⚖️ Weighted Average Calculator
Three exam scores at 20%, 30% and 50% weight — the exact course grade, with the multiply-add-divide working shown, and weights that don't need to total 100.
| Value (e.g. grade) | Weight (e.g. %) | |
|---|---|---|
84.3
weighted average
843/10
exact fraction
Working
- Multiply each value by its weight and add: Σ(value × weight) = 8430
- Add the weights: Σweight = 100
- Divide: 8430 ÷ 100 = 843/10
Weights don't need to sum to 100 — the division normalizes them. Grade example: 92 at 20%, 78 at 30%, 85 at 50% → the exact course grade.
Exact rational arithmetic — no float drift when your weights are thirds. Runs locally.
How the weighted average calculator works
A weighted average multiplies each value by its weight, sums those products, and divides by the sum of the weights: Σ(value × weight) ÷ Σweight. The calculator does this in exact rational arithmetic — enter values and weights as integers, decimals or fractions, add as many rows as you need, and read the result as both a decimal and an exact fraction with the three-step working displayed. Because the division normalizes, weights need not sum to 100 or 1: credit hours (3, 4, 3), percentages (20, 30, 50), or raw ratios all work identically.
The everyday case is grades — "homework 20%, midterm 30%, final 50%, what's my course grade?" — but the same arithmetic prices index funds, averages sensor readings by reliability, and computes GPA (grade points weighted by credit hours). The classic mistake is averaging the averages, which is only right when the weights are equal; the worked steps make the difference visible.
Frequently asked questions
How is a weighted average calculated?
Multiply each value by its weight, add the products, divide by the total weight: (92×20 + 78×30 + 85×50) ÷ (20+30+50) = 8430 ÷ 100 = 84.3. The tool shows exactly this working for your rows.
Do the weights have to add up to 100?
No — dividing by the weight total normalizes automatically. Credit hours, percentages and raw ratios all work; only the weights' relative sizes matter.
How do I compute a GPA?
Values are the grade points (A = 4.0 etc.), weights are the credit hours. A 4.0 in a 3-credit class and 3.0 in a 4-credit class → (4×3 + 3×4) ÷ 7 = 24/7 ≈ 3.43 — the tool keeps the exact fraction too.
Why not just average the numbers?
A plain average treats every value as equally important. If the final exam is half the grade, ignoring the weights misstates the result — sometimes by a full letter grade.
Is the arithmetic exact?
Yes — rational arithmetic throughout, so third-weights (1/3, 1/3, 1/3) don't drift into 0.9999 territory. Runs locally.