Weighted Average Formula

Formula to Calculate Weighted Average

Weighted average is a type of an average that takes into account the relative importance of each value under consideration and is calculated by multiplying the respective weights (in percentage terms) with its corresponding value

Here, w = respective weight (in percentage), x = value

Example

Let’s take a simple weighted average example to illustrate how we calculate a weighted average.

In this weighted average example, we are given both w and x.

Using the weighted average formula, we get –

• Weighted Avg = w₁x₁ + w₂x₂ + w₃x₃ + w₄x₄
• Weighted Avg = 10% * 5% + 20% * 10% + 30% * 15% + 40% * 20% = 0.005 + 0.02 + 0.045 + 0.08 = 15%.

Explanation

On a simple average, we don’t pay heed to the weight. That’s why when we calculate the simple average, the result becomes too generic. However, in the case of weighted average, we pay right emphasis on the right weight and we portray the weight in terms of percentages.

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If you look at the weighted average formula, you would see that the value is being multiplied by the right amount of weight and that is the beauty of wt average.

• For example, if we need to find out the average of 10, 13, and 25, on a simple average, we will just add three numbers and divide it by 3. Simple average of the above three numbers would be = (10 + 13 + 25) / 3 = 48 / 3 = 16.
• If we take the same example with weight; then the result would be quite different. Let’s say that the weight of number 10 is 25%, 13 is 30%, and 25 is 45%. Wt average of the above three numbers of would be = (10 * 25%) + (13 * 30%) + (25 * 45%) = 2.5 + 3.9 + 11.25 = 17.65.

Use

The usage of the weighted average is quite broad.

As for the weighted average example, we can talk about the weighted average cost of capital. In calculating the weighted average cost of capital, we take the cost of equity and the cost of debt into account. And depending on the capital structure of the company, we calculate the WACC.

Another example where we use the weighted average cost of capital is the issuance of outstanding shares. Let’s say that a firm has issued 100 shares on the 1^st day of January. And then another 100 shares are issued on the 1^st day of July.

Now, while calculating the outstanding shares available during the year, we will use the weighted average method. Since the first 100 shares are issued on the 1^st of January, it would be applicable for the whole year. But the next 100 shares are only issued in the middle of the year; that’s why the next 100 shares would be available only for 6 months. And here would be the calculation of weighted average of outstanding shares = (100 * 1) + (100 * 0.5) = 100 + 50 = 150.

Weighted Average in Excel (with excel template)

Let us now do the same example as above in Excel.

This is very simple. You need to provide the values of “X” and “Y”.

You can easily calculate the ratio in the Weighted Average in the Excel template provided.

Recommended Article

This is a guide to Weighted Average Formula. Here we learn how to calculate the weighted average using its formula along with practical examples, calculator and downloadable excel template. You may also take a look at the following useful articles –

• What is the Deadweight Loss Formula?
• Formula for Risk-Weighted Asset
• Average Formula in Excel
• Average in Power BI