How to use the curve score calculator
- Paste the scores, separated by commas, spaces or new lines, and enter the points the test is out of.
- Choose a curve: add flat points, raise the top score to the maximum, scale by one factor, a square root curve, or move the average to a target.
- Fill in the extra box that appears for flat points or a target average. Both are your own choices.
- Read the table of original and curved scores with the change and the percent of the maximum, and the average before and after.
Formula
flat: new = score + points
top score to max: new = score + (max - top score)
scale: new = score x max / top score
square root: new = max x sqrt(score / max)
target average: new = score + (target - current average)
Results are capped at the maximum unless you turn the cap off. Curved scores are shown to two decimals, and rounding them for a gradebook is up to your own policy.
Six scores out of 100
The scores are 58, 64, 71, 77, 82 and 90, with an average of 73.67. Raising the top score to 100 adds 10 to everyone, giving 68, 74, 81, 87, 92 and 100 with an average of 83.67. Adding a flat 5 points gives 63, 69, 76, 82, 87 and 95.
Scaling multiplies every score by 100 / 90, so 58 becomes 64.44 and 90 becomes 100, with an average of 81.85. The square root curve gives 10 x sqrt(score), so 58 becomes 76.16 and 90 becomes 94.87, with an average of 85.60. Moving the average to 75 adds 1.33 to every score.
How the curves differ
Adding points, whether flat or by lifting the top score, shifts everyone equally, so the gaps between students stay the same. Scaling widens the gaps at the top and shrinks them at the bottom in proportion to the score. The square root curve helps low scores the most and top scores the least, which makes it the strongest option for a hard test.
None of these is the right curve. Which to use is a decision for the instructor, and this page just shows what each would do.
Before and after
Check the average and the lowest and highest curved scores before you apply a curve. For the spread, pass rate and score distribution of the new scores, paste them into the class average calculator. For single scores, use the quiz score calculator, and for a weighted course grade, the grade calculator.
Assumptions and limits
- Scores must be between 0 and the maximum for the square root and scaling curves. Flat and average curves accept any non-negative score.
- The cap is on by default. Without it a curved score can be above the maximum.
- Rounding is not applied to curved scores. They are shown to two decimals.
- Your school or instructor may have rules about curving that this page does not know about.
Frequently asked questions
How do you curve a test?
Pick a rule that changes every score the same way, such as adding points or scaling to the top score. This page applies five common rules to your list and shows each curved score so you can compare.
What is the square root curve?
It replaces each score with the maximum times the square root of the score divided by the maximum. On a 100 point test that is 10 times the square root of the score, which lifts low scores more than high ones.
Does curving change the order of students?
No. Every curve here keeps higher scores above lower ones. Equal scores stay equal, and capping at the maximum can make several top scores equal.
Can a curved score go above the maximum?
Only if you turn the cap off, and only for rules that add points. With the cap on, any score above the maximum is shown as the maximum.