About the Z-Score to Grade Calculator
What is the Z-Score to Grade Calculator?
Under relative grading, used by IITs and many universities, your grade depends on how you did compared with the class. This calculator converts your score into a z-score – the number of standard deviations from the class average.
It then maps the z-score to a grade and shows your percentile in the class.
How to use the Z-Score to Grade Calculator
- Your Score (sample: 78)
- Class Average (sample: 65)
- Standard Deviation of Scores (sample: 10)
- Press Grade on the Curve (results also refresh as you type). The result card shows the Relative Grade, along with Z-score, Percentile, Share of class scoring higher and Grading scheme.
Formula used
z = (Your score − Class average) ÷ Standard deviation
- Percentile = Φ(z), the normal distribution
Each institution sets its own cut-offs for relative grades.
Worked example
These are the sample values already filled in the calculator above, and the result it returns for them:
| Input | Sample value |
|---|---|
| Your Score | 78 |
| Class Average | 65 |
| Standard Deviation of Scores | 10 |
| Result | Value |
|---|---|
| Relative Grade | A |
| Z-score | 1.3 |
| Percentile | 90.3% |
| Share of class scoring higher | 9.7% |
| Grading scheme | A+ ≥ mean + 1.5σ, A ≥ +1σ, B+ ≥ +0.5σ, B ≥ mean, C ≥ −0.5σ, D ≥ −1σ, F below |
Tips for using the Z-Score to Grade Calculator
- In relative grading, a tough paper hurts everyone equally.
- Ask your instructor for the class mean and standard deviation.