How To Calculate Grades With Weighted Percentages

Often, teachers and professors like to assign more weight to important exams or assignments. This means that those pieces of work contribute more to your final grade.

Without any weighted grades, you can simply average your test scores and figure out what your final grade will be. Weighted grades make it a little more difficult but not too much.

You have a class in which you have four midterms. Each midterm is worth 15 percent of your grade. The final is worth 40 percent of your grade. Your grades on the midterms are 61, 75, 90 and 79. Your grade on the final is 96. What is your final grade in the class?

1\. Begin by changing all weights into ​decimals​. This means that for each midterm which is worth 15 percent, the percentage is divided by 100 to yield 0.15. The weight of the final is thus 40/100 which yields 0.4. To ensure that you have calculated the weights correctly, you should add them all together. They should add up to one as shown below:

\(0.15\enspace +\enspace 0.15\enspace +\enspace 0.15\enspace +\enspace 0.15\enspace +\enspace 0.40\enspace =\enspace 1\)

Good! The weights add up to one. Now you can move on to the next step.

2\. Each grade must be multiplied by its weight to find your final grade:

\(0.15*(61)\enspace +\enspace 0.15*(75)\enspace +\enspace 0.15*(90)\enspace +\enspace 0.15*(79)\enspace +\enspace 0.40*(96)\enspace =\enspace 84.2\)

In this case your final grade is a 84.2. You can see that even though a couple of those grades were on the lower end, scoring well on the exam that was weighted the highest really helped to bring your grade up.

This process can be used to figure out what kind of grade you should aim for on a given exam if you want to end up with a certain grade. For example, say you want to have at least a 90 in the class. So far in the same class as above your grades on the four midterms are 89, 85, 91 and 78. What would you need to get on the final in order to have at least a 90 in the class?

You know the weights add up to one, so you don't need to check that. Instead, you can move on to multiplying weights by grades and adding them together. Except this time, instead of having a value for a grade on the final, it'll be a ​variable​. You can call it "f" for final. You also know the sum of all of these should at least be a 90. You can set it up as follows:

\(0.15*(89)\enspace +\enspace 0.15*(85)\enspace +\enspace 0.15*(91)\enspace +\enspace 0.15*(78)\enspace +\enspace 0.40*(f)\enspace =\enspace 90\)

Solving for "f" you get:

\(f\enspace =\enspace 96.4\)

This means that in order to get at least a 90 in the class you will have to score at least a 96.4 on the final exam.

This can get a little complicated depending on the type of weighted average you want. If you're keeping it simple as discussed above, then the following formula works well:

\(weighted\enspace average\enspace =\enspace (w_1*grade_1)\enspace +\enspace (w_2*grade_2)\enspace +\enspace ...\enspace +\enspace (w_{final})*(grade_{final})\)

The "w" with a subscript refers to a weight expressed as a decimal. All weights must add up to one. The "grade" with a subscript refers to the grade you got. This must be matched with the correct weight. You can add as many of these together as you want, as long as the weights all add up to one.

If the weight adds up to ​more than one​, then you may have made a mistake in converting from percentage into decimal. You should also go back and make sure that all the percentages added together equal 100. If that isn't the case, make sure and let your teacher know. They may have made a mistake.