Semester Grade Calculator

semester grade = (coursework × weight + midterm × weight + final × weight) ÷ (weight + weight + weight); each part's contribution = (its score × its weight) ÷ the same weight total

coursework score

The mark for the work done through the term — assignments, quizzes, labs — as a percentage. It has no upper bound, so a course that awards bonus marks can put this above 100

midterm score

The midterm examination's percentage, on the same footing as the other two. Which of the three a school counts as coursework and which as a midterm is a matter for the syllabus, not for this page

final exam score

The final's percentage. When the final has not been sat yet, this is a number you are supposing rather than one you have — which is exactly how people use the page before the last week of term

weights

Each part's share of the grade, entered as a percentage of the whole course. They do not have to add up to 100: the page normalises by their total, so 30/30/30 gives the same grade as 100/100/100 and the total row prints 90 so you can see what you typed

contribution

A part's score times its weight, divided by the same weight total the grade uses. Result: the three contributions add up to the semester grade exactly. In the default case 26.40 + 24.60 + 36.00 = 87.00

Use this page at the point where you want to know what a semester is heading for, or which part of it is doing the damage. The three contribution rows answer the second question directly: with the final weighted at 60%, a midterm mark barely shows up in the total, and the same grade can come from very different splits. It is also the page to use for a hypothetical final — type a score you have not earned yet and the grade updates. If the mark is not yet known and you want to know what it has to be, the final grade calculator solves backwards for it; that page shares this one's final exam weight.

1. 88, 82 and 90 at 30/30/40: 87.00%

   1. Weighted marks: 88 × 30 = 2640, 82 × 30 = 2460, 90 × 40 = 3600
   2. Weight total: 30 + 30 + 40 = 100
   3. Semester grade: (2640 + 2460 + 3600) ÷ 100 = 8700 ÷ 100 = 87%
   4. Contributions: 2640 ÷ 100 = 26.4, 2460 ÷ 100 = 24.6, 3600 ÷ 100 = 36
   5. Check: 26.40 + 24.60 + 36.00 = 87.00, the same as the grade

   The three rows are not decoration — they rebuild the answer. The final contributes 36 of the 87 points even though it counts for 40% of the grade, because 90% of a 40% share is 36. That is the reading the page is built for: the biggest contributor is not necessarily the most heavily weighted part, and here the coursework with the highest mark at the lowest weight is the smallest of the three.

2. Weights that total 90 instead of 100: 86.67%

   1. Weighted marks: 2640, 2460 and 2700, adding to 7800
   2. Weight total: 30 + 30 + 30 = 90, not 100
   3. Semester grade: 7800 ÷ 90 = 86.6667, printed as 86.67
   4. Contributions: 2640 ÷ 90 = 29.33, 2460 ÷ 90 = 27.33, 2700 ÷ 90 = 30
   5. Check: 29.33 + 27.33 + 30.00 = 86.67

   The three weights are equal here, so the grade is the plain average of 88, 82 and 90. It is also the case that proves the division is by the weight total rather than by 100 — dividing 7800 by 100 would give 78, and refusing the input because the weights do not sum to 100 would give nothing at all. The total row prints 90 so that a mistyped weight is visible rather than silently absorbed.

3. A final worth 60% and sat badly: 73.40%

   1. Weighted marks: 95 × 20 = 1900, 92 × 20 = 1840, 60 × 60 = 3600
   2. Weight total: 20 + 20 + 60 = 100
   3. Semester grade: (1900 + 1840 + 3600) ÷ 100 = 7340 ÷ 100 = 73.4%
   4. Contributions: 19, 18.4 and 36 — the final alone is worth more than the other two together

   A 95 and a 92 in the term, and the grade still lands at 73.4, because the final is worth three times either of them and it went badly. The contribution rows show why in one line: 36 out of 73.4 comes from the exam. Running the same three scores with the final at 20% instead puts the grade above 87, which is the whole argument for reading a syllabus's weights before the term rather than after it.

Only three parts exist here — coursework, a midterm and a final — so a course with two midterms, several projects or a separate participation mark cannot be reproduced exactly. For a course like that, use the grade calculator, which takes as many rows as you need; this page trades that freedom for naming the parts. The weights are each capped at 100% because they are shares of one course, but their total is not required to be 100: a total other than 100 is normalised, and the row that prints it is what tells you the weights are not what you expected. Scores have no upper bound, so bonus marks can push the semester grade above 100. Nothing here knows the score distribution, the grading policy or whether the final has been sat, and it does not turn the percentage into a letter grade — the test grade calculator does that with your own cutoffs.

How do I calculate my semester grade?

Multiply each part's score by its weight, add the three products, and divide by the total of the weights. With 88, 82 and 90 at 30/30/40 that is (2640 + 2460 + 3600) ÷ 100 = 87%. The page also shows what each part contributed — 26.4, 24.6 and 36 — and those three add back up to 87% exactly, so the arithmetic can be checked from the panel alone.

What if my school's weights add up to something other than 100?

It still works: the page divides by whatever the weights total rather than by 100. Weights of 30/30/30 give a total of 90 and a grade of 86.67%, which is the plain average of the three scores — the same answer 100/100/100 would give. The total row prints 90, so a weight typed in wrongly shows up instead of being quietly absorbed by the normalisation.

Why does a heavily weighted final matter so much?

Because the weight multiplies the score before anything is averaged. A 60% final at a mark of 60 contributes 36 points to a grade that comes out at 73.4 even when the term marks are 95 and 92 — more than the other two parts together. Running the same three scores with the final at 20% instead puts the grade above 87. The contribution rows exist to make that difference visible before the exam rather than after it.

Can the semester grade come out above 100?

Yes, if a part scores above 100. The three score fields have no upper bound, so bonus marks carry through the weighted average and a grade of 101.5% is a legitimate output rather than an error. The page does not clamp it, for the same reason the weights are not required to sum to 100: the arithmetic is the definition, and editing the inputs to fit a range would hide what actually happened.

What is the difference between this page and the grade calculator?

Freedom against names. The grade calculator takes two free lists — as many items as you like, with the weights typed in as you go — which is what a course with five assignments and two midterms needs. This page fixes the three parts that most syllabuses have and names them, which pays for itself in the contribution rows: knowing that the exam is 36 of your 73.4 is not something a general list of items gives you. Both compute the same weighted mean.

• Measures of Location — e-Handbook of Statistical Methods, section 1.3.5.1 (the weighted arithmetic mean and the role of the weights; the semester grade here is that mean, and the contribution rows are its individual terms) — National Institute of Standards and Technology (NIST)
• Measures of the Center of the Data — Introductory Statistics 2e, section 2.5 (the mean as the balance point of a set of values, and how a single value moves it — the behaviour the weight column controls) — OpenStax, Rice University
• GB/T 3358.1-2009, Statistics — Vocabulary and symbols, Part 1 (the Chinese national vocabulary standard for general statistical terms, including the weighted arithmetic mean; its record page notes that no online full text is offered) — State Administration for Market Regulation, China