Square Root Curve Calculator

What is the square root curve?

The square root curve is a grading method that applies the formula: Curved Score = 10 × √(Raw Score). It benefits lower-scoring students more than higher-scoring students, making it useful for difficult tests where the class average is low.

How is the square root curve calculated?

To apply the square root curve:

1. Take the square root of the raw score
2. Multiply the result by 10
3. The result is the curved score (maximum 100)

Example: Raw score 64 → √64 = 8 → 8 × 10 = 80% (curved)

What is a 50 on the square root curve?

A raw score of 50 becomes approximately 70.7 on the square root curve: √50 ≈ 7.07 × 10 = 70.7%. This gives a significant boost to students who scored just below passing.

When should I use a square root curve?

Use a square root curve when:

• The test was unusually difficult
• The class average is below 70%
• You want to help lower-scoring students more
• You want to maintain differentiation between students

Does the square root curve benefit low scores more?

Yes! Lower scores receive a larger percentage increase. For example:

• Raw 25 → Curved 50 (100% increase)
• Raw 64 → Curved 80 (25% increase)
• Raw 90 → Curved 94.9 (5% increase)

What is the highest possible curved score?

The maximum curved score is 100, achieved when a student scores 100 on the raw test: √100 = 10 × 10 = 100. Scores above 100 are capped at 100.

How do I convert a raw score of 36 on the square root curve?

Raw score 36: √36 = 6 × 10 = 60 (curved). This represents a 24-point increase, helping struggling students pass.

Is the square root curve fair?

The square root curve is generally considered fair because it preserves the ranking of students while providing more help to those who need it most. All students receive some benefit, but lower scores receive a larger proportional increase.

How does the square root curve compare to a linear curve?

A linear curve adds the same number of points to every student (e.g., add 10 points to all scores). The square root curve adds different amounts based on score: more points to low scores, fewer to high scores. This maintains more differentiation while helping struggling students.