Calculating a Course Grade
Purplemath
In your course syllabus, your instructor will have included a listing of course components (such as homework and quizzes) and how many points they're worth. This information can be used to determine what is your current grade in a class, at a particular point in time, such as right after the mid-term.
Different grading scales work in slightly different ways, but the typical student's concern regarding grading status usually boil down to "What do I need to get on the Final in order to pass the course, or to get a certain grade overall?" (That was always *my* concern, anyway.)
This page will demonstrate the general methodology of how to answer this question.
The simplest grading scheme is one that involves cumulative points.
How do I calculate my grade, when it's cumulative points?
When the grading scheme boils down to "the entire course is worth [some number of points]" and all points are equal, then, to find out how many points you need on the Final:
- Add up all the points that you have earned so far (that is, exclusive of the upcoming exam).
- Determine how many points, out of the total for the course, are from components of the total grade; that is, find how many points were available for everything before the Final.
- Divide the number from (2) by the number from (1). This gives you your current numerical grade as a decimal.
- Convert the decimal to a percentage to find where you stand, at this present time.
- To figure out how many points you need on the Final to get a certain grade, find the number of the total points available that represent the grade that you're wanting.
- Subtract the number from (1) from the number from (5). This tells you the number of points you need on the Final for the grade that you've picked.
- Compare the number from (6) to the points available on the Final. Interpret the results.
Let's see how this works in action.
- A student has earned 76 points (of the 125 points available) on the homework, 102 of 200 points on the Midterm, and 35 of 75 on the lab quizzes. The grading scale is as follows: A: 540 points, B: 480 points, C; 420 points, D 360 points. The Final is worth 200 points. He isn't worried about his grades so far, because he figures he can "pull it out" on the Final. (a) What is his current grade in the class? (b) What is the highest course grade the student can get? (c) What grade is he likely to get?
So far, he has 76 + 102 + 35 = 213 points.
The course, so far, is worth 400 points.
At this point, then, he has a percentage grade of 213 ÷ 400, or 0.5325, which is 53.25%. So, not great
The entire course is worth 600 points.
The minimum number of points for each grade is listed in the syllabus (so I don't have to do the computations myself).
To get an A, he would need an additional 540 − 213 = 327 points, but the Final is only worth 200 points. So he can't get an A.
To get a B, he would need an additional 480 − 213 = 263 points, which is also not possible.
To get a C, he would need an additional 420 − 213 = 207 points. Numerically, this isn't possible, but maybe his teacher would bump his grade if he got that close to the cut-off. (In other words, if he got a perfect score on his Final, the teacher might bump his grade up to a C as a reward for having improved so much.)
To get a D, he would need an additional 360 − 213 = 147 points. The Final has 200 points, so it is numerically possible for him to get a D.
However, to get the D overall, he would need to get 147 ÷ 200 = 0.735 = 73.5% on the Final. Looking at the points he's earned so far out of the points possible, he's only gotten 60.8% on his homework, 51% on his Midterm, and 46.7% on his quizzes. It is highly unlikely that he will raise his performance up to a 73.5% on the Final.
(a) His grade, before the Final, is 53.25%.
(b) Numerically, this student could conceivably get a D
(c) Realistically, he'll probably get an F in the course.
This example shows why it's important to invest a lot of effort early on in the course, while your mind is still fresh. In all my years of teaching, I've never yet seen a student "pull it out" on the Final, but I've seen many flunk trying. Don't wait until the end; learn the material up front and on time. Start asking for help as soon as you find yourself in difficulty.
A point-based grading scheme might have the course grade given in terms of percentages, but the computations will mostly be the same.
- A student has earned 112 points (of 125 points available) on the homework, 196 of 200 on the Midterm, and 68 of 75 on the lab quizzes. The course grade is out of 600 points, with the Final being worth 200 points. She wants an A, and the grading scale is as follows: A: 91%, B: 82%, C: 73%, D: 64%.
(a) What is her current grade in the class?
(b) Can she get an A in the course?
(c) If so, what does she need to get on the Final? If not, what is the highest grade she could get?
She has so far earned 112 + 196 + 68 = 376 points.
So far, 400 points are available.
Doing the division of 376 by 400, I see that she so far is running a 94% in the course.
The entire course is worth 600 points.
To get an A overall, she needs 91% of the 600 total course points, or 546 points. That is, she needs an additional 546 − 376 = 170 points to get an A in the course. Since the Final is worth 200 points, she needs to get 170 ÷ 200 = 0.85 = 85% on the Final.
Since she has 112 ÷ 125 = 90% on the homework, 196 ÷ 200 = 98% on the Midterm, and 68 ÷ 75 = 91% on the quizzes, she should be able to get an A in the course. That is, given her past performance, it is reasonable to expect that she can do sufficiently well on the Final to get the grade she's hoping for. And even if she has a brain fart on the Final, she shouldn't do worse than a B overall.
(a) Currently, she has a 94% in the class.
(b) She can get an A in the course.
(c) She only needs an 85% on the Final to get an A in the course.
- In a class worth 1,000 points in total, Bryce has earned 182 points (of 200 possible) on his homework, 124 points (of 200) on his essay, 79 points (of 100) on his quizzes, and 69, 72, and 81 points (of 100 points each) on the tests. He would like to get a B in the class.
(a) What is his current grade in the class?
(b) Can he get a B in the course?
(c) What grade would you expect him to get for the course? (Include your reasoning.)
Bryce's current point total is:
182 + 124 + 79 + 69 + 72 + 81 = 607
Before the Final, 800 points are available.
Therefore, his current grade in the class is 607 ÷ 800 = 0.75875, or 75.857%. He currently has a C in the class.
The entire course is worth 1000 points, of which 800 points come from before tjhe Final exam. He so far has 607 of these 800 points.
To get a B in the course, Bryce needs at least 80% of the 1,000 points; in other words, he needs 800 points overall. Given the points that he has already earned, he needs an additional 800 − 607 = 193 points on the Final for a B in the class.
The Final is worth 200 points, and he would need 193 of them to get a B. This means that he needs to get 193 ÷ 200, or 96.5%, on the Final in order to get a B overall. But his performance thus far has been in the mid-C's range. In other words, technically (that is, in terms only of the arithmetic), Bryce could get the B, but it seems unlikely, given his previous performance.
To get a C in the course, Bryce needs a 70% overall; this means that he needs 700 points in the class. He has 607 points, so he would need 700 − 607 = 93 points on the Final for a C. This would be 93 ÷ 200, or 46.5%. This is quite reasonable, given his past performance.
(a) Currently, Bryce's grade in the class is 75.857%, which is a C.
(b) Technically, Bryce can get a B in the class.
(c) Because Bryce has been consistently a C student, getting a high A on the Final seems unlikely. On the other hand, Bryce should easily be able to get more than 46.5% on the Final, which would give him a C for the overall course.
The grading schemes above are pretty easy to compute. To find out how you're doing in any grade component's subscore (for homework, for instance, or for the quizzes), you just divide the points you've earned by the points that have so far been available to be awarded in order to get your percentage on that subscore.
To find out what you need on the Final, you add up the points you've earned so far in each grade component. You subtract this from the number of points necessary for the grade you're wanting to get overall. Then divide the result by the number of points on the Final, to get the percentage grade you need on the Final.
And you can evaluate how reasonable that Final percentage grade is by comparing it with your subscore percentages.
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