Grade Curve Calculator
Curve a class's scores by flat points, highest score, target average, bell curve or square root — and see every student's new grade.
- Mean
- 68 → 74.8
- Median
- 68.5 → 75.5
- SD
- 13.86 → 13.47
- Scores lowered
- 0
| # | Before | After | Change | Letter |
|---|---|---|---|---|
| 1 | 45 | 52 | +7 | F → F |
| 2 | 52 | 59 | +7 | F → F |
| 3 | 58 | 65 | +7 | F → D |
| 4 | 63 | 70 | +7 | D → C |
| 5 | 67 | 74 | +7 | D → C |
| 6 | 70 | 77 | +7 | C → C |
| 7 | 72 | 79 | +7 | C → C |
| 8 | 76 | 83 | +7 | C → B |
| 9 | 82 | 89 | +7 | B → B |
| 10 | 95 | 100 | +5 | A → A |
Which curving method should you use?
| Method | What it does | When it's fair | Low vs high scorers |
|---|---|---|---|
| Flat points | Adds the same points to everyone | A question was too hard for the whole class | Same gain for all |
| Highest = 100 | Multiplies by 100 ÷ top score | The best student's mark sets the ceiling | Higher scorers gain slightly more |
| Shift to mean | Adds (target − mean) to everyone | You want a set class average, same gaps | Same gain; top may hit the cap |
| Scale to mean | Multiplies by target ÷ mean | You want a set average, proportional gains | Higher scorers gain more |
| Bell curve | Maps z-scores onto a target mean and SD | Large classes where a normal spread is expected | Can lower top scores |
| Square root | 10 × √score | A gentle boost weighted to the bottom | Low scorers gain most |
Worked example: one class, three curves to a 75 average
Scores: 45, 52, 58, 63, 67, 70, 72, 76, 82, 95 — mean 68, SD 13.86 (population). Curving to a target average of 75 with three methods, capped at 100:
| Raw | Shift (+points) | Scale (×factor) | Bell curve (SD 10) |
|---|---|---|---|
| 45 | 52 | 49.6 | 58.4 |
| 52 | 59 | 57.4 | 63.5 |
| 58 | 65 | 64 | 67.8 |
| 63 | 70 | 69.5 | 71.4 |
| 67 | 74 | 73.9 | 74.3 |
| 70 | 77 | 77.2 | 76.4 |
| 72 | 79 | 79.4 | 77.9 |
| 76 | 83 | 83.8 | 80.8 |
| 82 | 89 | 90.4 | 85.1 |
| 95 | 100 | 100 | 94.5 |
| Mean | 74.8 | 74.52 | 75 |
The shift and scale curves land slightly under 75 because the top score is capped at 100. The bell curve hits 75 exactly but tightens the spread to SD 10, which lowers the top student's score.
Common mistakes
- Scores pushed above 100 — turn on the cap, or the new average will overstate the class.
- Bell curves on very small classes — with a handful of students the mean and SD are unstable, so one score swings everyone.
- Mixing up sample and population SD — a full class is a population (divide by n); use n − 1 only for a sample.
- Methods that lower grades — bell curves and scaling can push some scores down — check the flagged rows.
Frequently asked questions
How do you curve grades to a target class average?
Either add the same number of points to every score (target average − current average), or multiply every score by target ÷ current average. Adding keeps the gaps between students the same; multiplying gives higher scorers slightly more points. Capping at 100 pulls the final average a little below the target.
What does grading on a bell curve mean?
Each score is converted to a z-score — how many standard deviations it sits from the class mean — and then mapped onto a chosen mean and standard deviation: new = target mean + z × target SD. Students keep their rank; the spread is set by the target SD.
Can curving lower a student's grade?
Yes. Bell curves and scaling down to a lower target can push scores below the raw mark, especially at the top. This calculator flags every score that goes down so you can choose another method or raise the target.
Which grade curve method is the fairest?
There is no single answer. A flat curve treats every student the same, scaling to the highest score helps when one question was faulty for everyone, a square root curve gives the biggest boost to the lowest scores, and a bell curve suits large classes where a normal spread is expected.
About this calculator
- Built and reviewed by James Whitfield · How we build and test calculators
- Last reviewed: October 14, 2026
- Report an error