Grade Curve Calculator
Paste a class's test scores and curve them with a flat curve, a bell curve, a square root curve or by scaling to a target mean, then compare the before and after statistics and export the new grades. Scores never leave your browser.
Score distribution
Letter grades
Scale: A 90+, B 80+, C 70+, D 60+, F below 60 (percent of max).
Per-student results
How to use the Grade Curve Calculator
- Paste the scores, one per line, separated by commas, or as Name, score lines, and set the maximum possible points.
- Pick a curve method: flat, add points, shift or scale to a mean, bell curve, square root or proportional.
- Set the target (for example a 75% class average and 10% standard deviation for a bell curve).
- Press Apply curve and compare the before and after statistics, histogram and letter distribution.
- Export CSV or copy the curved scores to paste them into your gradebook.
Grade curve formulas
| Method | Formula (scores in points, max = M) | Example (class mean 68, SD 12, top 88, M = 100) |
|---|---|---|
| Flat to top score | new = old + (target top − highest) | +12 points for everyone: 70 → 82 |
| Add points | new = old + k | k = 5: 70 → 75 |
| Shift to mean | new = old + (target mean − mean) | target 75: +7 points, 70 → 77 |
| Scale to mean | new = old × target mean ÷ mean | × 75/68 = 1.103: 70 → 77.2 |
| Bell curve | new = target mean + (old − mean) ÷ SD × target SD | target 75 / 10: 70 → 75 + (2/12) × 10 = 76.7 |
| Square root | new = √(old ÷ M) × M | 70 → √0.70 × 100 = 83.7 |
| Proportional | new = old ÷ highest × M | 70 ÷ 88 × 100 = 79.5 |
The flat, shift and add methods keep the point gaps between students. Scaling and the proportional method stretch gaps a little. The bell curve resets both the average and the spread. The square root curve compresses the top and lifts the bottom.
Square root curve reference
| Original % | 36 | 49 | 50 | 60 | 64 | 70 | 81 | 90 | 100 |
|---|---|---|---|---|---|---|---|---|---|
| Curved % | 60 | 70 | 70.7 | 77.5 | 80 | 83.7 | 90 | 94.9 | 100 |
Choosing and explaining a curve
- Look at the statistics first. If the mean is low but the spread is normal, a flat curve or shift to mean is simple and transparent. If the test was too hard for everyone, the square root curve is gentle on the strongest students and generous to the weakest.
- Bell curves need enough students. With fewer than about 30 scores the distribution is rarely close to normal, and forcing a set standard deviation can push some scores down. Tick "Never lower a score" to protect students.
- Cap at the maximum unless you want curved scores above 100% to count as extra credit.
- Round once, at the end. The calculator curves exact values and rounds only the final scores, so rounding errors do not add up.
- Keep a record. Export the CSV, which lists the original and curved scores, percentages and letter grades, and attach it to your gradebook notes.
For a deeper look at the spread of your scores, use the standard deviation calculator; to combine curved tests with other categories, use the weighted average calculator.
Frequently asked questions
How does a bell curve work for grades?
Each score is turned into a z-score, the number of standard deviations it is from the class mean: z = (score − mean) ÷ SD. The new score is target mean + z × target SD. A student exactly at the average gets the target mean, and the spread of the class is set to the target standard deviation. Ranks never change.
What is a flat curve?
A flat curve adds the same number of points to every score. The most common version adds the difference between the highest score and 100%, so the top student gets 100% and everyone else gets the same boost.
What is the square root curve?
The new percentage is the square root of the old percentage times 10 (for a 100-point test: √score × 10). A 64 becomes 80, an 81 becomes 90 and a 100 stays 100. Low scores gain the most and nobody goes above 100%.
Can curving lower a student's grade?
A bell curve or a scaled curve can lower scores if the class average is above the target. Tick Never lower a score to keep each student's original score whenever the curve would reduce it.
Which curve method is fairest?
It depends on the goal. A flat curve keeps the gaps between students, which is easy to explain. The square root curve helps weaker scores most. A bell curve standardizes results to a fixed average and spread, which suits large classes but can feel arbitrary in small ones. Always tell students which method you used.
Is population or sample standard deviation used?
The class is treated as the whole population, so the standard deviation divides by n. This is the usual choice for curving because you are describing this class, not estimating a wider group.
Are the scores uploaded anywhere?
No. Parsing, curving and the CSV export all happen in your browser. Nothing is sent to a server.