Weighted Average Calculator (Three Values)

This calculator finds the weighted average of three values, such as grades with different weights or prices paid for different quantities. Enter each value and its weight; you get the weighted average, the plain average for comparison and the total weight.

Formula

Weighted average = (v1 × w1 + v2 × w2 + v3 × w3) ÷ (w1 + w2 + w3). The plain average is (v1 + v2 + v3) ÷ 3. Weights can be percentages, credits, hours or quantities; only their ratios matter. Set a weight to 0 to leave a value out.

• v1-v3: the values
• w1-w3: their weights (0 or more, not all zero)

Worked Example

Scores 85, 92 and 78 weighted 30, 50 and 20.

1. Products: 85 × 30 = 2,550; 92 × 50 = 4,600; 78 × 20 = 1,560
2. Sum = 8,710; total weight = 100.00
3. Weighted average = 8,710 ÷ 100 = 87.10
4. Plain average = (85 + 92 + 78) ÷ 3 = 85.00

How to use the result

The weighted average sits closer to the values with bigger weights: here 92 counts for half, so the result is above the plain average. If the weights are percentages they should add to 100, but the formula works whatever they add to.

Limits and common mistakes

• If all weights are 0 there is no average (the page shows Cannot compute).
• Do not mix weights in different units, such as percent for one item and points for another.
• For more than three values, combine the first results: their weighted average with the total weight acts as one value.

Frequently Asked Questions

How do I calculate a weighted grade?

Multiply each score by its weight, add the products, and divide by the sum of the weights.

Do the weights have to add to 100?

No; dividing by the total weight takes care of it.

When is the weighted average equal to the plain average?

When all weights are equal.

Can a weight be negative?

No, weights are 0 or more here.