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Grades and averages

Weighted grade calculator

Work out your weighted average from percentage scores and see what you need on the next test or the final to reach your goal.

Your scores

Weights are relative: use the percentages from your syllabus (homework 20, midterm 30…) or simple numbers (1, 2, 3).

Weighted average

84.42%

3 scores · total weight 60

On a common 90/80/70/60 scale that’s B. Your school or instructor may use a different scale - check the syllabus.

What do I need on the next one?

With weight 40, you need at least 85.9% on the next assessment.

How is a weighted average calculated?

Multiply each score by its weight, add the results up and divide by the sum of the weights:

xˉ=s1w1+s2w2+⋯+snwnw1+w2+⋯+wn\bar{x} = \frac{s_1 w_1 + s_2 w_2 + \dots + s_n w_n}{w_1 + w_2 + \dots + w_n}

where sis_i are your scores and wiw_i their weights. For example, 92% on homework (weight 20), 78% on the midterm (weight 25) and 85% on quizzes (weight 15) give 92⋅20+78⋅25+85⋅1520+25+15=506560≈84.42%\frac{92 \cdot 20 + 78 \cdot 25 + 85 \cdot 15}{20 + 25 + 15} = \frac{5065}{60} \approx 84.42\%.

Which weights should I use?

The ones from your syllabus. Courses usually list each part as a share of the final grade - homework 20%, midterm 25%, final exam 40% - so you can type those numbers straight in. Only the proportions matter: weights 20, 25 and 15 give the same average as 4, 5 and 3.

What do I need on the final?

Pick your goal and enter the weight of the next assessment. The calculator finds the lowest score that brings your weighted average up to the goal:

snext=goal⋅(W+w)−∑siwiws_{\text{next}} = \frac{\text{goal} \cdot (W + w) - \sum s_i w_i}{w}

where WW is the total weight so far and ww is the weight of the next assessment. In the example above, reaching 85% with a final worth 40 takes at least 85.9% on the final.

Letter grades

Many schools use a 90/80/70/60 scale:

Average Letter grade
90% and up A
80–89.99% B
70–79.99% C
60–69.99% D
below 60% F

Your instructor may use plus and minus grades or a different scale, so treat the letter as a guide. The syllabus has the final word.

Sources

We checked the facts on this page against these sources. All of them may be reused freely: they carry an open licence or are not covered by copyright.

  1. OpenIntro - Online supplement: Weighted mean (the formula; a simple mean is a weighted mean with equal weights) · CC BY-SA 3.0
  2. Wikibooks - Primary Mathematics: Average, median, and mode (weighted average of test results) · CC BY-SA 4.0
  3. Apereo Foundation, Sakai Community Documentation - How do I set up a Gradebook with categories and weighting? (course parts as a percentage of the final grade) · CC BY 4.0
  4. U.S. Department of Education, International Affairs Office (2008) - Structure of the U.S. Education System: U.S. Grading Systems (90/80/70/60 scale, plus and minus grades, no national grading scheme; archived copy) · public domain
  5. The Florida Statutes, section 1003.437 - Middle and high school grading system (A 90–100%, B 80–89%, C 70–79%, D 60–69%, F below 60%) · official document
  6. Wikipedia - Weighted arithmetic mean · CC BY-SA 4.0
  7. Wikipedia - Academic grading in the United States · CC BY-SA 4.0

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