Grading scales differ slightly according to instructorsâ€™ preferences, and even department requirements, but students’ concerns usually boil down to “What do I need to get on the final exam in order to pass the course?â€ or, â€œWhat do I need to do to get a certain grade, overall?” Sometimes professors make optional exams or homework, and evaluating the consequences of doing them, or not, can be confusing.Â This page will demonstrate the general methodology of how to solve these conundrums.
How do I calculate my grades?Â
The simplest grading scheme is one that involves cumulative points. To find out where you are, just add up the points.
- A student has earned 76 points (of the 125 points available) on the homework, 102 (of the 200 points available) on the Midterm, and 35 (of the 75 points available) on the lab quizzes. The grading scale is as follows: A: 540 points, B: 480 points, C; 420 points, D 360 points. The final exam is worth 200 points. He isn’t worried about his grades so far, because he figures he can “pull it off” on the final exam. What is the highest course grade the student can get? What grade is he likely to get?
So far, he has scored 213 points of the 400 points so far awarded.Â As a grade, 213/400 is a 53% — not inspiring.
To get an overall A (90% or above), he would need an additional 540 (cumulative points) â€“ 213 (current points) = 327 points, but the Final is only worth 200 points. So he can’t get an A.
To get an overall B (80% or above), he would need an additional 480 (cumulative points) â€“ 213 (current points) = 263 points, which is also not possible.
To get an overall C (70% or above), he would need an additional 420 (cumulative points) â€“ 213 (current points) = 207 points. Numerically, this isn’t possible, but maybe his teacher would bump his grade if he got that “close”. (That is, if he got a perfect “200 of 200” on his Final, the teacher might bump his grade up to a C as a reward for having improved so much.)
To get an overall D (60% or above), he would need an additional 360 (cumulative points) â€“ 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 toÂ a score of 73.5% (get 147 Ã· 200 = 0.735 ) on the final exam. 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.
Numerically, this student could conceivably get a D, but more realistically, he’ll probably get an F. He should have done the work and paid more attentionâ€”or dropped the course back when he had a chance.Â His only option of improving this grade is negotiating extra credit or alternative assignments with the instructor.Â â€œPretty please with sugar on topâ€ and some tears might not hurt either.
This example shows why it’s important to invest a lot of effort early on in the course, while your mind is still fresh and your enthusiasm is high. In all my years of learning and teaching, I’ve never yet seen a student “pull it off” on the final exam, but I’ve seen many flunk trying and come to me confused and complaining afterwards. Don’t wait until the end; learn the material up front and on time and youâ€™ll get the grade you worked for.
A point-based grading scheme might have the course grade given in terms of percentages, but the computations will mostly be the same.
- Penelope has earned 112 points (of 125 points available) on the homework, 196 points (of 200 points available) on the midterm exam, and 68 points (of 75 points available) on the lab quizzes. The course grade is out of 600 points, with the final exam being worth 200 points. The student obviously wants an A, andÂ the grading scale is as follows: A: 91%, B: 82%, C: 73%, D: 64%. Can she get an A in the course? If so, what does she need to get on the Final? If not, what is the highest grade she could get?
So far, she has scored 376 points of the 400 points so far awarded.Â As a grade, 376/400 is a 94% — on track for an A average overall
To get an A overall, she needs 91% of the 600 total course points, or 546 points. That is, she needs an additional 546 (cumulative points) â€“ 376 (current points) = 170 points. Since the final exam is worth 200 points, she needs to score an Â 85% (170 Ã· 200 = 0.85) on the final exam.
Since she has already scored 90% on the homework, 98% on the midterm exam, and 91% on the lab 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 exam to get the grade she’s hoping for. Even if she has a “brain fart” on the final exam or shows up 30 minutes late to it, she shouldn’t do worse than a B overall.Â Â Â Copyright Â© Elizabeth Stapel 2004-2011 All Rights Reserved
Penelope can easily get an A in the course, but even if she has trouble on the final exam, she shouldn’t get lower than a B.Â Hopefully she can keep her head in the books and out of the clouds as the time draws near to hunker down for finals.
The two grading schemes above are pretty easy and similar to compute. To find out how you’re doing in any grade component’s subscore (for instance, homework, or quizzes), you just divide the points you’ve earned by the potential points that could have been awarded so far to get your score or percentage.
To find out what you need to score on the final exam,
- Add up the points you’ve earned so far in each grade component
- Subtract this from the number of points necessary for the grade you’re wanting to get overall
- Divide the result by the number of points on the final exam
This will give you Â 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.
How do I calculate my weighted grades?Â
Another basic type of grading scheme is a weighted program, where the course grade is divided into component parts, each part being worth some percentage of the total grade. The easiest way I’ve found to deal with this is to convert the grade components into points, and then work from there.
- Returning student Stella has worked hard on her homework (even swallowing her pride and asking her high-school son for help), and has at least attempted all of the extra credit points available. She has earned 356 points (of the 413 points available) on the homework, earned 172 quiz points (of 200 points available), and got 91%, 81%, 79%, and 84%, respectively, on the four tests. She got 13 points on the extra credit project, which will be added to her homework score.
The homework is 30% of her grade, the quizzes are 10%, each of the tests is 10% (40% total), and the final exam is 20%. She is hoping for a B in the course (on a standard ten-point scale). Can she get what she’s hoping for?
First, I’ll add the extra-credit-project points into her homework grade, so she has 356 (current points earned) + 13 (extra credit points earned) = 369 of the 413 possible homework points.
