How is a weighted average different from a regular average?

A regular (arithmetic) average treats every value equally. A weighted average lets each value carry its own weight, so values with larger weights pull the result toward them. The two are equal only when every weight is the same.

How do you calculate a weighted grade?

Multiply each category's score by its weight (for example exams 50%, homework 30%, quizzes 20%), add the products, and divide by the sum of the weights. An 88 weighted 50, a 95 weighted 30, and a 72 weighted 20 give (4400 + 2850 + 1440) ÷ 100 = 86.9%.

Do the weights have to add up to 100 or to 1?

No. Weights can be any numbers — percentages, credit hours, dollar amounts, or plain counts. The formula divides by the sum of the weights, so they are normalized automatically. Weights of 0.2, 0.3, 0.5 and weights of 2, 3, 5 give exactly the same result.

How do I calculate my GPA with a weighted average?

Convert each class grade to grade points on the 4.0 scale (A = 4.0, B = 3.0, and so on), then take the weighted average of those points using each class's credit hours as the weight. A 4-credit A and a 3-credit B give (4×4.0 + 3×3.0) ÷ 7 = 3.57.

What if some values are missing or a weight is zero?

A weight of zero removes a value from the average entirely — it contributes nothing to the numerator or denominator. Rows you leave blank are simply ignored. The calculator only includes rows where both the value and the weight are filled in.

Can a weighted average be higher than every value?

No. A weighted average is always between the smallest and largest value, just like a plain mean. Weights change where inside that range the answer lands, but they can never push it past the extremes.

What is a weighted mean used for in real life?

Course grades, GPAs, portfolio returns, survey scores, average prices paid (cost basis), economic indexes like the CPI, and any blended rate where the parts are different sizes. Whenever the things you are averaging are not equally important, you weight them.

Statistics

Weighted Average Calculator

Add a row for each value and its weight to get the weighted average instantly — the mean that lets some values count more than others. Built-in modes for class grades, GPA, and any values-and-weights problem, with every step shown.

Enter each item

3 rows

Any numbers. Weights can be counts, percentages, dollars — they need not add to 100.

LabelValueWeight

Weighted average

Σ(value × weight) ÷ Σweight = 830 ÷ 10

Heaviest weight · 50%

Contribution by weight

item 190 × 5 → 45
item 280 × 3 → 24
item 370 × 2 → 14

Σ weights

plain mean

items

The plain mean (80) ignores weights; the weighted average leans toward the heaviest-weighted items.

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The basics

What is a weighted average?

A weighted average is a mean where each value carries a weight reflecting how much it matters. You multiply every value by its weight, add up the products, then divide by the total of the weights. The heavier a value's weight, the more it pulls the answer toward itself.

x̄w = Σ(wᵢ · xᵢ) ÷ Σwᵢ

The formula

Each value x is scaled by its weight w, the scaled values are summed, and the total is divided by the sum of the weights. That final division is what turns a weighted sum into a weighted average.

(90·5 + 80·3 + 70·2) ÷ 10 = 83

weights need not sum to 1

Weights are relative

Only the ratio between weights matters. Doubling every weight, or writing them as percentages instead of counts, leaves the answer unchanged — because dividing by their sum normalizes them for you.

0.2, 0.3, 0.5 ≡ 2, 3, 5

Method

How to calculate it by hand

Four steps, whatever the values represent.

1
Multiply each value by its weight
Pair every value x with its weight w and multiply. These products are the weighted contributions.
90·5 = 450, 80·3 = 240, 70·2 = 140
2
Add the products
Sum those weighted contributions to get the numerator of the formula.
450 + 240 + 140 = 830
3
Add the weights
Sum the weights to get the denominator. This is what normalizes the result.
5 + 3 + 2 = 10
4
Divide
Divide the sum of products by the sum of weights. The result is the weighted average.
830 ÷ 10 = 83

Worked examples

See it across situations

The same procedure handles a report-card grade, a semester GPA, and an investment portfolio — only the meaning of the weights changes.

Three categories that weight to 100%.

Multiply each value by its weight

Exams: 88 × 50 = 4400

Homework: 95 × 30 = 2850

Quizzes: 72 × 20 = 1440

Σ products = 4400 + 2850 + 1440 = 8690

Σ weights = 50 + 30 + 20 = 100

Divide: 8690 ÷ 100

Final grade = 86.9%

Where it shows up

Why the weighted mean matters

Whenever the things you are averaging are not equally important, you weight them.

exams 50% · HW 30%

Course grades

A syllabus assigns each category a percentage of the final grade. The course grade is the weighted average of category scores.

points × credits

GPA

Grade points are weighted by credit hours, so a five-credit class moves your GPA more than a one-credit elective.

return × dollars

Investing

A portfolio's return is the average of each holding's return weighted by how much money sits in it.

Compared

Weighted average vs. plain mean

The plain arithmetic mean is just a weighted average where every weight is equal. Seeing them side by side shows exactly what the weights are doing.

all weights equal

Plain arithmetic mean

Every value counts the same. Add them up and divide by how many there are. This is the special case people usually mean by “average.”

(90 + 80 + 70) ÷ 3 = 80

weights differ

Weighted average

Values with larger weights pull harder. Here the 90 carries the heaviest weight, so the answer sits above the plain mean of 80.

(90·5 + 80·3 + 70·2) ÷ 10 = 83

Reference

The 4.0 GPA grade-point scale

For a GPA, convert each letter grade to its point value, then take the weighted average using credit hours as the weights. This is the standard US scale.

A4.0

A−3.7

B+3.3

B3.0

B−2.7

C+2.3

C2.0

C−1.7

D+1.3

D1.0

F0.0

Worth knowing

Rules and common mistakes

A handful of facts that keep a weighted average honest — and the slips that trip people up.

min ≤ x̄w ≤ max

Stays inside the range

The result can never exceed the largest value or fall below the smallest. If yours does, a sign or a weight is wrong.

equal weights → mean

Reduces to the plain mean

When every weight is identical, the weighted average is exactly the ordinary arithmetic mean.

wᵢ = 0 drops a value

Zero weight removes a term

A value with zero weight contributes nothing to either the numerator or the denominator — it simply isn't counted.

divide by Σw, not n

Don't divide by the count

The most common error: dividing the weighted sum by the number of values instead of by the sum of the weights.

ratios, not totals

Scale-free

Multiplying every weight by the same factor changes nothing. Percentages and raw counts describe the same weighting.

weight the right thing

Weight, don't average twice

Don't average sub-scores first and then average again with weights — multiply the raw values by their weights in one pass.

Quick chart

What will my final grade be?

Enter your current grade and how much the final exam is worth, then read off the final grade for each possible exam score — a weighted average of your existing grade and the final.

Current grade (%)Final exam weight (%)So far your grade counts for 70% and the final for 30%.

if final = 100%

89.5%

↑

if final = 95%

88%

↑

if final = 90%

86.5%

↑

if final = 85%

85%

↑

if final = 80%

83.5%

↓

if final = 75%

82%

↓

if final = 70%

80.5%

↓

if final = 65%

79%

↓

if final = 60%

77.5%

↓

if final = 50%

74.5%

↓

if final = 40%

71.5%

↓

if final = 0%

59.5%

↓

FAQ

Common questions

A weighted average is a mean in which some values count more than others. Each value is multiplied by a weight that reflects its importance, the products are summed, and the total is divided by the sum of the weights. The formula is Σ(value × weight) ÷ Σweight.

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