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
Chart
Square Root Curve Chart
Use the chart to look up the curved grade for any raw score from 0 to 100.
Download the complete one-page PDF, or use Print chart to print.
| 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 between 0 and 100 increase; both 0 and 100 remain unchanged.
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 calculatorCommon Square Root Curve Mistakes
Using points as percentages
32 out of 50 is 64%, which curves to 80%. Applying 10 × √32 directly would give about 56.6%, the wrong result for this test.
Convert earned points correctlyCurving an already curved grade
A raw 64% becomes 80%. Applying the formula again to 80 gives about 89.4%—a second adjustment, not the original result. Start with the unadjusted score unless your instructor explicitly specifies otherwise.
Assuming every score will pass
If the passing threshold is 60%, a raw 36% curves to exactly 60%. For a 70% threshold, the required raw score is 49%. Passing and letter-grade cutoffs depend on your grading policy.
Find the raw score for your targetRounding before finishing
Keep the original score and full calculation precision until the final result. For example, 50% curves to 70.710…%, displayed here as 70.7%. Your instructor may use a different final rounding rule.
Review when a grading curve is appropriateExamples
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. Need the full score table? View the searchable 0–100 square root curve table and score lookup.
Where the Boost Is Largest
The absolute boost grows from zero at 0 to 25 percentage points at a raw score of 25, then decreases to zero at 100. Both 0 and 100 stay unchanged.
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.