There is no single curve formula. A teacher may add flat points, scale to the top score, use a square-root curve, rescale with z-scores, move the cutoffs, use quotas, or apply no curve at all. The first step is always the same: find out whether a curve applies, and which method your teacher uses.
Step 1 — Ask whether a curve applies
Some courses state no curve. The University of Illinois CS 277 policy says the course “is not designed to operate on a curve,” and any curve is done by lowering cutoffs only, never raising them. The University of Alberta states that grades “shall not be mandated on the basis of a curve or historic distribution.” If your syllabus says nothing about a curve, do not assume one exists.
Step 2 — Find the method
Ask your teacher which method applies, and its settings: points added, target mean and SD, cutoffs, whether scores cap at the maximum, and the rounding rule. Without the method, the raw score alone cannot tell you the curved score — the proof in Step 4 shows why.
Step 3 — Apply the method’s formula
Flat. Curved = raw + points. Example: flat +10 turns 65 into 75 and 40 into 50.
Top-score. Curved = raw + (scale maximum − highest score). Example: top score 90, maximum 100 → every score gains 10. The highest score becomes 100 by construction. Different from flat: the points are derived from the scores, not chosen.
Scale-to-max. Curved = raw × (scale maximum ÷ highest score). Example: top score 90 → factor 100 ÷ 90 = 1.111. A 65 becomes 72.22; a 40 becomes 44.44. Higher scores gain more absolute points than lower ones.
Square-root. On a 0–100 scale, curved = 10 × √(raw). Example: 25 → 50, 64 → 80, 96 → 97.98. Low scores gain most. For another scale: curved = scale maximum × √(raw ÷ scale maximum).
Z-rescale. z = (score − class mean) ÷ class SD, then curved = target mean + z × target SD. Example with class set [40, 55, 65, 75, 90] (mean 65.0, population SD 17.03) and target 75/10: a raw 40 gives z = −1.468 → 60.32; a raw 90 gives z = +1.468 → 89.68. This method can lower a score.
Cutoff adjustment. No score changes. The teacher moves the letter boundaries — for example, the A− cutoff drops from 90% to 88%. Your raw score stays the same; the boundary for each letter moves.
Step 4 — The proof: one raw score, different curved scores
Same class set [40, 55, 65, 75, 90]. A raw 65 becomes 75.00 (flat +10), 72.22 (scale-to-max), 80.62 (square-root), 75.00 (z-rescale 75/10), or 80.00 (z-rescale 80/10) — an 8.4-point spread. A raw 40 becomes 50.00, 44.44, 63.25, or 60.32 — an 18.81-point spread. The ordering differs too: square-root lifts the bottom most; scale-to-max lifts the top most.
What varies by teacher
- Whether any curve applies. Some courses state no curve; some institutions forbid mandated curves or quotas.
- Which method. Flat, top-score, scale, square-root, z-rescale, cutoff adjustment, quota, none, or a combination.
- Parameters. Points added, target mean and SD, z cutoffs, cap at the maximum, rounding rule.
- SD convention. Population (÷N) versus sample (÷n−1) for any z method.
- What the curve applies to. One exam, the total course score, before or after extra credit — do not assume.
Common mistakes
- Assuming one standard curve. There is none.
- Assuming curves only raise scores. False for z-rescale and quota methods.
- Treating flat and top-score as the same. Flat points are chosen; top-score points are derived.
- Applying the 0–100 square-root form to another scale. Convert first, or use the general form.
- Treating example defaults as rules. Target mean/SD, cap, and rounding are editable defaults on the calculator.
- Treating the computed curve as the recorded grade. Your teacher’s actual method, if any, governs.
Calculate it: Grade Curve Calculator. Bell-curve grading: Bell Curve Grade Calculator. Test scores: Test Grade Calculator.