How To Calculate What Grade I Need On The Final

You've worked hard all year. You've done your best on your assignments, you've worked through your homework and you've read everything you're supposed to read. You've gotten good grades throughout, but the final is looming on the horizon. If you want to get an A in the class, how do you work out what score you need to get on the final? There are online calculators you can use (see Resources), but calculating it yourself is pretty simple once you understand the basics. If you're looking to work out your score and flex your math-muscles a little, here's how to do it.

The key concept you need is a "weighted percentage." This is basically a way of accounting for the fact that each assignment is worth a different proportion of your final grade.

Imagine your course has five assignments in total and the final exam. The final exam is worth 50 percent of your grade, and each of the assignments is worth 10 percent. So if you scored 100 percent on an assignment, this would only work out to 10 percent of your total grade for the course.

Weighted percentages allow you to account for this. All you have to do is convert the percentage the assignment is worth into a decimal and multiply that by your grade. To convert, just divide the percentage of your final grade the assignment represents by 100. So your 10 percent assignments turn into a weighted factor of 10 / 100 = 0.1, and your exam is 50 / 100 = 0.5.

Find the weighting for each assignment and go through this process.

Working out the total score on a module is easy once you have these weighted percentages. The basic formula is:

\(Final \; grade = a_1w_1 + a_2w_2 + a_3w_3 + a_4w_4 + a_5w_5 + a_ew_e\)

Where the a stands for your score on each assignment as a percentage (a₁ is assignment one, a₂ is assignment two, and so on, and a_e is the final exam) and the w values are the weightings you worked out in the previous section.

You can adjust this to suit the number of assignments on your module by adding or removing terms as needed (e.g. if your module has four assignments and an exam, you don't need a₅ and w₅).

Using the example where w₁ = w₂ = w₃ = w₄ = w₅ = 0.1 (i.e. each are worth 10 percent of your grade), and w_e = 0.5, let's imagine your scores (as percentages or out of 100) are a₁ = 68, a₂ = 80, a₃ = 56, a₄ = 75, a₅ = 77 and a_e = 73. Your final grade is:

\(\begin{aligned}
Final \; grade &= a_1w_1 + a_2w_2 + a_3w_3 + a_4w_4 + a_5w_5 + a_ew_e \
&= (68 × 0.1) + (80 × 0.1) + (56 × 0.1) + (75 × 0.1) + (77 × 0.1) + (73 × 0.5) \
&= 6.8 + 8 + 5.6 + 7.5 + 7.7 + 36.5 \
&=72.1
\end{aligned}\)

So your final grade in this case would be 72.1. You can translate this into your letter grade by looking up the thresholds on your module. For example, if an A was 80 percent or more, a B between 70 and 80 percent, a C was between 60 and 70 percent and so on, this grade would represent a B.

To work out what score you need to achieve a certain grade, you can re-arrange the equation we came up with before to give an equation for the score you'll need on your final. This is the original equation:

\(Final \; grade = a_1w_1 + a_2w_2 + a_3w_3 + a_4w_4 + a_5w_5 + a_ew_e\)

So you need to find a_e, which means we can subtract the first five terms from both sides to get:

\(a_ew_e = Final \; grade – a_1w_1 – a_2w_2 – a_3w_3 – a_4w_4 – a_5w_5\)

Now all we need to do is divide by the weighting for the exam to get:

\(a_e={ Final \; grade – a_1w_1 – a_2w_2 – a_3w_3 – a_4w_4 – a_5w_5 \above{1pt} w_e}\)

Insert the minimum for the grade you want where it says "final grade" (e.g. in the example, if you wanted an A you'd insert 80 here). Then add insert the other values and calculate. Using the example values:

\(\begin{aligned}
a_e&={ 80 – (68× 0.1) – (80× 0.1) – (56× 0.1) – (75× 0.1) – (77× 0.1)\above{1pt} 0.5} \
&={ 80 – 6.8 – 0.8 – 5.6 – 7.5 – 7.7\above{1pt} 0.5}\
&=88.8
\end{aligned}\)

So you'd need to get a score of 88.8 percent on the final to achieve an A overall. This might be quite a tall order, but it's possible!