The next step is to convert the subscore percentages into points out of 100. If the homework is worth 30% of her grade, and if I regard her grade as being out of 100 points (with “100% in the course” being “100 grade points”), then homework is worth 30 points of her grade. The quizzes are 10 points, each of the tests is 10 points (for a total of 40 points), and the final exam is 20 points.
To find Stellaâ€™s subscore percentages for each grade component (homework, quizzes, etc.), I’ll divide the points that she’s earned by the points that are available. To find out how many grade points she has so far, I’ll then multiply each subscores’ grade-points by the percentage she earned in that grade component. Putting it neatly into a table, I get the following:
Stella wants an A in the course, which means she has to get a 91%, or 91 grade points of 100. She has 68.89 grade points earned, so she needs another 22.11 points. But the final exam is worth only 20 points, so she can’t get an A.
For a B, Stella needs 82 grade points of 100. This means she needs 82 (total points needed) â€“ 68.89 (already earned) = 13.11 more grade points, which means she needs 13.11 (points earned) Ã· 20 (final exam point weight) = 66% on the Final. Since she’s done way better than a 66% on every other part of the course, she shouldn’t have any trouble getting a B.
It isn’t numerically possible to get an A, but Stella should easily be able to get a B.Â Her previous good scores and attempts at extra credit might even be enough to help sway her instructor to â€œround upâ€ any discretionary points.
Sometimes the computations may be thrown off a bit by the instructorâ€™s ability to â€œdropâ€ scores. This gives students a chance to wipe out any major low marks from their record, which may be pulling down their cumulative average.Â For instance, I took a chemistry course where we were allowed to drop one of our test scores; heck, we didn’t even have to show up for that test, if we didn’t feel like it (and I didn’t). If the scores were averaged together as 100 + 100 + 100 + 0, my average would have been a 75%, misleading considering my previous perfect test scores.Â â€œDroppingâ€ a low score, means that the 0 score is wiped off the slate and my 100% average remains representative of my success in the class.Â Computing the grade in such a situation is just like the previous examples, except that each student will probably be â€œthrowing outâ€ different scores. If your class hasÂ a grading scheme like this, you should definitely keep all of your papers, so you have proof of your scores.
- In a certain course, the quizzes are 15% of the grade, the lab score is 25%, the tests are 30%, and the final exam is 30%. Students are allowed to drop the two lowest quiz scores and the one lowest test score. This gives students 3 total chances to miss class, study the wrong material, or try taking a test hungover (for the first and last time).Â Course grades are on a standard ten-point scale: 90% or more is an A, 80% or more is a B, and so forth.
Miguel has worked very hard in this class, but was hospitalized for a while near the beginning of the semester (weâ€™re going to give him the benefit of the doubt and assume keg stands were not involved), so he’s glad he can drop some of those lower scores. His sixteen quiz scores are 10, 10, 9, 6, [absent], 9, 8, 10, 7, 10, 10, 9, 9, 10, 8, and 9. His four test scores are 92, 73, 89, and 94. He was a butterfingers in the lab (don’t even ask how many crucibles and pipettes he broke), so he earned only 71% for his lab grade.
To get a scholarship next near, he really needs an A in this course. Can he do it?
Since the quiz component of the grade is the sum of the fourteen highest scores on the 10-point quizzes, the quiz component is out of 140 points. Dropping his 6 and the zero for when he was absent, Miguel’s quiz total is 128.
Since the test component is based on three tests, I can view this as being out of 300 points. Dropping the 73, his test total is 275.Â Â Â Copyright Â© Elizabeth Stapel 2004-2011 All Rights Reserved
Now I’ll make a table, just like in the previous example:
Â |
component |
component |
Â component |
grade |
grade |
quizzes |
128 |
140 |
0.914 |
15 |
13.71 |
tests |
275 |
300 |
0.917 |
30 |
27.51 |
labs |
— |
— |
0.71 |
25 |
17.75 |
total |
— |
— |
— |
70 |
58.97 |
So far, Miguel is running a 58.97 (grade points earned) Ã· 70 (grade points available) = 84% in the course. To get an A overall, he needs 90% overall, which means he needs to do really well on the Final. How well?
To get 90 grade-points in the course, he’ll need 90 (points available) â€“ 58.97 (points earned) = 31.03 points on the Final. But the Final is worth only 30 grade-points– It is numerically impossible for him to get an A.
However, to get a B, he’ll need only 80 (points available) â€“ 58.97 (points earned) = 21.03 points on the final exam, or 21.03 (points needed) Ã· 30 (final exam point weight) = 70.1%. Since he’s done better than 70% on everything (outside of the time he was sick), he should have no trouble getting a B.
It is numerically impossible for Miguel to get an A, but he can easily get a B.
For the scholarship, it might help if he got a letter from his doctor regarding his illness and a testimonial from his instructor or his lab TA regarding his good performance once he got out of the hospital, and include these with his application. He shouldn’t give up on the scholarship just because of his illness, because he really did do quite well the rest of the time.
Good luck Miguel.Â Letâ€™s make everyoneâ€™s lives easier and stay out of the hospital next semester, OK?
Different grading schemes will have different details, and there are probably innumerous ways to design a syllabus, so the above examples can’t possibly cover every situation. But if you can understand the basic methodology of the examples, you should be able to figure out what you need on the final exam, or any other parts of your course, for nearly any class you take.Â
Bottom line: go to class, do your coursework, and study for exams.Â If in doubt, use the grade calculator to fill in the blanks and unfurrow your browâ€”youâ€™re too young for wrinkles. Â Â
Best of luck, and may the grades be ever in your favor!