Bell Curve Grade Calculator
Turn a raw score into a curved letter grade using the class mean and standard deviation on a normal curve.
How it works
z = (score − mean) ÷ standard deviation · letter: A z≥1.5, B z≥0.5, C z≥−0.5, D z≥−1.5, else F
Curving to a bell rescales each score by how far it sits from the class mean, measured in standard deviations (the z-score). A common scheme centres the C grade on the mean and awards higher letters as scores climb further above it: roughly a B one half-deviation up, an A a deviation and a half up, and symmetric bands below. Because it grades relative to the class, the same raw score can earn different letters depending on how the whole class performed.
Worked example
A raw 82 with a class mean of 74 and standard deviation of 8 gives z = (82 − 74) ÷ 8 = 1.00. That is the 84th percentile and falls in the 0.5-to-1.5 band, so it curves to a B.
Sources: Normal distribution — Wikipedia
Frequently asked questions
Is there one official bell-curve scheme?
No. This tool uses the common half-deviation bands centred on the mean, but instructors set their own cutoffs — some target fixed percentages per grade, others shift the whole curve up. Treat the letter as a typical mapping, not a rule.
Where do I get the mean and standard deviation?
From the class results. Enter every score into a standard deviation or mean/median/mode calculator to get both figures, then bring them here to see where any one score lands.
Does curving ever lower a grade?
On a true normal curve, yes — scores well above the mean stay high, but if the mean is high and the spread small, a middling raw score can land at only a C. Pure "add points to the top" curves never lower a grade, but this relative method can.
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This calculator is for educational purposes. Double-check important results before acting on them.