What each curve actually does

"I curved the test" hides a decision. Every standard curve raises the class mean, but they hand the points to completely different students — some pay the bottom of the roster, some pay the top, and a teacher who picks one without seeing the per-student table is choosing winners blind. This guide runs five curves on one six-score roster and shows the choice in numbers. The roster: 42, 55, 61, 70, 78, 85 — mean 65.17, the calculator's pre-loaded example.

Flat points: everyone the same

Add 5 to every score and the mean moves 65.17 → 70.17, mechanically. Every student gains exactly 5, which sounds neutral — and in points it is. In letters it is not: on the common scale, +5 moves five of these six students up a letter (55 crosses into D− territory, 61 into D, 70 into C, 78 into B, 85 into A−) while the 42 stays an F. Boundary geography, not the curve, decides who converts points into letters.

Shift the top to 100: a flat curve in disguise

"Highest score becomes 100" sounds like a rescale but is usually implemented as a shift: the top is 85, so everyone gains 15. Mean 65.17 → 80.17. It is exactly the flat curve with the amount chosen by the best student — worth knowing, because the class's gain then depends on one performance. If the top score is already 100, the tool refuses to run this curve rather than shift the class downward.

Rescale the top to 100: the multiplier that favors the top

Multiply every score by 100/85 (about 1.176) and the top lands exactly on 100. But a multiplier pays proportionally: the 85 gains 15.0 points while the 42 gains only 7.4 (to 49.4). Mean 65.17 → 76.67. The students who least needed help received the most — which is sometimes the intent (rewarding the strong test) and sometimes the opposite of it. The per-student table makes the direction impossible to miss.

The square-root curve: the one that favors the bottom

The classic square-root curve replaces each score with 10×√score. The 42 becomes 64.8 — a gain of 22.8 — while the 85 becomes 92.2, a gain of 7.2. Mean 65.17 → 80.21. Set it beside the rescale: nearly the same after-mean (80.21 versus 76.67 here), opposite recipients. Square root compresses the roster (the gap between the extreme students shrinks from 43 points to 27.4); the multiplier stretches it. Two curves, one class, and the "same" generosity lands on different desks.

Curve to a target mean: name the number, accept the direction

Shift every score so the mean hits a target: for a target of 75, everyone gains 75 − 65.17 = 9.83. It is the flat curve again, with the amount picked by an outcome instead of a feel. One honest wrinkle: if the class mean already sits above the target, this curve shifts scores down — the tool applies it, because you named the target, and says plainly that the shift was downward. The other curves never lower a score, so this is the one to double-check before pasting into a gradebook.

The cap question

Any additive or multiplied curve can push scores past 100. The tool leaves them uncapped by default so the arithmetic stays visible, with a toggle to trim at 100. Capping is not free: it quietly lowers the after-mean whenever anyone hits the ceiling, and it takes the most from exactly the students the curve paid most. Decide it, do not default into it.

Policy, stated honestly

Whether to curve at all is policy — a syllabus and sometimes a department decision — and nothing on this page argues for it. What the curve applier does is make the arithmetic of each option visible before anyone commits: before and after means, every student's delta, and the letter distribution both ways, computed on the spot with nothing leaving the page. Measure first with the gradebook average calculator; if the numbers say the assessment ran cold, pick the curve whose winners you actually intend.