Example: 64%
- Step 1
√64 = 8 - Step 2
8 × 10 = 80
- Result
- 64% → 80%
- Boost
- +16 percentage points
Grading reference
Square Root Curve Calculator
Enter a raw grade to see its square-root curved score instantly.
Calculate
Visualize
How the Square Root Curve Changes Grades
The curved score rises quickly at lower grades and gradually approaches 100.
Chart
Square Root Curve Chart
Use the chart to look up the curved grade for any raw score from 0 to 100.
Opens the print dialog. Choose “Save as PDF” to save a copy.
| Raw | Curved | Raw | Curved | Raw | Curved |
|---|---|---|---|---|---|
| 0 | 0 | 34 | 58.3 | 68 | 82.5 |
| 1 | 10 | 35 | 59.2 | 69 | 83.1 |
| 2 | 14.1 | 36 | 60 | 70 | 83.7 |
| 3 | 17.3 | 37 | 60.8 | 71 | 84.3 |
| 4 | 20 | 38 | 61.6 | 72 | 84.9 |
| 5 | 22.4 | 39 | 62.4 | 73 | 85.4 |
| 6 | 24.5 | 40 | 63.2 | 74 | 86 |
| 7 | 26.5 | 41 | 64 | 75 | 86.6 |
| 8 | 28.3 | 42 | 64.8 | 76 | 87.2 |
| 9 | 30 | 43 | 65.6 | 77 | 87.7 |
| 10 | 31.6 | 44 | 66.3 | 78 | 88.3 |
| 11 | 33.2 | 45 | 67.1 | 79 | 88.9 |
| 12 | 34.6 | 46 | 67.8 | 80 | 89.4 |
| 13 | 36.1 | 47 | 68.6 | 81 | 90 |
| 14 | 37.4 | 48 | 69.3 | 82 | 90.6 |
| 15 | 38.7 | 49 | 70 | 83 | 91.1 |
| 16 | 40 | 50 | 70.7 | 84 | 91.7 |
| 17 | 41.2 | 51 | 71.4 | 85 | 92.2 |
| 18 | 42.4 | 52 | 72.1 | 86 | 92.7 |
| 19 | 43.6 | 53 | 72.8 | 87 | 93.3 |
| 20 | 44.7 | 54 | 73.5 | 88 | 93.8 |
| 21 | 45.8 | 55 | 74.2 | 89 | 94.3 |
| 22 | 46.9 | 56 | 74.8 | 90 | 94.9 |
| 23 | 48 | 57 | 75.5 | 91 | 95.4 |
| 24 | 49 | 58 | 76.2 | 92 | 95.9 |
| 25 | 50 | 59 | 76.8 | 93 | 96.4 |
| 26 | 51 | 60 | 77.5 | 94 | 97 |
| 27 | 52 | 61 | 78.1 | 95 | 97.5 |
| 28 | 52.9 | 62 | 78.7 | 96 | 98 |
| 29 | 53.9 | 63 | 79.4 | 97 | 98.5 |
| 30 | 54.8 | Current calculator score: 64 | 80 | 98 | 99 |
| 31 | 55.7 | 65 | 80.6 | 99 | 99.5 |
| 32 | 56.6 | 66 | 81.2 | 100 | 100 |
| 33 | 57.4 | 67 | 81.9 |
| Raw score | Curved score |
|---|---|
| 0 | 0 |
| 1 | 10 |
| 2 | 14.1 |
| 3 | 17.3 |
| 4 | 20 |
| 5 | 22.4 |
| 6 | 24.5 |
| 7 | 26.5 |
| 8 | 28.3 |
| 9 | 30 |
| 10 | 31.6 |
| 11 | 33.2 |
| 12 | 34.6 |
| 13 | 36.1 |
| 14 | 37.4 |
| 15 | 38.7 |
| 16 | 40 |
| 17 | 41.2 |
| 18 | 42.4 |
| 19 | 43.6 |
| 20 | 44.7 |
| 21 | 45.8 |
| 22 | 46.9 |
| 23 | 48 |
| 24 | 49 |
| 25 | 50 |
| 26 | 51 |
| 27 | 52 |
| 28 | 52.9 |
| 29 | 53.9 |
| 30 | 54.8 |
| 31 | 55.7 |
| 32 | 56.6 |
| 33 | 57.4 |
| 34 | 58.3 |
| 35 | 59.2 |
| 36 | 60 |
| 37 | 60.8 |
| 38 | 61.6 |
| 39 | 62.4 |
| 40 | 63.2 |
| 41 | 64 |
| 42 | 64.8 |
| 43 | 65.6 |
| 44 | 66.3 |
| 45 | 67.1 |
| 46 | 67.8 |
| 47 | 68.6 |
| 48 | 69.3 |
| 49 | 70 |
| 50 | 70.7 |
| 51 | 71.4 |
| 52 | 72.1 |
| 53 | 72.8 |
| 54 | 73.5 |
| 55 | 74.2 |
| 56 | 74.8 |
| 57 | 75.5 |
| 58 | 76.2 |
| 59 | 76.8 |
| 60 | 77.5 |
| 61 | 78.1 |
| 62 | 78.7 |
| 63 | 79.4 |
| Current calculator score: 64 | 80 |
| 65 | 80.6 |
| 66 | 81.2 |
| 67 | 81.9 |
| 68 | 82.5 |
| 69 | 83.1 |
| 70 | 83.7 |
| 71 | 84.3 |
| 72 | 84.9 |
| 73 | 85.4 |
| 74 | 86 |
| 75 | 86.6 |
| 76 | 87.2 |
| 77 | 87.7 |
| 78 | 88.3 |
| 79 | 88.9 |
| 80 | 89.4 |
