What is the formula for a weighted mean?

x̄w = Σ(w × x) ÷ Σw. Multiply each value by its weight, add up the products, then divide by the sum of the weights.

Do the weights have to add up to 100%?

No. Any positive weights work because the formula divides by their total. Weights of 2, 3 and 5 give the same result as 20%, 30% and 50%.

How do I calculate a weighted grade?

Use each category's percentage score as the value and its share of the final grade as the weight. A 90 in an exam worth 60% and an 80 in coursework worth 40% gives 0.6 × 90 + 0.4 × 80 = 86.

When is a weighted mean equal to the ordinary mean?

When every weight is the same. The weighted mean then reduces to the sum of the values divided by their count.

Weighted Mean Calculator

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Weighted Mean Calculator

A weighted mean multiplies each value by its weight, adds the products and divides by the total weight. It is the right average when some values count more than others: a course grade where the exam is worth 40% and homework 20%, a portfolio return, or a survey where each response carries a sampling weight.

Enter the values and their weights in the same order. Weights do not need to add to 1 or 100; the calculator divides by their sum. The steps show the products, the two sums and the division, and the plain (unweighted) mean is printed next to the result so you can see how much the weighting changed the answer. A weighted standard deviation is reported as well.

For grade calculations specifically, the site’s grade calculator and weighted final grade calculator handle percentages and letter cutoffs directly; this page is the general-purpose version that accepts any set of values and weights, including survey weights and portfolio shares.

Values (x)

Separate values with commas, spaces or new lines.

Weights (w)

One weight per value, in the same order. Weights need not add to 1.

Result and step-by-step solution

Weighted mean

87.1

The unweighted mean would be 86. Weighted standard deviation (population form): 3.9611.

Formula
x̄_w = Σ(w × x) ÷ Σw
Multiply each value by its weight
x w w × x
88 0.2 17.6
92 0.3 27.6
79 0.1 7.9
85 0.4 34
Add the products and the weights
Σ(w × x) = 87.1; Σw = 1
Divide
87.1 ÷ 1 = 87.1

x	w	w × x
88	0.2	17.6
92	0.3	27.6
79	0.1	7.9
85	0.4	34

Frequently asked questions

What is the formula for a weighted mean?: x̄w = Σ(w × x) ÷ Σw. Multiply each value by its weight, add up the products, then divide by the sum of the weights.
Do the weights have to add up to 100%?: No. Any positive weights work because the formula divides by their total. Weights of 2, 3 and 5 give the same result as 20%, 30% and 50%.
How do I calculate a weighted grade?: Use each category’s percentage score as the value and its share of the final grade as the weight. A 90 in an exam worth 60% and an 80 in coursework worth 40% gives 0.6 × 90 + 0.4 × 80 = 86.
When is a weighted mean equal to the ordinary mean?: When every weight is the same. The weighted mean then reduces to the sum of the values divided by their count.

Last reviewed: September 25, 2026. Calculations run in your browser and were validated against SciPy.

Weighted Mean Calculator

Result and step-by-step solution

Frequently asked questions

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