\frac{\text{Decrease}}{\text{Original}} \times 100\) |
10. Tips for Percentage Calculation
Quick Tips
- Always divide obtained marks by total marks first, then multiply by 100
- Round percentages to 2 decimal places for precision
- Check if obtained marks exceed total marks (impossible scenario)
- For multiple subjects, add all obtained marks and all total marks separately
- Use a calculator for complex calculations to avoid errors
- Remember: Percentage is always out of 100
- To convert fraction to percentage: multiply by 100
- To convert percentage to fraction: divide by 100
11. Common Mistakes to Avoid
- Forgetting to multiply by 100 - This gives you a decimal, not a percentage
- Dividing total by obtained - Always divide obtained by total
- Adding wrong marks - Double-check your addition in multi-subject calculations
- Using wrong total - Make sure you're using the correct maximum marks
- Rounding too early - Round only at the final step for accuracy
💡 Pro Tip
Always verify your percentage calculation by doing the reverse calculation. If you got 80%, multiply it by total marks and divide by 100 - you should get back your obtained marks!