Weighted Average Calculator

Weighted average versus a simple average

A simple average treats every number the same way: add them all up, divide by how many there are. A weighted average instead lets some numbers count for more than others, by multiplying each one by a weight before adding them up, and dividing by the total of the weights rather than by the count of items.

The difference only shows up once the weights are unequal. Suppose a student earns 90 in a 4-credit course, 70 in a 3-credit course, and 60 in a 1-credit course. The simple average treats all three grades as equally important: (90 + 70 + 60) / 3 = 73.33. But the 4-credit course should count four times as much as the 1-credit course, so the weighted average multiplies each grade by its credit hours first: (90×4 + 70×3 + 60×1) / (4 + 3 + 1) = 630 / 8 = 78.75. The weighted figure is more than five points higher, because it correctly gives the strongest result the most influence.

That gap is not a rounding quirk, it is the entire point of weighting: whenever the items being averaged are not equally important, a simple average quietly misrepresents the result, and a weighted average corrects for it.

What the weighted average calculator returns

The weighted average calculator returns three figures: the weighted average itself, the plain average of the same values for comparison, and the total weight it divided by. The statistical name for the same result is the weighted mean, so a weighted mean calculator and this page do the same job. To calculate weighted average figures for a new list, type the values and weights, press Calculate and read the result; to see how it was reached, follow the three steps in the section below, which work as a weighted average calculator with steps and a weighted mean calculator with steps. There is nothing to install, so it is a weighted average calculator online that also works on a phone.

Weighted average calculator for grades, scores and marks

A weighted average calculator for grades takes each result as a value and the credit hours, units or category share as the weight. As a weighted average grade calculator it fits a semester of courses with different credit loads, and as a weighted score calculator or weightage calculator it fits a marking scheme where each paper counts for a set share. For a course built from quizzes, assignments and exams, the dedicated weighted grade calculator on this site takes scores out of a maximum, which is usually easier than converting them by hand.

Some universities publish their own weighted averages under local names. A general weighted average calculator, often called a GWA calculator, is common for course units in the Philippines, and a WAM calculator is the equivalent search in Australia, where marks are weighted by credit points. The arithmetic is the one on this page, but the rules for which courses count and how marks are rounded belong to each university, so enter the weights your institution specifies. A weighted average calculator uni students use is therefore only as good as the course list and weights typed into it.

Weighted average for prices, costs and interest rates

Money problems use the same formula with amounts as weights. A weighted average price calculator answers what you paid per share when you bought at different prices: 100 shares at 20 and 50 shares at 26 cost 3,300 in total for 150 shares, a weighted average price of 22.00. The same entries work as a weighted average calculator for stocks, and as a weighted average cost calculator when the values are unit costs and the weights are quantities. Accountants use the idea under the weighted average cost method, so a weighted average calculator accounting teams need is this one with quantities as weights.

A weighted average interest rate calculator works the same way, with each loan balance as the weight and its rate as the value. A balance of 10,000 at 6% and another of 5,000 at 9% carry yearly interest of 600 and 450, so the weighted average rate is 1,050 divided by 15,000, which is 7.0%. The weighted average of two numbers calculator case is just two rows, and the plain average of 6% and 9% would wrongly report 7.5%.

Hours, overtime and other everyday weights

A weighted average calculator for payroll covers staff who work at more than one hourly rate in a week, and a weighted average calculator for overtime helps when a rule bases the overtime rate on the blended rate. Thirty hours at 20 and ten hours at 25 give (600 + 250) divided by 40, which is 21.25 an hour. Whether that blended figure is the right base for overtime depends on the labour rules that apply to you, so use the calculator for the arithmetic and check the rule separately.

How to calculate weighted average by hand

What is weighted average in one line? It is the total of value times weight, divided by the total weight. How to calculate weighted average by hand therefore takes three steps: multiply each value by its weight, add the products, and divide by the sum of the weights. Anyone asking how to find weighted average for a short list, or how do you calculate a weighted average when the weights are percentages, follows the same steps. The weighted average formula and the weighted mean formula are two names for the one expression shown earlier, and a weighted average example such as the credit-hour case above is the quickest way to check you have it right.

Where a weighted average is used

Weighted averages turn up anywhere some inputs matter more than others. A few common examples:

• Course grades weighted by credit hours. A three-credit course should influence a semester average three times as much as a one-credit lab. Universities compute a GPA this way, weighting each course’s grade point by its credit hours rather than just averaging the grades.
• Investment portfolio returns weighted by allocation. If 70% of a portfolio sits in one fund earning 8% and 30% sits in another earning 2%, the portfolio’s overall return is not the simple average of 8% and 2%. It is the weighted average, using the share of money in each fund as the weight: (8×0.70 + 2×0.30) = 6.2%, much closer to the larger holding’s return.
• Survey or index scores weighted by sample size. Combining results from several survey waves of different sizes should not let a 50-person wave count the same as a 5,000-person wave. Weighting each wave’s average score by how many people answered it keeps the combined figure representative of the larger samples.
• Product or supplier ratings weighted by review count. A product with a 5.0 average from two reviews and a product with a 4.6 average from two thousand reviews are not equally trustworthy figures; weighting each average by its review count reflects that.

A worked example

A small business tracks its monthly profit margin across three product lines, each with a different share of total sales: Line A made a 12% margin on 50% of sales, Line B made an 18% margin on 30% of sales, and Line C made a 4% margin on 20% of sales. Treating these as three equal numbers gives a misleading simple average of (12 + 18 + 4) / 3 = 11.33%. Weighting each margin by its share of sales gives (12×50 + 18×30 + 4×20) / (50 + 30 + 20) = (600 + 540 + 80) / 100 = 12.2%, a more accurate picture of the business’s overall margin, because it reflects that half of all sales came from Line A.

In every one of these cases, the calculation is identical to the one above the fold on this page: a list of values, a list of weights, and one number at the end that reflects how much each value actually mattered.

How the calculator gets from your rows to one number

Each row you fill in contributes a value and a weight. Behind the scenes the calculator follows three steps every time you type:

1. Multiply. Every value is multiplied by its own weight, so a row with a larger weight produces a larger contribution before anything is added up.
2. Add. Those weighted contributions are summed across every row, and separately the weights themselves are summed to get a total weight.
3. Divide. The sum of the weighted contributions is divided by the total weight. That division is what makes the result an average rather than just a bigger number, and it is also why the weights do not need to add up to any particular total: whatever they add up to becomes the divisor.

The simple average shown alongside it skips the weighting step entirely, adding the raw values and dividing by how many rows there are. Comparing the two numbers is often more informative than either one alone, because a large gap between them tells you the weights are doing real work, while a small gap tells you the weighting barely mattered for this particular set of numbers.

One row worth watching is anything with a weight of zero. It still shows up in the count used for the simple average, so it can pull that number up or down, but it drops out of the weighted average completely, since multiplying a value by zero always gives zero. A zero-weight row is a useful way to keep an item visible in your list, perhaps a course you audited without credit, without letting it influence the weighted result at all.