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Square Root Curve Calculator
The square root curve is one of the simplest ways to curve a test. Take the square root of the raw percentage and multiply by 10: curved % = 10 × √(raw %). A 64% becomes 80%, a 49% becomes 70%, and a 100% stays 100%. Paste one score or a whole class, set the points possible, and the calculator lists every curved score with the points added.
The curve is popular because it needs no statistics and treats students fairly in one sense: it never changes the rank order, it never lowers a score, and it helps low scores the most. A 36% gains 24 points, while a 90% gains less than 5. The downside is that it cannot be tuned. If a test was extremely hard, even curved scores can stay low, and on an easy test it inflates grades. Teachers who want to set a target average or standard deviation usually use a linear or bell curve instead.
Default example: nine scores out of 100 average 69.8% raw and 83.0% after the curve. To check one by hand: 52 ÷ 100 = 52%, √52 = 7.211, × 10 = 72.1%.
One score or a whole class. Separate scores with commas, spaces or new lines.
Result and step-by-step working
Raw average 69.8% → 83.0% (9 scores)
| Raw score | Raw % | Curved % = 10 × √raw% | Points added |
|---|---|---|---|
| 45 | 45.0 | 67.1 | +22.1 |
| 52 | 52.0 | 72.1 | +20.1 |
| 60 | 60.0 | 77.5 | +17.5 |
| 64 | 64.0 | 80.0 | +16.0 |
| 70 | 70.0 | 83.7 | +13.7 |
| 73 | 73.0 | 85.4 | +12.4 |
| 81 | 81.0 | 90.0 | +9.0 |
| 88 | 88.0 | 93.8 | +5.8 |
| 95 | 95.0 | 97.5 | +2.5 |
- Convert to a percentageraw % = score ÷ 100 × 100. For the first score: 45 ÷ 100 × 100 = 45%.
- Take the square root and multiply by 1010 × √45 = 67.08%.
- Read the effectLow scores gain the most (36% → 60%), 100% stays 100%, and the order of students never changes.
Square root curve table
| Raw % | Curved % | Raw % | Curved % |
|---|---|---|---|
| 25 | 50.0 | 64 | 80.0 |
| 36 | 60.0 | 70 | 83.7 |
| 40 | 63.2 | 75 | 86.6 |
| 49 | 70.0 | 81 | 90.0 |
| 50 | 70.7 | 90 | 94.9 |
| 60 | 77.5 | 100 | 100.0 |
Frequently asked questions
- What raw score becomes a 90 with a square root curve?
- 81%. Because 10 × √81 = 90. Likewise 64% becomes 80, 49% becomes 70 and 36% becomes 60.
- Can a square root curve lower a grade?
- No. For any score between 0% and 100%, the square root of the percentage times 10 is at least as large as the percentage itself, so every student gains or stays the same.
- Does the curve work on points instead of percentages?
- Convert to a percentage first. The calculator does this for you from the points possible.
- What other curves are there?
- Common alternatives are adding a flat number of points, scaling the top score to 100%, and linear or bell-curve methods that hit a chosen class average. See the grade curve calculator for those.
Last reviewed: October 9, 2026. Calculations run in your browser; nothing you enter is sent anywhere.