{
  "id": "semester-grade",
  "version": "6e3cddb114a6",
  "status": "published",
  "name": "Semester Grade Calculator",
  "question": "What is my semester grade?",
  "summary": "Computes a semester grade as the weighted average of two quarter grades and a final exam (40%, 40% and 20% by default), or the final exam or quarter grade needed for a target semester grade.",
  "category": "education",
  "subcategory": "grades",
  "url": "https://www.acalculator.org/education/semester-grade-calculator",
  "markdown": "https://www.acalculator.org/education/semester-grade-calculator.md",
  "kind": "formulas",
  "method": "semester = (w1 × Q1 + w2 × Q2 + wE × exam) ÷ (w1 + w2 + wE); solved for any one grade from the other three.",
  "assumptions": [
    "The semester grade is a weighted average of two quarter grades and one final exam. The weights are divided by their total, so they need not add up to 100.",
    "The default weights are 40%, 40% and 20%, the split many US high schools use. Check your school’s split and change the weights to match.",
    "Grades are percentages from 0 to 1,000 (above 100 allows extra credit). A needed grade above 100% means the goal is out of reach without extra credit.",
    "Every step is exact on the numbers as typed; grades are rounded to two decimal places only for display."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "q1": {
        "title": "Quarter 1 grade",
        "description": "Your grade for the first quarter (or term), in percent.",
        "type": "number",
        "x-unit": "percent",
        "minimum": 0,
        "maximum": 1000
      },
      "q2": {
        "title": "Quarter 2 grade",
        "description": "Your grade for the second quarter (or term), in percent.",
        "type": "number",
        "x-unit": "percent",
        "minimum": 0,
        "maximum": 1000
      },
      "exam": {
        "title": "Final exam grade",
        "description": "Your grade on the semester final exam, in percent.",
        "type": "number",
        "x-unit": "percent",
        "minimum": 0,
        "maximum": 1000
      },
      "sem": {
        "title": "Semester grade",
        "description": "The semester grade: the weighted average of the three parts, in percent.",
        "type": "number",
        "x-unit": "percent",
        "minimum": 0,
        "maximum": 1000
      },
      "w1": {
        "title": "Quarter 1 weight",
        "description": "How much quarter 1 counts toward the semester grade, in percent.",
        "type": "number",
        "x-unit": "percent",
        "minimum": 0,
        "maximum": 100
      },
      "w2": {
        "title": "Quarter 2 weight",
        "description": "How much quarter 2 counts toward the semester grade, in percent.",
        "type": "number",
        "x-unit": "percent",
        "minimum": 0,
        "maximum": 100
      },
      "we": {
        "title": "Final exam weight",
        "description": "How much the final exam counts toward the semester grade, in percent.",
        "type": "number",
        "x-unit": "percent",
        "minimum": 0,
        "maximum": 100
      }
    }
  },
  "solve": {
    "fillAny": 6,
    "variables": [
      "q1",
      "q2",
      "exam",
      "sem",
      "w1",
      "w2",
      "we"
    ],
    "inputsOnly": [
      "w1",
      "w2",
      "we"
    ]
  },
  "outputs": {
    "q1": {
      "label": "Quarter 1 grade",
      "description": "The first quarter grade, typed or needed for the semester grade.",
      "format": "percent"
    },
    "q2": {
      "label": "Quarter 2 grade",
      "description": "The second quarter grade, typed or needed for the semester grade.",
      "format": "percent"
    },
    "exam": {
      "label": "Final exam grade",
      "description": "The final exam grade, typed or needed for the semester grade.",
      "format": "percent"
    },
    "semester": {
      "label": "Semester grade",
      "description": "The weighted average of the two quarters and the final exam, in percent.",
      "format": "percent"
    },
    "w1": {
      "label": "Quarter 1 weight",
      "description": "How much quarter 1 counts toward the semester grade, in percent.",
      "format": "percent"
    },
    "w2": {
      "label": "Quarter 2 weight",
      "description": "How much quarter 2 counts toward the semester grade, in percent.",
      "format": "percent"
    },
    "we": {
      "label": "Final exam weight",
      "description": "How much the final exam counts toward the semester grade, in percent.",
      "format": "percent"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "q1": 88,
      "q2": 92,
      "exam": 85,
      "w1": 40,
      "w2": 40,
      "we": 20
    },
    "outputs": {
      "semester": 89
    },
    "text": "With quarter grades of 88% and 92% and 85% on the final exam, the semester grade is 89%."
  },
  "examples": [
    {
      "given": {
        "q1": 88,
        "q2": 92,
        "exam": 85,
        "w1": 40,
        "w2": 40,
        "we": 20
      },
      "expect": {
        "sem": 89
      },
      "source": "Akron Public Schools grade calculator (1st quarter 40%, 2nd quarter 40%, exam 20%), https://homeaccess.akron.k12.oh.us/finalgrade/; hand calculation in content.mdx: (40 × 88 + 40 × 92 + 20 × 85) ÷ 100 = 8,900 ÷ 100 = 89"
    },
    {
      "given": {
        "q1": 88,
        "q2": 92,
        "sem": 90,
        "w1": 40,
        "w2": 40,
        "we": 20
      },
      "expect": {
        "exam": 90
      },
      "source": "hand calculation in content.mdx: (90 × 100 − 40 × 88 − 40 × 92) ÷ 20 = 1,800 ÷ 20 = 90 (weights from the Akron Public Schools grade calculator, https://homeaccess.akron.k12.oh.us/finalgrade/)"
    },
    {
      "given": {
        "q1": 70,
        "q2": 72,
        "sem": 80,
        "w1": 40,
        "w2": 40,
        "we": 20
      },
      "expect": {
        "exam": 116
      },
      "source": "hand calculation in content.mdx: (80 × 100 − 40 × 70 − 40 × 72) ÷ 20 = 2,320 ÷ 20 = 116"
    },
    {
      "given": {
        "q1": 80,
        "exam": 70,
        "sem": 85,
        "w1": 40,
        "w2": 40,
        "we": 20
      },
      "expect": {
        "q2": 97.5
      },
      "source": "hand calculation in content.mdx: (85 × 100 − 40 × 80 − 20 × 70) ÷ 40 = 3,900 ÷ 40 = 97.5"
    },
    {
      "given": {
        "q1": 88,
        "q2": 92,
        "exam": 85,
        "w1": 2,
        "w2": 2,
        "we": 1
      },
      "expect": {
        "sem": 89
      },
      "source": "hand calculation in content.mdx: (2 × 88 + 2 × 92 + 1 × 85) ÷ 5 = 445 ÷ 5 = 89"
    },
    {
      "given": {
        "q1": 90,
        "q2": 80,
        "exam": 75,
        "w1": 45,
        "w2": 45,
        "we": 10
      },
      "expect": {
        "sem": 84
      },
      "source": "hand calculation in content.mdx: (45 × 90 + 45 × 80 + 10 × 75) ÷ 100 = 8,400 ÷ 100 = 84"
    }
  ],
  "sources": [
    "Akron Public Schools, Grade Calculator (classes with one final exam: 1st quarter 40%, 2nd quarter 40%, exam 20%). https://homeaccess.akron.k12.oh.us/finalgrade/",
    "OpenStax, Introductory Statistics 2e, §2.5 Measures of the Center of the Data (a mean with frequencies: Σ value × frequency ÷ Σ frequency, the same sum as a weighted mean). https://openstax.org/books/introductory-statistics-2e/pages/2-5-measures-of-the-center-of-the-data"
  ],
  "related": [
    "final-grade",
    "grade",
    "weighted-grade",
    "gpa"
  ],
  "changelog": []
}