{
  "id": "square-root-curve",
  "version": "1d7a2a01c46b",
  "status": "published",
  "name": "Square Root Curve Calculator",
  "question": "What is my square root curve grade?",
  "summary": "Curves a test score with the square root rule: the curved percent is 10 × √(raw percent), so 64% becomes 80%. Or finds the raw score that gives a curved percent.",
  "category": "education",
  "subcategory": "grades",
  "url": "https://www.acalculator.org/education/square-root-curve-calculator",
  "markdown": "https://www.acalculator.org/education/square-root-curve-calculator.md",
  "kind": "formulas",
  "method": "curved % = 100 × √(score ÷ total) = 10 × √(raw %). To find the score for a curved grade: score = total × (curved ÷ 100)².",
  "assumptions": [
    "The curve is applied to the percent score: 10 × √(raw %). A raw 100% stays 100% and 0% stays 0%.",
    "A score above the points possible (extra credit) gives a curved grade above 100%.",
    "Values run in double precision; the curved grade is shown to 2 decimal places."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "s": {
        "title": "Your score (points)",
        "description": "The points you scored on the test.",
        "type": "number",
        "minimum": 0,
        "maximum": 1000000
      },
      "t": {
        "title": "Points possible",
        "description": "The most points the test allows; 100 when your score is a percent.",
        "type": "number",
        "exclusiveMinimum": 0,
        "maximum": 1000000
      },
      "c": {
        "title": "Curved grade",
        "description": "The grade after the square root curve, as a percent.",
        "type": "number",
        "x-unit": "percent",
        "minimum": 0,
        "maximum": 1000
      }
    }
  },
  "solve": {
    "fillAny": 2,
    "variables": [
      "s",
      "t",
      "c"
    ],
    "inputsOnly": []
  },
  "outputs": {
    "score": {
      "label": "Your score (points)",
      "description": "The points you scored on the test.",
      "format": "number"
    },
    "total": {
      "label": "Points possible",
      "description": "The most points the test allows; 100 when your score is a percent.",
      "format": "number"
    },
    "curved": {
      "label": "Curved grade",
      "description": "10 × √(raw percent).",
      "format": "percent"
    },
    "raw": {
      "label": "Raw grade",
      "description": "Score ÷ points possible × 100, before the curve.",
      "format": "percent"
    },
    "gain": {
      "label": "Points added by the curve",
      "description": "Curved percent minus raw percent, in percentage points.",
      "format": "number"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "s": 64,
      "t": 100
    },
    "outputs": {
      "curved": 80,
      "raw": 64,
      "gain": 16
    },
    "text": "Your curved grade is 80%."
  },
  "examples": [
    {
      "given": {
        "s": 64,
        "t": 100
      },
      "expect": {
        "c": 80,
        "raw": 64,
        "gain": 16
      },
      "source": "CompSci.rocks, Should you grade on a curve? (take the square root of the grade and multiply by 10; 25 becomes 50), https://compsci.rocks/blog/curve-grades/ (retrieved 2026-10-02); hand calculation in content.mdx from the stated rule, curved % = 10 × √(raw %) = 100 × √(score ÷ total): 10 × √64 = 80"
    },
    {
      "given": {
        "s": 36,
        "t": 50
      },
      "expect": {
        "c": 84.8528137423857,
        "raw": 72
      },
      "source": "CompSci.rocks, Should you grade on a curve? (take the square root of the grade and multiply by 10; 25 becomes 50), https://compsci.rocks/blog/curve-grades/ (retrieved 2026-10-02); hand calculation in content.mdx from the stated rule, curved % = 10 × √(raw %) = 100 × √(score ÷ total): 100 × √(36 ÷ 50) = 100 × √0.72; Python 3: 100*math.sqrt(36/50)"
    },
    {
      "given": {
        "c": 70,
        "t": 100
      },
      "expect": {
        "s": 48.99999999999999
      },
      "source": "CompSci.rocks, Should you grade on a curve? (take the square root of the grade and multiply by 10; 25 becomes 50), https://compsci.rocks/blog/curve-grades/ (retrieved 2026-10-02); hand calculation in content.mdx from the stated rule, curved % = 10 × √(raw %) = 100 × √(score ÷ total): score = 100 × (70 ÷ 100)² = 49; Python 3: 100*(70/100)**2"
    }
  ],
  "sources": [
    "CompSci.rocks, Should you grade on a curve? (a teacher describes the square root curve: take the square root of the grade and multiply by 10; 25 becomes 50 and 75 becomes 87). https://compsci.rocks/blog/curve-grades/ (retrieved 2026-10-02)"
  ],
  "related": [
    "grade",
    "test-grade",
    "final-grade",
    "weighted-grade"
  ],
  "changelog": []
}