# What is my square root curve grade?

Curves a test score with the square root rule: the curved percent is 10 × √(raw percent), so 64% becomes 80%. Or finds the raw score that gives a curved percent.

- Page: https://www.acalculator.org/education/square-root-curve-calculator
- JSON spec: https://www.acalculator.org/education/square-root-curve-calculator.json
- Version: 1d7a2a01c46b

## Default answer

Example with the default inputs (Your score (points) 64, Points possible 100): Your curved grade is 80%.

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| s | Your score (points) | The points you scored on the test. |
| t | Points possible | The most points the test allows; 100 when your score is a percent. |
| c | Curved grade | The grade after the square root curve, as a percent. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| score | Your score (points) | The points you scored on the test. |
| total | Points possible | The most points the test allows; 100 when your score is a percent. |
| curved | Curved grade | 10 × √(raw percent). |
| raw | Raw grade | Score ÷ points possible × 100, before the curve. |
| gain | Points added by the curve | Curved percent minus raw percent, in percentage points. |

## Method

curved % = 100 × √(score ÷ total) = 10 × √(raw %). To find the score for a curved grade: score = total × (curved ÷ 100)².

## Assumptions

- The curve is applied to the percent score: 10 × √(raw %). A raw 100% stays 100% and 0% stays 0%.
- A score above the points possible (extra credit) gives a curved grade above 100%.
- Values run in double precision; the curved grade is shown to 2 decimal places.

## Worked examples

1. s = 64, t = 100 gives c = 80%, raw = 64%, gain = 16. Source: CompSci.rocks, Should you grade on a curve? (take the square root of the grade and multiply by 10; 25 becomes 50), https://compsci.rocks/blog/curve-grades/ (retrieved 2026-10-02).
2. s = 36, t = 50 gives c = 84.852814%, raw = 72%. Source: CompSci.rocks, Should you grade on a curve? (take the square root of the grade and multiply by 10; 25 becomes 50), https://compsci.rocks/blog/curve-grades/ (retrieved 2026-10-02).
3. c = 70%, t = 100 gives s = 49. Source: CompSci.rocks, Should you grade on a curve? (take the square root of the grade and multiply by 10; 25 becomes 50), https://compsci.rocks/blog/curve-grades/ (retrieved 2026-10-02).

## FAQ

### How does a square root curve work?

Take the raw percent, find its square root, and multiply by 10. A raw 64% becomes 10 × √64 = 80%. The same rule written with points is 100 × √(score ÷ points possible).

### What does a 50% become on a square root curve?

10 × √50 = 70.71%. Lower scores gain the most: 25% becomes 50%, 50% becomes 70.71%, 81% becomes 90%, and 100% stays 100%.

### What raw score do I need for a 70% after the curve?

Reverse the rule: raw % = (curved % ÷ 10)². For 70%, (70 ÷ 10)² = 49%, so 49 points out of 100. Type 70 as the curved grade and leave your score empty.

### Can the square root curve lower a grade?

No, not for scores from 0% to 100%. The square root of a number between 0 and 1 is at least as large as the number, so every curved grade is at least the raw grade. Only 0% and 100% stay the same.

### What if my score is not out of 100?

Type the points possible. The page divides your score by it first: 36 out of 50 is 72%, and 10 × √72 = 84.85%.

### Is the square root curve standard?

No. It is one way a teacher may choose to curve grades, and some use other curves (adding points, scaling to the top score, or a bell curve). Check with your teacher how your class is curved.

## Sources

- CompSci.rocks, Should you grade on a curve? (a teacher describes the square root curve: take the square root of the grade and multiply by 10; 25 becomes 50 and 75 becomes 87). https://compsci.rocks/blog/curve-grades/ (retrieved 2026-10-02)