Grade Curve to Normal Calculator
Curve a raw score onto a target normal distribution — set a desired class mean and spread and see the rescaled grade and its percentile.
How it works
z = (raw − class mean) ÷ class SD · curved = target mean + z · target SD
A linear (z-score) curve rescales raw scores so the class fits a chosen mean and spread while preserving each student’s relative standing. Each score is turned into a z-score against the actual class statistics, then mapped onto the target distribution. Setting the target standard deviation to zero collapses everyone to the target mean; larger target spreads keep more separation between students.
Worked example
A raw score of 63 in a class with mean 58 and SD 12 gives z = (63 − 58) ÷ 12 ≈ 0.417. Curving to a target mean of 75 and SD 10 yields 75 + 0.417 × 10 ≈ 79.2, lifting the score while keeping it just above the new average.
Sources: Grading on a curve — Wikipedia
Frequently asked questions
Does this change the order of students?
No. A linear curve is monotonic, so anyone who scored higher on the raw test still scores higher after curving. Only the mean and spread of the grades change, not the ranking.
How is this different from adding a flat bonus?
Adding a constant shifts every score by the same amount but leaves the spread untouched. A z-score curve adjusts both the centre and the spread, so it can compress a wildly variable class or stretch a bunched-up one to hit a target distribution.
Can a curved score exceed 100 or fall below 0?
Yes — the linear formula has no built-in ceiling or floor, so extreme z-scores can land outside a 0–100 range. Instructors often cap the curved values afterward or pick a target mean and SD that keep results in range.
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For education — check the assumptions (sample size, distribution shape) before using statistics in real decisions.