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Grades · Grading

Grade Curve Calculator

Apply a flat, linear-scale, or square-root curve to a raw score.

Curve method
The uncurved score, 0–100.
Not used by the square-root curve.
Try an example
Curved score
80/ 100B-

Raw 64 → curved 80 (+16 points).

How each method maps a raw score (0–100) to a curved score
Curved score versus raw score for three methods, using a top score of 88. The square-root curve lifts low scores the most, the linear scale rises in proportion, and the flat method adds a constant bonus until it caps at 100.1000raw 0raw 100
Square rootLinearFlat

Curving raises raw scores using a rule the instructor picks. The square-root curve is curved = √raw × 10: a raw 64 becomes √64 × 10 = 8 × 10 = 80. A flat curve adds fixed points; a linear scale multiplies by 100 ÷ the top score. Every curved score is capped at 100.

What curving does

A curve is a formula an instructor applies to every raw score so the class average or the top score lands where they want it. It does not change how many questions you answered — it remaps the raw number to a higher curved number. The three common methods differ in who benefits most.

Flat (add points). Every student gains the same number of points. A frequent choice sets that bonus so the highest score in the class becomes 100 — the bonus is 100 − highest score. It shifts everyone up equally.

Linear scale. Every score is multiplied by 100 ÷ the highest score, so the top paper becomes exactly 100 and everything below scales in proportion. Lower scores rise, but by a smaller number of points than the top.

Square root. The curved score is √raw × 10 on a 0–100 scale. Because a square root grows fastest near zero, this method boosts low scores the most and barely touches scores already near 100.

Square root: curved = √raw × 10

Linear: curved = raw × 100 ÷ top · Flat: curved = raw + (100 − top)

Worked example

A raw score of 64, square-root curve.

  1. 1
    Pick the curve method. Here, the square-root curve: curved = √raw × 10.
  2. 2
    Take the square root of the raw score. √64 = 8.
  3. 3
    Multiply by 10. 8 × 10 = 80.
  4. 4
    Cap at 100. 80 is below 100, so the curved score is 80 — a B−.

Same raw score under each method

A raw score of 64 with a class-high of 88; the square-root curve lifts it most.

MethodFormula with numbersCurved score
Flat (add points)64 + (100 − 88) = 64 + 1276
Linear scale64 × 100 ÷ 8872.7
Square root√64 × 1080

Reading the results

Every method raises scores — none can lower a raw score below what you earned. Which one helps you most depends on where you sit: the square-root curve gives the biggest lift to low scores and almost none to scores near 100, so it compresses the class toward the top.

Flat and linear preserve rank. Adding the same points, or multiplying by the same factor, keeps everyone in the same order they started. The square-root curve also keeps the order, but it narrows the gaps between students.

The curve is the instructor’s call. These formulas show what each method would give — your teacher decides whether a curve is applied and which one. Compute your raw percentage first, then apply the announced curve.

What is the square-root curve?
It sets the curved score to √raw × 10 on a 0–100 scale. Because a square root rises fastest near zero, it boosts low scores the most and barely changes scores already close to 100 — for example a raw 64 becomes √64 × 10 = 80.
Does curving change the ranking?
No. The flat, linear-scale, and square-root methods all keep students in the same order — a higher raw score always maps to a higher curved score. Curving raises scores; it does not reshuffle who is ahead.
How is a flat curve calculated?
It adds the same points to every score: curved = raw + bonus. A common choice sets the bonus so the class-high becomes 100, so bonus = 100 − highest score. With a top of 88, that is +12 points for everyone.
What is a linear-scale curve?
Every score is multiplied by 100 ÷ the highest score, so the top paper becomes exactly 100 and the rest scale in proportion. With a top of 88, a raw 64 becomes 64 × 100 ÷ 88 ≈ 72.7.
Why is the curved score capped at 100?
A score above 100 is not usually meaningful on a percentage scale, so any curved value over 100 is held at 100. Flat and linear curves are built so the top score lands at 100 rather than beyond it.
Which curve helps a low score the most?
The square-root curve. A raw 49 becomes √49 × 10 = 70, a 21-point lift, while a raw 81 becomes 90, only a 9-point lift — the boost shrinks as the raw score climbs.