The short answer
Five common curves: flat (score + k), linear (score × 100 ÷ top score), square root (10 × √score), bell (target mean + z × target SD) and lowest-to-passing (everyone + passing − lowest). On the sample class (mean 71.3%, SD 10.95), +5 flat gives a mean of 76.3%, linear 78.4%, square root 84.2%, a bell curve to 78/10 exactly 78.0%, and lifting the lowest score to 60 gives 83.2% with a 100% cap.A test that most of the class did poorly on usually says something about the test, not just the students. Curving is one way to adjust for it. The five methods here are the ones teachers use most, and they behave very differently — so the calculator shows the whole class before and after instead of a single number.
The five curves, in one line each
| Method | Formula | Keeps | Best for |
|---|---|---|---|
| Flat points | score + k | Every gap between students | A question that was wrong or unfair for everyone |
| Highest to 100 | score × 100 ÷ top score | Ratios between scores | A test that was too long or too hard overall |
| Square root | 10 × √score | Order of students | Lifting low and middle scores most |
| Bell curve | target mean + z × target SD | Each student’s z-score | Matching a planned average and spread |
| Lowest to passing | score + (passing − lowest) | Every gap between students | Making sure no one fails the test |
Scores are converted to percents first using points possible, so you can paste raw points from a 60-point test and set points possible to 60.
Worked example: the sample class
The calculator opens with 20 scores out of 100, from 48 to 91. Before any curve, the mean is 71.3%, the median 71.5% and the standard deviation 10.95 points. On a 90/80/70/60 split that’s 1 A, 4 Bs, 7 Cs, 5 Ds and 3 Fs. Here’s what each curve does to the same class (cap at 100% on):
| Curve | Mean | Median | SD | Low | High | A / B / C / D / F |
|---|---|---|---|---|---|---|
| None (raw) | 71.3 | 71.5 | 10.95 | 48 | 91 | 1 / 4 / 7 / 5 / 3 |
| Flat +5 | 76.3 | 76.5 | 10.95 | 53 | 96 | 3 / 5 / 6 / 5 / 1 |
| Highest to 100 | 78.4 | 78.6 | 12.03 | 52.7 | 100 | 4 / 5 / 6 / 4 / 1 |
| Square root | 84.2 | 84.6 | 6.58 | 69.3 | 95.4 | 4 / 11 / 4 / 1 / 0 |
| Bell, mean 78, SD 10 | 78.0 | 78.2 | 10.00 | 56.7 | 96.0 | 3 / 6 / 7 / 3 / 1 |
| Lowest to 60 | 83.2 | 83.5 | 10.70 | 60 | 100 | 6 / 7 / 5 / 2 / 0 |
Notice how the square-root curve squeezes the class together (SD falls from 10.95 to 6.58): a 48 becomes 69.3 while a 91 becomes only 95.4. Linear scaling does the opposite and stretches the spread slightly, because higher scores gain more points.
How the bell curve really works
A bell curve here means re-centering and re-scaling: each student’s z-score (how many SDs they are from the raw mean) is kept, and the class is placed on a new mean and SD you choose. Formula: new = target mean + (score − raw mean) ÷ raw SD × target SD.
With a target of 78 and an SD of 10, the class mean lands exactly on 78 and the spread on 10, as long as the cap doesn’t cut off any top scores. It does not force a fixed number of As and Fs — that would be grading on a strict quota, which is a different policy. And it can lower scores if the target mean is below the raw mean, so check the table before you publish anything.
How to curve test scores to a target average: a five-student example
The sample class above shows the averages. This smaller example shows what happens to each student when the goal is “bring the class average from 68 up to about 75”. Raw scores: 52, 61, 68, 74 and 85 out of 100 (mean 68.0, population SD 11.22). On the standard plus/minus scale that is an F, D−, D+, C and B.
Five raw scores under four curves (letters on the standard plus/minus scale)
| Raw score | Flat +7 | Highest to 100 | Square root | Bell, mean 75, SD 10 |
|---|---|---|---|---|
| 52 (F) | 59 (F) | 61.2 (D−) | 72.1 (C−) | 60.7 (D−) |
| 61 (D−) | 68 (D+) | 71.8 (C−) | 78.1 (C+) | 68.8 (D+) |
| 68 (D+) | 75 (C) | 80.0 (B−) | 82.5 (B−) | 75.0 (C) |
| 74 (C) | 81 (B−) | 87.1 (B+) | 86.0 (B) | 80.3 (B−) |
| 85 (B) | 92 (A−) | 100 (A+) | 92.2 (A−) | 90.1 (A−) |
| Class mean | 75.0 | 80.0 | 82.2 | 75.0 |
How each number was found:
- Flat: the target is 75 and the mean is 68, so everyone gets 75 − 68 = 7 points. The average hits 75 exactly and every gap stays the same.
- Highest to 100: each score × 100 ÷ 85. The mean lands at 80, more than the target, because the top score was far from 100.
- Square root: 10 × √score. 52 becomes 72.1, so the weakest paper gains 20 points while the strongest gains 7.
- Bell curve: 75 + (score − 68) ÷ 11.22 × 10. It hits the target mean and also narrows the spread to 10.
If the goal is a precise class average, scaling grades with a flat or bell curve does it; the other two overshoot. Before you curve, look at which questions most students missed, since one broken item is better fixed directly. Students can confirm their own curved percent with the test score calculator, and the easy grader for teachers turns the next quiz’s wrong answers into percents in one step.
Choosing a curve you can explain
Students and parents accept a curve much more easily when the reason is clear. A few practical rules:
- Fix the cause when you can. If one question was broken, drop it or give everyone the point. That’s a flat curve with a clear reason.
- Announce the method, not just the result. “Everyone gets 10 × √score” is easy to check; a hand-adjusted list isn’t.
- Watch the top. Flat and lowest-to-passing curves can push scores past 100%. The cap keeps them at 100.
- Don’t mix methods across sections of the same course unless the tests differed.
Ana 72 or Ana, 72 on a line to keep names next to scores. The calculator reads them only in your browser, never puts them in the link, and writes them only to the CSV you download.Exporting and next steps
Download CSV saves a spreadsheet with the raw score, the percent and letter before, and the percent and letter after for every student — ready to paste into your gradebook. Then:
- Grading a stack of tests quickly? The EZ Grader turns wrong answers into percents with a printable chart.
- Need a class average from mixed letters and percents? Use the average grade calculator.
- Students asking what a single score means: the test score calculator.
- Building the next assessment: the rubric maker.
Frequently asked questions
What is the fairest way to curve a test?
How does the square-root curve work?
Can a bell curve lower someone's grade?
Should curved scores go over 100%?
Are student names uploaded?
How do you curve grades step by step?
How do I curve a test so the top score is 100?
What is a flat curve vs a linear curve?
Sources & method
- Formulas computed in your browser: flat x + k; linear x × 100 ÷ max; square root 10√x; bell curve μ′ + (x − μ) ÷ σ × σ′; lowest-to-passing x + (p − min). SD is the population standard deviation.
- Letters use the common US plus/minus scale (A 93, A− 90, B+ 87…); distribution bars group by 90/80/70/60. See the grading scale converter.
Formulas checked October 2026. Spotted an error? Tell us via the about page.