How to Use the Weighted Average Calculator

Enter each value and the weight assigned to that value. Click Add Another Value if you need additional entries.

You can use either relative weights or percentage weights.

The calculator shows:

• The weighted average;
• The simple arithmetic average;
• Total weight;
• Weighted sum;
• Normalised weight for each value;
• Each value’s contribution to the result;
• Highest and lowest entered values; and
• The value needed on one additional weighted item to reach a target average.

What Is a Weighted Average?

A weighted average is an average where some values contribute more to the result than others.

Instead of treating every value equally, each value is multiplied by a weight representing its relative importance.

Weighted Average Formula

The symbol Σ means to add all of the relevant values together.

Weighted Average Example

Weighted Average vs Simple Average

A simple arithmetic average treats all values equally.

A weighted average allows individual values to have more or less influence.

For example, suppose the values are:

• 60;
• 80;
• 100.

The simple average is:

(60 + 80 + 100) ÷ 3 = 80

If the value 100 has a much larger weight, the weighted average will be greater than 80.

What Are Relative Weights?

Relative weights do not need to add to 100.

For example, the following sets of weights have the same relative proportions:

• 1, 2, 3;
• 10, 20, 30;
• 100, 200, 300.

Because the proportions are identical, they produce the same weighted average.

What Are Percentage Weights?

Percentage weights are usually expressed as percentages such as:

• 20%;
• 30%;
• 50%.

For a complete calculation they often total 100%, but the calculator normalises the weights mathematically even if they total another amount.

Do Weighted Average Weights Have to Add to 100?

No, not for the standard weighted-average formula.

For example:

have the same proportions as:

Both produce the same weighted average when applied to the same values.

What Is a Normalised Weight?

Normalisation converts each weight into its share of the total weight.

For example, if weights are 20, 30 and 50, their normalised weights are:

• 20%;
• 30%;
• 50%.

If the weights are 2, 3 and 5, the normalised percentages are still 20%, 30% and 50%.

How Is Each Weighted Contribution Calculated?

Each item’s contribution to the final weighted average is:

For example, if a value of 80 represents 25% of the total weight:

80 × 0.25 = 20

That item contributes 20 points to the final weighted average.

Weighted Average Calculator for Grades

Weighted averages are commonly used for school and university grades.

For example:

• Assignment: 80%, worth 20%;
• Test: 70%, worth 30%;
• Final exam: 90%, worth 50%.

The weighted grade is:

For more education-specific features, use the Grade Percentage Calculator.

Weighted Average Calculator for Investments

Weighted averages can also be used to calculate portfolio returns when different investments represent different proportions of a portfolio.

For example:

• Investment A return: 5%, portfolio weight 30%;
• Investment B return: 8%, portfolio weight 50%;
• Investment C return: 4%, portfolio weight 20%.

The weighted portfolio return is:

Weighted Average Calculator for Prices

A weighted average price can be useful when the same product is purchased at different prices and quantities.

For example:

• 10 units at $20;
• 30 units at $25.

The weighted average price is:

Weighted Average Cost per Unit

The same approach can be used for inventory and cost calculations.

This can be useful for basic inventory planning and average purchase-price analysis.

Weighted Average Calculator for Survey Results

Survey responses can be weighted when certain categories represent different numbers of people or different levels of importance.

The weight may represent:

• Number of respondents;
• population proportion;
• sampling adjustment;
• importance score; or
• another relative factor.

Weighted Average Calculator for GPA

A GPA-style weighted average can be calculated by using each grade-point value as the value and credit hours as the weight.

For example:

• Grade points 4.0 with 3 credit units;
• Grade points 3.0 with 6 credit units;
• Grade points 3.5 with 3 credit units.

The credits become the weights in the weighted-average calculation.

Official GPA systems can use institution-specific rules, so always check your university’s grading method.

How to Calculate the Value Needed to Reach a Target Weighted Average

Suppose you already have several weighted values and want to know what value you need on one additional item.

The calculator rearranges the weighted-average equation to estimate the required future value.

Target Weighted Average Example

Suppose your current weighted average is 70 across a total weight of 80. You want an overall average of 75 after adding another item with a weight of 20.

Current weighted sum:

70 × 80 = 5,600

Target weighted total:

75 × 100 = 7,500

Required additional weighted contribution:

7,500 − 5,600 = 1,900

Required new value:

1,900 ÷ 20 = 95

The new item would need a value of 95 to produce a final weighted average of 75.

Can Weighted Averages Include Decimal Values?

Yes. Both values and weights can contain decimal numbers.

For example:

• Value 72.5 with weight 12.5;
• Value 81.3 with weight 22.75; and
• Value 90.2 with weight 64.75.

The calculator handles these values automatically.

Can Weights Be Zero?

Yes. A value with a weight of zero has no effect on the weighted average.

However, the combined weight of all values must be greater than zero for a meaningful weighted average to be calculated.

Can Weights Be Different Units?

Weights should represent the same type of relative quantity within a particular calculation.

Examples include:

• All weights as percentages;
• all weights as quantities;
• all weights as credit hours;
• all weights as portfolio proportions; or
• all weights as importance scores.

Why Is My Weighted Average Different From My Normal Average?

The simple average gives equal importance to every value. The weighted average gives more importance to entries with larger weights.

If high values have larger weights, the weighted average tends to be higher. If low values have larger weights, the weighted average tends to be lower.

Weighted Average Calculator Assumptions

This calculator assumes:

• Each entered value is numeric;
• Each weight is non-negative;
• Total weight is greater than zero;
• Weights represent comparable relative importance;
• Percentage weights do not need to total exactly 100% because they are normalised;
• Zero-weight values do not affect the result;
• No statistical sampling correction is applied;
• No institution-specific GPA rules are applied;
• No investment fees, taxes or compounding are included; and
• Results are general mathematical calculations only.

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