Explanation
How the final exam changes your grade
Your course grade is a weighted average of coursework and the final exam. Find the final score you need for a target, project the course grade from a final score, or find the coursework grade a target needs. Current grade means your average on everything except the final.
f = (T − c × (1 − w)) ÷ w
| f | Final exam score |
|---|---|
| T | Target grade |
| c | Current grade |
| w | Final exam weight, as a fraction (30% = 0.3) |
From 80% to 83% with a final worth 30%
| Current grade | 80 |
|---|---|
| Target grade | 83 |
| Final exam weight | 30 |
| Result | 90% |
f = (T − c × (1 − w)) ÷ w = (83 − 80 × (1 − 30%)) ÷ 30% = 90%
G = c × (1 − w) + f × w
| G | Course grade |
|---|---|
| c | Current grade |
| f | Final exam score |
| w | Final exam weight, as a fraction (30% = 0.3) |
80% coursework and a 90% final
| Current grade | 80 |
|---|---|
| Final exam score | 90 |
| Final exam weight | 30 |
| Result | 83% |
G = c × (1 − w) + f × w = 80 × (1 − 30%) + 90 × 30% = 83%
c = (T − f × w) ÷ (1 − w)
| c | Current grade |
|---|---|
| T | Target grade |
| f | Final exam score |
| w | Final exam weight, as a fraction (30% = 0.3) |
An 83% target after a 90% final
| Target grade | 83 |
|---|---|
| Final exam score | 90 |
| Final exam weight | 30 |
| Result | 80% |
c = (T − f × w) ÷ (1 − w) = (83 − 90 × 30%) ÷ (1 − 30%) = 80%
Diagram of this result
Under the answer, a percent scale marks the inputs and the result. The course grade is a weighted average, so it always sits between the coursework grade and the final exam score; the heavier the final, the closer it pulls.
The same numbers appear in the answer and the steps, so the diagram is never the only place to read them.
Common mistakes
Enter the final’s weight as a share of the whole course. Do not use a current grade that already counts the unwritten final as zero. A required score above 100% needs extra credit; a negative one means even a zero would reach the target.
Assumptions and limits
Grades and targets are zero or more and may exceed 100% for extra credit. Weight lies from 0 to 100%: above 0 to solve for the final, below 100 to solve for coursework. Results above 100 or below 0 are shown as they are, not clamped. No letter-grade, rounding or curve policy is assumed.
How do the worked examples fit together?
With coursework at 80% and a final worth 30%, a 90% exam gives 83% overall. To reach 83% you need 90% on the final, and with a 90% final, 83% needs 80% coursework.
Sources
Weighted-average arithmetic as in OpenStax Prealgebra 2e, https://openstax.org/details/books/prealgebra-2e. Your syllabus and institution decide weights, rounding and curves; this calculator does not replace those policies.