Grade Curve Calculator
Curve a list of test scores with a square root curve, top-score shift, flat points, target mean or bell-curve z-score mapping, and compare means and spreads.
Interactive calculator · Method GRADE-CURVE-1.0 · Last reviewed: 2026-11-04
Calculate your scenario
Each score is first converted to a percent: p = score ÷ points possible × 100.
Your inputs
Default worked example. Edit the inputs to calculate your scenario.
Default worked example
10 scores on 100 points: mean 70.6% (SD 13.33) becomes 83.64% (SD 8) after the curve, capped at 100%.
How to use the calculator
Paste the raw scores, enter the points possible, pick a curve and its setting, and choose whether to cap at 100%. The table shows the first 12 scores in the order entered.
What the result means
With the square root curve, the 10 sample scores averaging 70.6% rise to about 83.6%, and the spread narrows because low scores gain the most.
Formula and units
Each score is first converted to a percent: p = score ÷ points possible × 100. Square root: 10 × √p. Top shift: p + (100 − highest p). Flat: p + points. Target mean: p + (target − mean). Bell curve: target mean + target SD × (p − mean) ÷ SD. Curved scores below 0 become 0 and, if chosen, scores above 100 become 100. Means and SDs use every score; SD is the population SD (divide by n).
Worked examples
Square root curve on 10 scores: Points possible: 100 points; Points to add (flat curve): 5 percentage points; Target mean (target-mean and bell curves): 75 %; Target standard deviation (bell curve): 10 percentage points; Curve: sqrt; Cap curved scores at 100%: yes; Scores (separate with commas, spaces or new lines; up to 500): 62, 71, 55, 88, 79, 64, 70, 93, 48, 76.
Example result: Curved mean: 83.64%; Curved SD: 8 points; Original mean: 70.6%; Original SD: 13.33 points; Curved min / max: 69.28% / 96.44%; Scores read: 10.
Bell curve on 7 scores out of 50: Points possible: 50 points; Points to add (flat curve): 5 percentage points; Target mean (target-mean and bell curves): 75 %; Target standard deviation (bell curve): 10 percentage points; Curve: z; Cap curved scores at 100%: yes; Scores (separate with commas, spaces or new lines; up to 500): 31 44 38 50 27 35 41.
Example result: Curved mean: 75%; Curved SD: 10 points; Original mean: 76%; Original SD: 14.5 points; Curved min / max: 59.83% / 91.55%; Scores read: 7.
Limitations and common mistakes
A curve is a teacher or institution policy choice, not an official standard and not inherently fair: each method rewards different students (the square root curve helps low scores most; a bell curve can lower some scores). Capping changes the curved mean and SD. Scores are processed on this page only.
Applying the square root curve to raw points on a test that is not out of 100; this calculator converts to percent first, which is how the curve is defined.
Sources and assumptions
Method GRADE-CURVE-1.0; last formula review 2026-11-04. Sources and their supported claims. Calculation methodology.