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Square Root Curve Calculator
Your test score
The square root curve works on a test out of 100. If your test is out of a different total, enter it as the max score and the calculator scales the result to a 100-point grade.
Example: a raw score of 64 out of 100 curves to 80.0 — a B — a gain of 16.0 points.
Behind the numbers
How the square root curve works
A square root curve takes the square root of your raw score and multiplies it by 10. Because the square root of a number below 100 is always larger than that number divided by 10, every score below 100 goes up — and the lower the score, the bigger the boost. A 36 jumps 24 points to 60, while an 81 rises only 9 points to 90. A perfect score stays perfect: 10 × √100 = 100.
For a test out of 100. Worked example: 10 × √64 = 10 × 8 = 80.0, a grade of B. If your test is out of a different total, the general form is curved score = 100 × √(raw ÷ max) — for a max of 100 the two are identical.
The letter grade scale
Grade cutoffs follow the standard US scale; your teacher may use different boundaries.
A few comparisons
Example curved scores
| Raw score | Curved score | Letter grade | Points gained |
|---|---|---|---|
| 25 out of 100 | 50.0 | F | +25.0 |
| 36 out of 100 | 60.0 | D | +24.0 |
| 49 out of 100 | 70.0 | C | +21.0 |
| 64 out of 100 | 80.0 | B | +16.0 |
| 81 out of 100 | 90.0 | A | +9.0 |
| 100 out of 100 | 100.0 | A | +0.0 |
Make the curve work for you.
The boost is biggest at the bottom: if you are near a grade boundary from below, a square root curve is more likely to lift you over it than a flat-point curve.
To reach a curved 90 you need a raw 81, a curved 80 needs a raw 64, and a curved 70 needs a raw 49 — square the curved target divided by 10 to find the raw score you need.
A curve never lowers a score below 100, but it also cannot fix a missing assignment: a raw 0 still curves to 0.
Ask your teacher which curve they use before you plan around one — a square root curve, a flat +10 points, and a curve to the highest score all give very different results.
Good to know
Your square root curve questions, answered.
What is a square root curve?
It is a grading curve that raises every score by taking its square root and multiplying by 10: curved score = 10 x the square root of the raw score. A raw 64 becomes 80, a raw 49 becomes 70, and a raw 100 stays at 100.
Why do teachers curve grades?
Teachers curve when a test turns out harder than planned, so the class average lands where it should. A square root curve is popular because it helps the lowest scores the most while leaving top scores almost unchanged, and it never pushes a score above 100.
Does a square root curve always raise a score?
Yes, for any raw score below 100. The square root of a number below 100 is always bigger than the number divided by 10, so 10 x the square root is always above the raw score. A raw 100 stays at 100, and the gain shrinks as the raw score rises: a 36 gains 24 points, while an 81 gains only 9.
What score do I need to get a curved 90?
A raw score of 81. The math is 10 x the square root of 81 = 10 x 9 = 90. In general, to reach a curved target T, you need a raw score of (T / 10) squared: for a curved 80 you need a raw 64, and for a curved 70 you need a raw 49.