Grade curve calculator
Enter your score and a few numbers about the class. You see your score under the four curves instructors use most, with the formula and the arithmetic for each one.
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The four curves
Every formula works in percentages: your points divided by the points possible, times 100. Scores above 100 are capped at 100 unless you untick that option.
Flat curve. Everyone gets the same number of points added. Often the amount is whatever brings the top score to 100.
curved = score + k, where k = 100 − highest score
Scale to the highest score. The top score becomes 100 and everyone else is scaled by the same factor.
curved = score × 100 / highest score
Square root curve. Take the square root of the score and multiply by 10. A 100 stays 100, an 81 becomes 90 and a 64 becomes 80, so low scores gain the most.
curved = 10 × √score
Bell curve to a target average. Every score moves by the gap between the class average and the average the instructor wants. If a target spread is also given, scores are first measured in standard deviations from the class average (a z-score) and then placed on the new average and spread.
curved = score + (target average − class average)
curved = target average + (score − class average) × target spread / class standard deviation
When you paste the whole class’s scores, the standard deviation is the population one: divide by the number of scores, not one fewer.
A worked example
A test is out of 80 points. You scored 58, the top score was 74, the class average was 48.8 and the standard deviation was 7.2 points. In percentages: you have 72.5%, the top is 92.5%, the average is 61% and the standard deviation is 9 points.
- Flat: k = 100 − 92.5 = 7.5, so 72.5 + 7.5 = 80%.
- Scale to highest: 72.5 × 100 / 92.5 = 78.38%.
- Square root: 10 × √72.5 = 10 × 8.515 = 85.15%.
- Target average of 75: 72.5 + (75 − 61) = 86.5%.
- Target average 75, spread 10: 75 + (72.5 − 61) × 10 / 9 = 75 + 12.78 = 87.78%.
The same raw score lands anywhere from a C+ to a B+ on a common syllabus scale, depending on the curve. Press “Fill in the example” to see it in the calculator.
Which curve helps you most
The square root curve lifts low scores far more than high ones: 40 becomes 63.25 and 90 becomes 94.87. Scaling to the highest score gives everyone the same proportional lift, so higher scores gain more points. A flat curve gives everyone the same points. A shift to a target average helps everyone equally too, but when the class average is already above the target it lowers scores, and the calculator flags that. If you paste the class’s scores, each curve also shows the class average it produces.
What this does not cover
Some instructors curve by rank instead, for example giving an A to the top 15% of the class whatever their scores. That depends on everyone’s rank, not a formula on your score, so it isn’t here. Your syllabus or instructor decides which curve, if any, applies. To see what the curved score does to a single test’s letter or to your course grade, use the test score calculator or the weighted grade calculator.
Grade curve calculator FAQ
How does curving a grade work?
The instructor applies the same rule to every score on a test so that the results land higher, usually because the test turned out harder than intended. The four common rules are adding points, scaling to the top score, the square root curve and moving the class to a target average. The calculator shows all four side by side.
What is the square root curve?
Your curved score is 10 times the square root of your percentage. A 64 becomes 80, an 81 becomes 90 and a 100 stays 100. Low scores gain the most, which is why some instructors like it after a hard test.
How do I curve scores to a target average?
Add the difference between the target average and the class average to every score. If the class averaged 61% and the target is 75%, everyone gains 14 points. To set a target spread as well, use the z-score formula above.
Can a curve lower my grade?
Yes, by formula. Scaling lowers scores when the top score is above the value it is scaled to, and a target average lowers scores when the class is already above it. Instructors rarely apply a curve that does that, and the calculator flags it when it happens.
Which curve gives the highest score?
It depends on where your score sits. The square root curve helps low and middle scores most, scaling to the highest helps high scores most in points, and a flat curve or a shift gives everyone the same. The calculator lists your score under each one so you can compare.
Does this calculator send or save my grades?
No. The math runs in your browser, and the numbers and names you type are not sent to any server or stored on your device. Close the tab and they are gone. Like every page on this site, the page itself is counted in our visit statistics, which never include what you type.
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