Explanation
How grade percentages work
A score as a percent is points earned divided by points possible, times 100. When an assessment counts for part of a course, its contribution is that percent times its weight. Raw points, percentages and weights are different quantities, so the calculator keeps them apart.
p = e ÷ t × 100
| p | Score (%) |
|---|---|
| e | Points earned |
| t | Points possible |
40 out of 50 points
| Points earned | 40 |
|---|---|
| Points possible | 50 |
| Result | 80% |
p = e ÷ t × 100 = 40 ÷ 50 × 100 = 80%
c = p × w ÷ 100
| c | Contribution to the course grade |
|---|---|
| p | Score (%) |
| w | Weight in course (%) |
An 80% score worth 30% of the course
| Score | 80 |
|---|---|
| Weight in course | 30 |
| Result | 24 percentage points |
c = p × w ÷ 100 = 80 × 30 ÷ 100 = 24 percentage points
e = T × t ÷ 100
| e | Points earned |
|---|---|
| T | Target score (%) |
| t | Points possible |
An 80% target on a 50-point test
| Target score | 80 |
|---|---|
| Points possible | 50 |
| Result | 40 points |
e = T × t ÷ 100 = 80 × 50 ÷ 100 = 40 points
Diagram of this result
Under the answer, a bar splits the whole into its parts: points earned and missed, or what one weighted assessment adds to the course grade beside what it lost and what the rest of the course still decides.
The same numbers appear in the answer and the steps, so the diagram is never the only place to read them.
Common mistakes
40 out of 50 is 80%, not 40%. If that test is worth 30% of the course, it adds 24 percentage points, not 80. A weighted contribution is one piece of the course grade, not the course grade itself.
Assumptions and limits
Points earned may exceed points possible to represent extra credit; nothing is capped. Points possible must be above zero, and weight lies from 0 to 100%. Letter-grade cutoffs and rounding rules belong to your institution.
How do the worked examples fit together?
40 out of 50 is 80%. An 80% test worth 30% of the course adds 24 percentage points. An 80% target on a 50-point test means 40 points.
Sources
Percentage and weighted-average arithmetic as in OpenStax Prealgebra 2e, https://openstax.org/details/books/prealgebra-2e. Your institution’s handbook decides cutoffs, rounding and weighting policy; this calculator does not replace those policies.