Grade Curve Calculator

How Grade Curving Works

Curving adjusts a set of raw test scores upward, usually because a test performed harder or scored lower than intended. This calculator supports two common curving methods, chosen with the tabs above the score list.

Linear (Highest to 100) Curving

This method finds the highest raw score in the set, calculates how many points short of 100 it is, and adds that same fixed number of points to every score in the class — capped so no curved score exceeds 100.

$$\text{Curved Score} = \min(100,\ \text{Raw Score} + (100 - \text{Highest Raw Score}))$$

Worked example: raw scores of 62, 71, 55, 88, and 79, with a highest score of 88. Points added: 100 − 88 = 12. Every score gets 12 points added: 62 becomes 74, 71 becomes 83, 55 becomes 67, 88 becomes 100, and 79 becomes 91.

Because every score receives the exact same number of added points, Linear curving preserves the original ranking and the original spread between scores — it shifts the whole distribution upward by a constant amount rather than reshaping it.

Square Root Curving

This method takes the square root of each raw score and multiplies it by 10, producing a curved score that lifts low scores by a larger amount than high scores.

$$\text{Curved Score} = \min(100,\ \text{round}(\sqrt{\text{Raw Score}} \times 10))$$

Worked example: a raw score of 64 becomes sqrt(64) × 10 = 8 × 10 = 80 — a gain of 16 points. A raw score of 81 becomes sqrt(81) × 10 = 9 × 10 = 90 — a gain of only 9 points. A raw score of 100 stays at sqrt(100) × 10 = 100 — no gain at all.

Square root curving is concave: the square root function rises steeply at low input values and flattens out as the input approaches 100. That shape is exactly why it helps low scorers more than high scorers in proportional terms — a student who struggled gets pulled up by a larger number of points than a student who was already near the top, whose score has little room left to climb toward the 100-point ceiling anyway.

Why the Two Methods Feel So Different

Linear curving is predictable and easy to explain — everyone gains the same flat amount, so the relative gaps between students stay identical to the raw-score gaps. Square root curving is less predictable at a glance but is often seen as fairer when a test's low scores were unusually low relative to its high scores, since it narrows the spread of the class rather than just shifting it — students who were struggling the most see their scores pulled disproportionately closer to the class's stronger performers.

Common Grade Curving Mistakes

Applying a curve method meant for one situation to the wrong one is a common mistake — Linear curving still leaves a very low score very low relative to the rest of the class (it just shifts everyone up by the same flat amount), while a class with unusually spread-out scores may see more benefit from Square Root curving. Forgetting that curved scores are capped at 100 is another: without a cap, Linear curving especially could push an already-high score above the maximum possible, which doesn't make sense for a percentage grade.

Grade Curving Terms You Should Know

Raw Score — a student's original, uncurved percentage score on a test, before any curve is applied.

Concave Function — a function whose rate of increase slows as its input grows, like the square root function used in Square Root curving — it's what causes low scores to gain more points than high scores.

Class Average — the mean of every score in the set; comparing it before and after curving shows how much the curve shifted the class's overall performance.