A weighted average shows up everywhere: course grades, GPAs, exam boards, stock indexes, survey results. The idea is simple, but the arithmetic trips people up, usually because they divide by the wrong number. This guide explains how to calculate weighted average values by hand, with worked examples for grades and a few other everyday cases, and shows the mistakes to avoid.
If you’d rather have the numbers done for you, our free calculator handles any number of items and weights that don’t total 100.
What a weighted average is
In a simple average, every value counts equally. In a weighted average, each value is multiplied by a weight that reflects its importance, and the total is divided by the sum of the weights rather than by the number of values. Weights can be percentages, points, credits, hours, or any measure of how much each item should count.
The formula
weighted average = (v₁ × w₁ + v₂ × w₂ + … + vₙ × wₙ) ÷ (w₁ + w₂ + … + wₙ)
When the weights are percentages that add up to 100, the division is by 100, so you can also think of it as adding up “score × weight ÷ 100” for each item.
How to calculate weighted average grades: step by step
| Item | Score | Weight | Score × weight |
|---|---|---|---|
| Homework | 94 | 15 | 1,410 |
| Lab reports | 88 | 15 | 1,320 |
| Quizzes | 79 | 10 | 790 |
| Midterm | 81 | 25 | 2,025 |
| Final exam | 86 | 35 | 3,010 |
| Total | 100 | 8,555 |
Divide 8,555 by 100 and the course grade is 85.55%. The simple average of the five scores is 85.6%, close this time because the low and high scores happened to have similar weights. Change the final exam to 70% and the weighted grade drops to 79.95%, while the simple average only falls to 82.4%: the heavier item pulls harder.
When not everything is graded yet
Mid-term, only some items have scores. Divide by the weight of the graded items, not by 100. Using the first four rows above: 1,410 + 1,320 + 790 + 2,025 = 5,545, divided by 15 + 15 + 10 + 25 = 65, gives 85.3%. If you divide by 100 instead you get 55.5%, which wrongly treats the final as a zero. This is the single most common weighted-average mistake, and the reason some gradebooks show a scary “total” in October.
Weights that don’t add up to 100
Nothing changes: divide by the actual total. A project worth 40 points and an exam worth 160 points, scored 90% and 75%, give (90 × 40 + 75 × 160) ÷ 200 = 78%. If a syllabus offers 5% extra credit and totals 105, divide by 105, or by 100 if the teacher treats the extra credit as a bonus on top. Ask which.
Other everyday weighted averages
- GPA: grade points weighted by credit hours. An A (4.0) in a 4-credit course and a B (3.0) in a 2-credit course give (4 × 4 + 3 × 2) ÷ 6 = 3.67.
- Average price paid: 100 shares at $10 and 50 shares at $16 average (1,000 + 800) ÷ 150 = $12 per share.
- Customer ratings: a product rated 4.8 by 20 reviewers and 3.5 by 80 reviewers averages (96 + 280) ÷ 100 = 3.76, not 4.15.
- Mixed groups: a class of 20 averaging 72% and a class of 30 averaging 80% together average (1,440 + 2,400) ÷ 50 = 76.8%.
How to calculate weighted average in a spreadsheet
With scores in B2:B6 and weights in C2:C6, use =SUMPRODUCT(B2:B6, C2:C6) / SUM(C2:C6). SUMPRODUCT multiplies each pair and adds the results; dividing by SUM of the weights handles totals other than 100. To ignore blank scores, restrict the ranges to graded rows or use =SUMPRODUCT(B2:B6, C2:C6) / SUMPRODUCT((B2:B6"") * C2:C6).
Common mistakes
- Dividing by the number of items instead of the total weight.
- Dividing by 100 when some weights are still ungraded.
- Mixing percentages and raw points in the same column.
- Rounding each item before multiplying; round only at the end.
- Forgetting that “weight” must be the same unit for every row.
Summary
To calculate a weighted average, multiply each value by its weight, add the products, and divide by the sum of the weights you used. For grades, that means dividing by the graded weight until the course is over, and by the syllabus total once every score is in. The weighted grade calculator does the arithmetic and shows what you need on the rest, and the Final Grade Calculator focuses on the one exam that usually matters most. For the maths behind it, see this explanation of the weighted arithmetic mean.
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