Weighted Average Calculator (GPA, Portfolios, ENEM)
Compute weighted average vs simple average. Use cases: GPA (course grade × credit hours), portfolio allocations, survey aggregation. Shows per-item contribution and weighted-vs-simple delta.
Based on 2 references↓Weighted average
3.45
Simple average: 3.5 · Weighted vs simple delta: -0.05
Calculation
[(4 × 3) + (3 × 4) + (3.5 × 3)] / [3 + 4 + 3] = 3.45Contributions
| Label | Value | Weight | % |
|---|---|---|---|
| Math 101 | 4 | 3 | 30% |
| English 200 | 3 | 4 | 40% |
| History 150 | 3.5 | 3 | 30% |
Weighted average is the upgrade of "simple average" when items in your dataset are not equal in importance. GPA: an A in a 4-credit class matters twice as much as an A in a 2-credit class. Portfolio return: a 10% gain on 80% of your assets matters far more than a 30% gain on 1%. ENEM: redação tem peso 3 enquanto biologia tem peso 1 em algumas universidades. The math: sum(value × weight) / sum(weight). Simple average is the special case where all weights are equal.
The calculator surfaces three numbers side by side: the weighted average (what you actually get), the simple average (what the unweighted formula would give), and the delta between them — which makes obvious how much the weighting changes the answer. Per-item contribution table shows what % of total weight each row carries, so you can see at a glance which item is dragging the average up or down.
The weighted-average formula
Formula: weighted_average = Σ(value × weight) / Σ(weight). For values v₁, v₂, ..., vₙ with weights w₁, w₂, ..., wₙ.
Example — GPA: Math 101 (A=4.0, 3 credits) + English 200 (B=3.0, 4 credits) + History 150 (B+=3.5, 3 credits). Numerator: 4.0×3 + 3.0×4 + 3.5×3 = 12 + 12 + 10.5 = 34.5. Denominator: 3 + 4 + 3 = 10. GPA = 3.45.
Special case — equal weights: when w₁ = w₂ = ... = wₙ, the weighted formula collapses to the simple arithmetic mean. The "weighted vs simple delta" the calc shows is exactly zero in that case.
Edge cases: all-zero weights → undefined (division by zero); calc returns null. Negative weights → invalid (weights must be ≥ 0); calc returns null. Single item → weighted = simple = that value.
Practical examples
GPA — three classes with different credit hours
Setup: Math 101 (4.0 × 3cr) + English 200 (3.0 × 4cr) + History 150 (3.5 × 3cr)
(12 + 12 + 10.5) / 10 = **3.45 GPA**
Takeaway: A simple average would give (4 + 3 + 3.5) / 3 = 3.50. Weighted is 3.45 because the larger English class drags the average down. Delta: -0.05.
ENEM (BR) — 5 áreas with different pesos
Setup: Linguagens 700 (peso 2) + Mat 650 (peso 3) + CN 750 (peso 2) + CH 600 (peso 3) + Redação 800 (peso 2)
(1400 + 1950 + 1500 + 1800 + 1600) / 12 = 8250 / 12 = **687.5**
Takeaway: Pesos refletem importância da universidade. Redação peso 3 vs peso 2 muda muito o resultado final.
Portfolio return — 3 asset classes
Setup: Stocks 12% (60% of portfolio) + Bonds 5% (30%) + Cash 2% (10%)
(12×60 + 5×30 + 2×10) / 100 = (720 + 150 + 20) / 100 = **8.9%**
Takeaway: Simple average would say (12 + 5 + 2) / 3 = 6.33%. The weighted view shows the actual portfolio return, dominated by the 60% stock allocation.
Survey aggregation — 3 cohorts of different sizes
Setup: Cohort A: 4.5 satisfaction (n=200), B: 3.8 (n=500), C: 4.2 (n=300)
(900 + 1900 + 1260) / 1000 = **4.06**
Takeaway: Pure average of 4.5/3.8/4.2 = 4.17, but the bigger Cohort B (more weight) pulls the true mean down to 4.06.
Frequently asked questions
When should I use weighted average instead of simple average?▾
Whenever items have different importance, frequency, or sample size. GPA (credits), portfolio return (allocation %), survey results (cohort size), grade calculation (assignment weight), opinion polls (population strata).
What happens if all weights are equal?▾
Weighted average equals the simple average. The calc shows this explicitly via the "weighted vs simple delta" being exactly zero.
Can weights be percentages that sum to 100?▾
Yes, that's the most natural form for portfolio + survey use cases. The math works the same: sum(value × pct) / 100 = weighted average. The calc handles raw numbers (3, 4, 3 for credits) and percentages (60, 30, 10 for allocation) interchangeably — only the relative ratios matter.
Why is my weighted average different from the simple average?▾
The "weighted vs simple delta" tells you the direction and magnitude. Positive delta = high-weight items have above-average values pulling the result up. Negative delta = high-weight items below average. The contributions table shows exactly which item is causing the shift.
How do I handle missing data?▾
Drop the missing items entirely (do not enter as 0 unless 0 is a valid value). The calc auto-filters non-finite values. For partial weights, just use the actual numbers — the formula normalises by total weight automatically.
Sources & references
Cross-check every number in this calculator against the primary sources below.
- ReferenceInvestopedia — Weighted average
- ReferenceKhan Academy — Statistics + averages
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