Multi-subject weighted average across coefficients.
Few tools are more universally useful to students than a weighted average calculator. Schools rarely give equal weight to every subject: a coefficient-three maths exam matters three times as much as a coefficient-one art class for the term ranking, and a coefficient-eight final year written test in the French baccalauréat dominates anything that came before it. The same arithmetic applies in countries with grade-point systems: a four-credit chemistry course at a US university is double-weighted against a two-credit elective. Computing a weighted average by hand is feasible but error-prone — the most common mistake is forgetting to divide by the total weight rather than by the number of subjects. This calculator handles up to five subjects, three grade-scale conventions (the French /20, the US-style /100 percentage, the /10 used in many continental systems, and the /5 used in some grade scales), and computes the resulting weighted average along with a status interpretation (Excellent, Good, Pass, Fail) calibrated to the chosen scale.
A weighted average is the sum of (grade × weight) divided by the sum of weights — emphatically not the sum of grades divided by the number of subjects, and not the sum of (grade × weight) divided by the number of subjects. Formally: ḡ = Σ(gᵢ × wᵢ) / Σwᵢ. The two pitfalls — using count-of-subjects in the denominator, or forgetting to weight the numerator — are exactly the kinds of bug that compute a number close enough to the truth to look right but fundamentally wrong. The calculator parses each row independently: it reads the grade and the weight from each row, drops rows with missing or invalid weights (so an empty trailing row is silently ignored), accumulates the two sums, divides, and reports the average along with the count of subjects actually included and the total weight. The status bands are computed relative to the scale: "Pass" means at or above half of the maximum (10/20, 50/100, 5/10, 2.5/5), "Good" means at or above 60 % of the way from pass to max, and "Excellent" means at or above 80 % of the way from pass to max.
Pick the grade scale at the top of the form. The defaults match the French /20 system, where a passing grade is 10/20. Each row takes a grade in the left column and its coefficient (or weight) in the right column. Five rows are provided; if you have fewer subjects, leave the rest empty — they will not be counted. If you have more, you can adapt by combining several minor subjects into a single row with the sum of their weights and a weighted-average grade. The calculator updates the result panel live as you change values: the headline is the weighted average to two decimal places out of the chosen scale, alongside the count of contributing rows, the total weight, and the status verdict.
A French high-school student with four classes and the defaults loaded: 14 (coef 3), 11 (coef 4), 16 (coef 2), 9 (coef 1). Sum of (grade × weight) = 14×3 + 11×4 + 16×2 + 9×1 = 42 + 44 + 32 + 9 = 127. Sum of weights = 3 + 4 + 2 + 1 = 10. Weighted average = 127 / 10 = 12.7/20, status "Good." Compare to the unweighted average: (14 + 11 + 16 + 9) / 4 = 50 / 4 = 12.5 — close, but not the same. The weighting matters more in cases where the heaviest-weighted subject is unusually high or low: same student with the 11 in maths upgraded to 17 (coef 4) gives 14×3 + 17×4 + 16×2 + 9×1 = 42 + 68 + 32 + 9 = 151, average = 15.1, status "Excellent." The unweighted average would have moved by only 1.5 points. A US-style example on /100: a student with 88 (4 credits), 92 (3 credits), 76 (3 credits), 95 (2 credits): (88×4 + 92×3 + 76×3 + 95×2) / 12 = (352 + 276 + 228 + 190) / 12 = 1046 / 12 ≈ 87.2 — "Good."
First, dividing by the count of subjects instead of the sum of weights. This produces a number that is "sort of right" for unweighted averages but always wrong for weighted ones. Second, treating the weights as percentages that must sum to 100. They don't — coefficients can be any positive number; only the ratios matter. Coefficients of 3, 4, 2, 1 are equivalent to coefficients of 30, 40, 20, 10 or to 0.3, 0.4, 0.2, 0.1; the calculator's only requirement is that the weights are positive. Third, applying a single coefficient when subjects have multiple components. A French "épreuve de spécialité" with a written part (coef 8) and an oral part (coef 8) is really two separate rows, not one row with coefficient 16 and the average of the two grades — the math gives the same result only if the two component weights are equal, which is the special case here. Fourth, mixing scales. A 14/20 and a 90/100 are not directly averageable; convert one to the other (14/20 = 70/100) before entering them. Fifth, ignoring grade boundaries. The status bands are conventional approximations, not the official ones for any specific exam — for the French baccalauréat, the official mention thresholds are 12 (assez bien), 14 (bien), 16 (très bien), so adjust your interpretation accordingly.
Weighted averages crop up far beyond schoolwork. Beam balance in physics is a weighted average of positions weighted by mass — the centre of gravity. Portfolio return in finance is a weighted average of asset returns weighted by the dollars allocated to each. Composite indices like the Consumer Price Index are weighted averages of component price changes weighted by household-spending shares. The arithmetic is identical: numerator is sum of (value × weight), denominator is sum of weights. Geometric weighted average swaps the sum and product in the formula, useful for averaging multiplicative quantities like growth rates over time. Harmonic weighted average uses the reciprocal trick, useful for averaging speeds over equal-time legs. All of those generalise the simple arithmetic weighted average that students compute every term, but the simple version is by far the most common, and the one this calculator implements.