Weighted Average Calculator

What this calculator does

Sometimes a plain average is not fair, because some of your numbers deserve to count for more than others. A final exam that is worth more than a quiz. A big order that matters more than a small one. A weighted average handles exactly that: each value carries a weight, and the ones with bigger weights pull harder on the result.

You give it your values and their weights, and it works out the weighted average for you, right here in the browser.

Using the calculator

1. Enter your data as value and weight pairs, one pair per line. Put a space or a comma between the two numbers.
2. For example, three lines reading 50 2, then 25 3, then 40 1, means a value of 50 with weight 2, a value of 25 with weight 3, and a value of 40 with weight 1.
3. Press Calculate.

The weighted average comes back rounded to two decimal places. Reset clears the box.

What a weighted average is

A plain average treats every number as equal. A weighted average lets you say how much each one counts. The weight is really just a way of saying "this value gets a bigger vote".

The neat way to picture it: a weight is how many times a value effectively appears. A value with weight 3 is like having that number in the set three times over. In fact, if you gave every value the same weight, a weighted average collapses straight back into the ordinary mean. The weights only start to matter once they differ.

The formula

Multiply each value by its weight, add those up, and divide by the total of the weights:

weighted average = (sum of value × weight) ÷ (sum of the weights)

The bottom of the fraction is the total weight, not the number of values. That is the one difference from a plain mean, and it is the whole reason the heavier values count for more.

A worked example with grades

This is where weighted averages earn their keep. Say a course grade is built from three pieces: coursework scored 50 and worth 2 parts, a project scored 25 and worth 3 parts, and a quiz scored 40 and worth 1 part.

1. Value times weight for each: 50 × 2 = 100, 25 × 3 = 75, 40 × 1 = 40.
2. Add those: 100 + 75 + 40 = 215.
3. Add the weights: 2 + 3 + 1 = 6.
4. Divide: 215 ÷ 6 = 35.83.

The plain average of 50, 25 and 40 would have been about 38.33. The weighted figure is lower because the piece scored 25 carried the most weight, so it pulled the result down. That gap between the two is the whole point of weighting.

When you need this instead of a plain average

Reach for a weighted average whenever the things you are averaging are not all the same size or importance. A few everyday cases: a school grade where each assignment is worth a different percentage, a GPA where each course carries a number of credit hours, the average price you paid for shares bought in different amounts, or a review score where some ratings are based on far more votes than others. In every one of those, a plain average would quietly treat a tiny thing and a huge thing as equals, and give you a misleading number.

Questions people ask

How do you calculate a weighted average?

Multiply each value by its weight, add up those results, then divide by the sum of the weights. Not by the number of values, which is what a plain average uses.

How is it different from a normal average?

A normal average counts every value equally. A weighted average lets some values count for more. If all the weights are equal, the two give the same answer.

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

No. The weights can be any numbers, like 2, 3 and 1. Dividing by the total of the weights sorts out the scale automatically, so they do not need to add up to anything in particular.

What format do I enter the data in?

One value-and-weight pair per line, with a space or comma between the two numbers, for example 50 2 on one line and 25 3 on the next.

Can I use it for a GPA or a course grade?

Yes, that is a classic use. Enter each grade as the value and its credit hours or percentage weight as the weight.

References

A note on where this comes from. The weighted mean is a standard measure in statistics, used whenever the values being averaged carry different importance, and it is covered in general statistics references such as the NIST/SEMATECH e-Handbook of Statistical Methods. With equal weights it reduces to the ordinary arithmetic mean. For further reading, see Weighted arithmetic mean.

1. NIST/SEMATECH, e-Handbook of Statistical Methods, on weighted measures of location. https://www.itl.nist.gov/div898/handbook/