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Weighted average grade calculator

Weighted average (GPA-style class average): one line per grade, on a 100-point, 20-point or any other scale.

Parameters

One line per grade: “grade” or “grade coefficient”, separated by a space. Example: “85 2” for an 85 with coefficient 2. Without a coefficient, the grade counts once.

100 or 20 depending on the scale; leave empty for free values.

Result

Weighted average

87.33 / 100

Calculation
average = Σ(grade × coef) ÷ Σcoef = 524 ÷ 6 = 87.33
8085900123gradecoefficient8587.3
Simple average (no coefficients)
85 / 100
Total of coefficients
6
Number of grades
3

Calculation, assumptions and sources

OverviewA grade list (one grade per line, with its coefficient) gives the weighted average, the total of coefficients and the simple unweighted average, for comparison.

A grade list (one grade per line, with its coefficient) gives the weighted average, the total of coefficients and the simple unweighted average, for comparison. Any unreadable line is flagged with its number.

Method & formulasweighted average = Σ(gradeᵢ × coefᵢ) / Σ coefᵢ
weighted average = Σ(gradeᵢ × coefᵢ) / Σ coefᵢ

The sum of the grades multiplied by their coefficients is divided by the total of coefficients. A grade without a coefficient counts once. The gap with the simple average measures the effect of the weighting.

Coefficient
the weight of a grade in the average; a coefficient of 3 counts three times as much as a coefficient of 1. A zero coefficient is accepted, the grade stays in the list without counting.
Simple average
the arithmetic mean of the same grades, every coefficient set to 1.
Grading scale
the maximum possible grade (100 in most systems, 20 in France). Optional; when set, any grade above it is flagged with its line number.
Validity domainInstitution-specific rules are not modelled: minimum-grade requirements, compensation between blocks, jury rounding, dropped lowest grades.

Institution-specific rules are not modelled: minimum-grade requirements, compensation between blocks, jury rounding, dropped lowest grades.

The average of averagesAn average of averages must be weighted: 15/20 over a 10-credit semester and 10/20 over a 20-credit semester give (15×10 + 10×20)/30 ≈ 11.7, not 12.5.

An average of averages must be weighted: 15/20 over a 10-credit semester and 10/20 over a 20-credit semester give (15×10 + 10×20)/30 ≈ 11.7, not 12.5. Each average is entered as a grade, with its number of credits as the coefficient.