Exam Curve Calculator

A z-score curve preserves each student's relative standing. z = (your score − class mean) ÷ class standard deviation. Curved score = target mean + z × target standard deviation.

If the class averaged 72 with SD 10 and you want the curved exam centered at 80 with SD 8, a raw 82 (z = +1.0) becomes 80 + 1×8 = 88. This is a linear scale — it does not add flat points unless the target SD equals the original.

Example: raw 65, mean 72, SD 10 → z = −0.7. Target mean 80, SD 8 → curved ≈ 74.4. Verify your instructor's actual curve policy — some add fixed points instead.

Curving methods differ in what they change, and the labels are often used loosely. A flat bump adds the same points to everyone and shifts the mean without touching the spread. Scaling to a highest score divides by the top mark. Z-score rescaling sets both a target mean and a target spread. Percentile binning ignores raw distances entirely and assigns grades by rank.

Z-score rescaling can compress as well as lift. Moving a class from a mean of 72 with SD 10 to a mean of 80 with SD 8 raises almost everyone, but it narrows the distance between students: a raw 92 (z = +2.0) becomes 96 rather than 100, so strong performers gain less than the middle of the class. Whether that is fair depends on what the instructor intends the spread to mean.

You need the class mean and standard deviation, and standard deviation is the harder one to obtain. If the instructor publishes a histogram or quartiles, a workable estimate is the interquartile range divided by 1.35, or the full range divided by four for a roughly normal distribution of moderate size. An estimated SD makes the result indicative, not exact.

Rescaling assumes the score distribution is roughly symmetric, and exam scores often are not. When a test is easy, scores pile up near the ceiling and the distribution skews left, so a z-based curve can push top students above 100 and overstate gains in the upper tail. This tool does not cap results at 100 — apply your instructor's cap manually.

A curve redistributes standing rather than creating knowledge, so treat any result as a projection of policy, not a grade. Ask which method your course actually uses before comparing raw and curved marks with classmates, since a flat bump and a z-score curve of the same average size reward completely different students.

Curves redistribute points relative to class performance — a flat +5 bump helps everyone equally, while scaling to a target mean shifts low and high scores differently. Know which policy your instructor applies before comparing raw and curved grades.