Square Root Curve Calculator

A square root curve (also called a Texas curve) is a grading technique that boosts every student's score, while giving a bigger boost to lower scores than higher ones. Enter a set of raw scores below to instantly calculate the curved grades for your entire class.

Square Root Curve Calculator

If you have a set of grades to calculate, enter them in the box below — one score per line. Duplicates are automatically removed. Scores are accepted in the range of 0–100; anything outside that range is clamped to the nearest boundary.

Grades

How the Square Root Curve Works

The formula is straightforward:

Curved Score = √(Raw Score) × 10

Take the square root of the raw score and multiply by 10. That's it. Because square roots grow more slowly for larger numbers, lower scores receive a proportionally larger boost.

Example: High Score

Jimmy earns a raw score of 75%.

$$ \LARGE \begin{align} \text{Score} &= 10 \times \sqrt{\text{Raw Score}} \\ &= 10 \times \sqrt{75} \\ &= 10 \times 8.66 \\ &= 86.6 \\ &= 87\% \end{align} $$

√75 × 10 = 86.6 — a gain of about 12 points.

Example: Low Score

Sue earns a raw score of 25%.

$$ \LARGE \begin{align} \text{Score} &= 10 \times \sqrt{\text{Raw Score}} \\ &= 10 \times \sqrt{25} \\ &= 10 \times 5 \\ &= 50 \\ &= 50\% \end{align} $$

√25 × 10 = 50 — a gain of 25 points.

Sue's score improved more than Jimmy's in absolute terms. That's the defining characteristic of a square root curve: it narrows the gap between high and low performers without compressing the top end of the distribution.

How to Use This Calculator

Enter raw scores in the text area above, one score per line.
Duplicate scores are automatically removed — no need to enter the same score twice.
Click Calculate to see a table of raw scores alongside their curved equivalents.
Scores outside 0–100 are clamped: a 102 is treated as 100, a -5 is treated as 0.
Non-numeric entries are silently ignored.

Should You Use a Square Root Curve?

Whether to curve grades — and which method to use — is entirely at the teacher's discretion. A square root curve is a good fit when:

The class average came in lower than expected but the distribution looks reasonable (use our class average calculator to check quickly)
You want to help struggling students more than students who already scored well
You need a simple, defensible method that's easy to explain to students and parents
You want a gentle curve that doesn't inflate high scores past 100

It's less ideal when scores are clustered at the top (little room for differentiation) or when you need to move everyone up by a fixed amount (a linear bump is better for that).

Alternative: Linear Grade Distribution

Another option is to scale grades so the highest score becomes 100 and set a floor for the lowest. This preserves relative differences between students while adjusting the overall range. There's no single right answer — the best curve depends on your class, the assessment, and your grading philosophy.

Frequently Asked Questions

What is a square root curve?: A square root curve is a grading adjustment where each raw score is transformed using the formula √(score) × 10. It boosts all scores but gives a larger boost to lower scores.
Why is it called a Texas curve?: The name is informal teacher slang. The origin isn't precisely documented, but it's been widely used in secondary and post-secondary education for decades.
Does a square root curve ever hurt a student's grade?: No. Because √x × 10 ≥ x for all values of x between 0 and 100, no score can decrease. A score of 100 maps exactly to 100. All other scores increase.
What score does a 0 become?: A raw score of 0 remains 0. √0 × 10 = 0.
What score does a 100 become?: A raw score of 100 stays at 100. √100 × 10 = 100. The curve never inflates a perfect score.
How much does a 50 go up?: √50 × 10 ≈ 70.7. A student who scored 50 ends up with about a 71 after the curve.
Can I use this for scores not on a 100-point scale?: This specific formula is designed for 0–100 scales. For other scales, adjust accordingly: for a 50-point scale you'd use √(score) × √50, for example.
How does this compare to adding a flat curve?: A flat curve (e.g., add 10 points to everyone) moves all grades up equally. A square root curve gives more help to lower scores and less to higher ones, which some teachers prefer as it's more targeted. If you want to compare both methods side by side — or preview a flat or percentage boost alongside raw scores — our Easy Grader & Grade Curve Calculator has all three curve types built in.
Is curving grades ethical?: Curving is a widely accepted academic practice when the assessment was more difficult than intended or when scores don't reflect student mastery. How and whether to curve is a professional judgment call for the teacher.