CCalclabhub

Grades

How To Calculate A Weighted Grade

Most courses do not count every assignment equally. A weighted grade applies each category's share of the total before adding the scores up.

Quick Answer

course grade = score1 x weight1 + score2 x weight2 + ...

score
The percentage earned in a category
weight
That category's share of the course grade, as a decimal
grade
The weighted course grade
sum of weights
Must come to 1.00, or the division that follows corrects for it

Multiply each category score by its weight as a decimal and add the products. Scores of 85 on assignments worth 20 percent, 90 on quizzes worth 15 percent, 78 on the midterm worth 25 percent and 88 on the final worth 40 percent come to a course grade of 85.2, which is 0.04999999999999716 below the plain average of 85.25.

What Is A Weighted Grade?

A weighted grade is a course grade built from categories that count for different amounts. A final exam worth 40 percent of the course matters four times as much as a quiz category worth 10 percent, and a weighted calculation is what puts those shares into the arithmetic.

The method is to multiply each score by its weight and add the results. A 78 on a midterm worth 25 percent contributes 19.5 points to the total, while an 88 on a final worth 40 percent contributes 35.2. Adding all four contributions gives the course grade directly, with no further division needed when the weights add up to one.

The weights must sum to one hundred percent. If they do not, either the syllabus is missing a category or one weight has been copied down wrongly. Dividing by the actual sum is a useful safety net, but a total that is not one is worth investigating before trusting the answer, because the missing weight is often a participation or attendance component.

The difference between a weighted and an unweighted grade is where the weights sit relative to your strengths. Weighting pulls the result towards the categories that carry the most weight, so a strong final can lift a mediocre term and a weak final can sink a good one. In the default example the weighting moves the grade down by 0.04999999999999716 because the heaviest category, the final, is not the strongest.

Working backwards is the more useful direction. If you know your current standing, the weight of what remains and the grade you want, you can solve for the score needed on the remaining work. This is the same arithmetic rearranged, and it is what a final grade calculator does.

The number of categories does not matter. Two categories, four or ten all use the same procedure: multiply and add. What matters is that every score is on the same scale, normally a percentage of the marks available in that category, so that a 90 in a small quiz and a 90 in a large exam mean the same thing before weighting.

Points-based weighting is the main alternative and is worth recognising. Instead of percentages with weights, the instructor simply awards raw points: a 90 out of 100 on the final, a 45 out of 50 on the midterm, and the course grade is the total earned divided by the total available. That system produces a weighted grade without ever naming a weight.

Weighted grades interact with the grade scale. The course grade arrives as a percentage, the scale turns it into a letter, and the letter carries grade points into a GPA. A course grade of 85.2 and one of 85.25 can produce the same letter, so the precision of the weighting is often lost at the next step.

Dropped scores complicate the picture. Many courses drop the lowest quiz, which means the weights are redistributed across the remaining ones. Recomputing with the remaining categories and dividing by their actual weight total handles this correctly, and it is why a course grade rarely matches a hand calculation done without the drop.

Extra credit is the one case where the weights may not add to one by design. If an instructor allows a bonus category worth 5 percent, the total can exceed one hundred percent and the grade can exceed one hundred. That is intentional, and the normalising division should be skipped in that case.

Formula

grade = sum of (score x weight)

Multiply each category score by its weight and add the products. Valid when the weights add up to one.

SymbolMeaning
gCourse grade
sCategory score
wCategory weight

grade = sum of (score x weight) / sum of weights

Divide by the actual weight total so the result stays correct when the weights do not add to one, as happens after dropping a score.

SymbolMeaning
gCourse grade
sCategory score
wCategory weight

needed = (target - current) / remaining weight

The rearranged form used to work out what the remaining work has to score to reach a target grade.

SymbolMeaning
nScore needed
tTarget grade
cCurrent standing
w_rRemaining weight

How To Calculate A Weighted Grade

  1. 1

    List every category with its score and its weight

    Copy the weights from the syllabus rather than from memory, and check that they add up to 100 percent. Four categories weighted 20, 15, 25 and 40 give exactly 100, which means no division is needed at the end.

  2. 2

    Convert each weight to a decimal

    Twenty percent becomes 0.20 and forty percent becomes 0.40. Forgetting this step is the most common error, and it inflates the answer by a factor of a hundred while still looking like a plausible grade.

  3. 3

    Multiply each score by its weight

    Eighty five times 0.20 is 17, ninety times 0.15 is 13.5, seventy eight times 0.25 is 19.5, and eighty eight times 0.40 is 35.2. These contributions are the category's share of the final grade.

  4. 4

    Add the contributions

    17 plus 13.5 plus 19.5 plus 35.2 comes to 85.2, which is the course grade. If the weights added to something other than one, divide by their actual total at this point.

  5. 5

    Compare against the unweighted average

    The plain average of 85, 90, 78 and 88 is 85.25, so the weighting moved the grade down by 0.04999999999999716. The direction tells you whether the heavier categories are your stronger or weaker ones, which is the most useful thing the comparison reveals.