| 81 | 90 |
| 82 | 90.6 |
| 83 | 91.1 |
| 84 | 91.7 |
| 85 | 92.2 |
| 86 | 92.7 |
| 87 | 93.3 |
| 88 | 93.8 |
| 89 | 94.3 |
| 90 | 94.9 |
| 91 | 95.4 |
| 92 | 95.9 |
| 93 | 96.4 |
| 94 | 97 |
| 95 | 97.5 |
| 96 | 98 |
| 97 | 98.5 |
| 98 | 99 |
| 99 | 99.5 |
| 100 | 100 |
Calculate more
More Ways to Use the Square Root Curve
Work backward from a target grade or calculate directly from points earned.
Class calculator
Curve a Whole Class
Paste multiple raw grades to calculate every student's square-root curved score at once.
Formula
Square Root Curve Formula
Curved grade = 10 × √raw grade
Curved grade = 100 × √(raw grade ÷ 100)
The formula takes the square root of the raw percentage and multiplies it by 10. Scores below 100 increase, while 100 remains 100.
Try the formula in the calculatorExample: 50%
√50 × 10 = 70.710...
- Displayed result
- 70.7%
Results are not always whole numbers.
Example: 32 out of 50
- Convert to a percentage
32 ÷ 50 = 64% - Apply the curve
√64 × 10 = 80%
Do not apply the square-root formula directly to earned points unless the assessment is scored out of 100.
Use the points-based calculatorReverse calculation
To find the raw score needed for a target curved grade:
Raw grade = (Curved grade ÷ 10)²
(80 ÷ 10)² = 64
Therefore, 64% raw → 80% curved.
Use the reverse calculatorExamples
Square Root Curve Examples
| Raw score | Curved score |
|---|---|
| 25% | 50% |
| 36% | 60% |
| 49% | 70% |
| 50% | 70.7% |
| 64% | 80% |
| 81% | 90% |
| 100% | 100% |
Perfect-square values produce clean whole-number results. See every score in the complete curve chart.
Why Lower Scores Increase More
Square-root growth is steepest at lower raw scores. The increase becomes smaller as scores approach 100, and 100 stays 100.
Ranking Stays in Order
Because the square-root function increases across the valid range, score order is preserved. If Student A starts higher than Student B, Student A remains higher after the curve.
Questions
Square Root Curve FAQ
What is a square root curve?
It is a grading transformation that multiplies the square root of a raw percentage by 10.
What is the square root curve formula?
Curved grade = 10 × √raw grade
What does a 64 become on a square root curve?
64% becomes 80%.
What does a 50 become?
50% becomes approximately 70.7%.
Does a 100 change?
No. 100% → 100%.
Can a square root curve lower a grade?
For valid percentages between 0 and 100, it does not lower the numerical percentage.
How do I calculate the curve for a test not worth 100 points?
First convert earned points to a percentage, then apply the square-root formula.
How do I reverse a square root curve?
Use Raw grade = (Curved grade ÷ 10)².
Is a square root curve the same as a bell curve?
No. A square-root curve transforms each score mathematically. Bell-curve grading typically depends on the class distribution or relative performance.
Is the square root curve fair?
Whether it is appropriate depends on the instructor, assessment difficulty, grading policy, and educational context.