Examples

Example 1: Four categories with the final worth 40 percent

Assignments
85 at 20%
Quizzes
90 at 15%
Midterm
78 at 25%
Final
88 at 40%
StepCalculationResult
Assignments contribution85 x 0.2017
Quizzes contribution90 x 0.1513.5
Midterm contribution78 x 0.2519.5
Final contribution88 x 0.4035.2
Unweighted average(85 + 90 + 78 + 88) / 485.25
Course grade17 + 13.5 + 19.5 + 35.285.2

Result: Scores of 85, 90, 78 and 88 weighted 20, 15, 25 and 40 percent give a course grade of 85.2, which is below the unweighted average of 85.25 because the heaviest category is not the strongest one.

Example 2: Weights that pull in the opposite direction

Assignments
92 at 25%
Quizzes
88 at 15%
Midterm
79 at 20%
Final
85 at 40%
StepCalculationResult
Assignments contribution92 x 0.2523
Quizzes contribution88 x 0.1513.2
Midterm contribution79 x 0.2015.8
Final contribution85 x 0.4034
Course grade23 + 13.2 + 15.8 + 3486

Result: Scores of 92, 88, 79 and 85 with weights of 25, 15, 20 and 40 percent come to a course grade of 86, which happens to match the plain average of 86 exactly.

Example 3: A strong final rescuing a weak midterm

Assignments
70 at 30%
Quizzes
80 at 20%
Midterm
65 at 20%
Final
90 at 30%
StepCalculationResult
Assignments contribution70 x 0.3021
Quizzes contribution80 x 0.2016
Midterm contribution65 x 0.2013
Final contribution90 x 0.3027
Course grade21 + 16 + 13 + 2777

Result: A final score of 90 on a category worth 30 percent lifts the course grade to 77, which is 0.75 above the unweighted average of 76.25 because the strongest result carries real weight.

Calculator

Weighted course grade

85.2

Weighted points earned
85.2
Unweighted average for comparison
85.25
Lift from weighting
-0.05

Values update as you type. This calculator covers the single scenario its formula assumes — see Common Mistakes for what it leaves out.

Prefer a full-width tool? Open the A Weighted Grade calculator page.

Common Mistakes

  • Forgetting to convert percentages to decimals

    A weight of 20 must become 0.20 before it multiplies a score. Leaving it as 20 inflates the contribution twentyfold, and a course grade of 85.2 becomes 1704, which is at least obviously wrong rather than subtly wrong.

  • Weighting the average instead of the scores

    The weights apply to the category scores, not to the final average. Averaging the scores first and then applying weights gives a different and incorrect result, because the average has already discarded the information the weights need.

  • Not checking that the weights add up to 100 percent

    Weights that sum to 95 usually mean a category has been missed, often participation or attendance. Normalising by the actual total hides the problem, so it is better to track down the missing five percent before trusting the grade.

  • Ignoring a dropped score

    If the lowest quiz is dropped, the weights are redistributed across the remaining quizzes. Calculating with the original weights overstates the influence of the dropped category and produces a grade that will not match the official one.

  • Using the raw points instead of the category percentage

    A 45 out of 50 is 90 percent, and it is the 90 that gets weighted. Using 45 in the calculation mixes a points scale with a percentage scale and drags the course grade down sharply.

  • Normalising away genuine extra credit

    A course that allows a bonus category worth 5 percent is designed to let the total exceed 100 percent. Dividing by the weight total in that case removes the very bonus the category exists to provide.

FAQ

How do I calculate a weighted grade?

Multiply each category score by its weight as a decimal and add the products. Scores of 85, 90, 78 and 88 with weights of 0.20, 0.15, 0.25 and 0.40 give 17, 13.5, 19.5 and 35.2, which add up to a course grade of 85.2.

What if my weights do not add up to 100 percent?

Divide the total by the actual sum of the weights. That keeps the answer correct if a category has been dropped, but a total below 100 usually means a category is missing from your list, so it is worth checking the syllabus first.

Why is my weighted grade different from my average?

Because weighting pulls the result towards the categories that count for more. If your heaviest category is your weakest, the weighted grade lands below the plain average, as it does in the default example where 85.2 sits below 85.25.

How do I work out what I need on the final?

Subtract your current weighted points from the target grade and divide by the weight of the final. If you have 62 points so far and want 80 with a final worth 40 percent, you need 18 divided by 0.40, which is 45 percent.

Does a dropped score change the calculation?

Yes. Dropping the lowest score removes that category's score, so the remaining weights no longer add to 100 percent. Recalculate using only the counted categories and divide by their actual weight total.

Can a weighted grade be above 100 percent?

Only if the course includes extra credit. A bonus category worth 5 percent is designed to let the total exceed 100, and in that case you should not divide by the weight total, because that would cancel the bonus out.

References

  1. [1]Wikipedia, Weighted arithmetic mean — https://en.wikipedia.org/wiki/Weighted_arithmetic_mean
  2. [2]Wikipedia, Academic grading in the United States — https://en.wikipedia.org/wiki/Academic_grading_in_the_United_States
  3. [3]Wikipedia, Educational assessment — https://en.wikipedia.org/wiki/Educational_assessment
  4. [4]Wikipedia, Grading in education — https://en.wikipedia.org/wiki/Grading_in_education