State the completed and remaining weights
Coursework average is 78%, and it represents 80% of the course. The final exam supplies the other 20%. A desired course grade of 85% is the target. The completed contribution is 78 × 0.80 = 62.4 percentage points.
Solve the target equation
The exam must contribute 85 − 62.4 = 22.6 points. Dividing by its 0.20 share gives a required score of 113%. The target is above the full-mark bound for this model. Rounding or capping the result at 100 would falsely imply that full marks can reach 85%.
Compute the best full-mark result
At exam score 100, the final grade is 62.4 + 20 = 82.4%. At exam score 90, it is 62.4 + 18 = 80.4%. An 80% target requires (80 − 62.4)/0.20 = 88%. These forward checks explain how a different target changes the reverse answer.
| Exam score | Final course grade |
|---|---|
| 88% | 80% |
| 90% | 80.4% |
| 100% | 82.4% |
| 113% | 85% only if that exam score is permitted |
Quantify one exam-point change
Every additional exam percentage point raises the course result by 0.20 percentage point. A five-point improvement raises it by one course point. The exam has limited leverage because only one fifth of the course remains.
Review documented exceptions separately
If bonus marks permit 113%, the mathematical target may be feasible under that expanded policy. If the instructor curves the exam, the adjusted score may be the relevant input. Neither should be assumed just because the target result is inconvenient. Preserve the entered weights and compare any policy-adjusted scenario as a separate calculation.
Change the remaining weight without changing the current average
Keep the illustrative current average of 78% and target of 85%, but compare three hypothetical final-exam weights. With a 20% final, the required score is 113%, as in the baseline. With a 30% final, completed work contributes 78 × 0.70 = 54.6 points and the required exam score is (85 − 54.6)/0.30 = 101.333…. With a 40% final, the completed contribution is 46.8 and the required score becomes 95.5%. The target crosses the attainable boundary because more of the final course result remains open.
These weights are separate course policies, not choices the calculator makes on a student's behalf. Change a weight only when the actual syllabus or a documented revision permits it. A current average of 78 remains an average over the completed portion in each case; it is not already the weighted contribution. Entering 62.4 as the current grade in the 20% scenario would weight the completed share twice and produce a false requirement.
The maximum course grade provides an independent check: C(1 − w) + 100w. At weights 20%, 30% and 40%, the ceilings are 82.4%, 84.6% and 86.8%. Compare each ceiling with 85 before planning around the corresponding required score. For a 40% final, substituting 95.5 into the forward formula gives 46.8 + 38.2 = 85 exactly, so the inverse and forward calculations agree.
| Final weight | Required exam score | Course ceiling at 100% |
|---|---|---|
| 20% | 113% | 82.4% |
| 30% | 101.333…% | 84.6% |
| 40% | 95.5% | 86.8% |
Two independent records with feasible targets
For a second illustrative course, let completed work average 91%, the final represent 35%, and the target be 90%. Completed work contributes 91 × 0.65 = 59.15 course points. The remaining 30.85 points require 30.85/0.35 = 88.142857… on the final. A score of 89 gives 59.15 + 31.15 = 90.3%. A score of 88 gives 89.95%, which is below an exact 90% threshold even though some displays round it to 90.0. The calculator preserves the numerical distinction; the institution decides whether such display rounding changes a grade boundary.
For a third course, let current work average 61%, the final weight be 40%, and the target be 70%. The current contribution is 36.6 points, so the required exam score is (70 − 36.6)/0.40 = 83.5%. An exam score of 80 produces 68.6%; a score of 85 produces 70.6%. These forward scenarios bracket the target and make the reversed answer easier to verify than inspecting 83.5 alone.
An uncertainty of one percentage point in the first course's current average changes the required exam score by 0.65/0.35 = 1.857142… points in the opposite direction. If the gradebook's 91 is a rounded number rather than its exact average, that uncertainty can matter near a boundary. Retrieve the underlying coursework average or test the plausible range instead of treating a displayed whole number as exact. This is a sensitivity calculation, not a forecast of the exam score.
| Current average / final weight | Exam score | Course result |
|---|---|---|
| 91% / 35% | 88% | 89.95% |
| 91% / 35% | 89% | 90.3% |
| 61% / 40% | 80% | 68.6% |
| 61% / 40% | 85% | 70.6% |
Write down rounding, extra-credit and missing-work assumptions
Required scores above 100 are intentionally visible because they reveal a target outside the entered model. The forward final-grade form accepts ordinary scores from zero to 100, so a displayed requirement of 113 should not be pasted into that form as an ordinary exam score. If a documented extra-credit system permits more than 100, reproduce that exceptional policy separately rather than silently treating it as a standard score. The stated ceiling is conditional on the ordinary scale.
A required score below zero has the opposite interpretation: completed work already provides at least the target contribution, even if the remaining exam contributes zero. For example, current 95%, final weight 10% and target 80% give (80 − 85.5)/0.10 = −55%. Forward calculation at exam zero yields 85.5%. That arithmetic does not grant permission to skip an exam; a course may require participation or a minimum exam score independently of its weighted average.
Before relying on any target, reconcile ungraded work, dropped assessments and category normalization. A gradebook may currently exclude missing items while a syllabus calculation includes them as zeros. Save the assumptions and reproduce one forward score on paper. These examples check equations and thresholds only; they do not establish an instructor's grading policy, predict learning outcomes or guarantee a particular letter grade.
Questions and checks
Is 113% a calculator error?
It is the score required by the entered equation. Under a 100% cap the target is beyond the model’s bound.
Does 100% on the final produce 85% here?
No. It produces 82.4%.
How much does a five-point exam improvement help?
With a 20% exam share it adds one course percentage point.
Sources and scope
The examples are illustrative calculations, not records of individual users. Check the policy or measurements that apply to your situation.
Try the calculations
Required Grade Calculator
Solve for the remaining exam grade needed to reach a chosen overall grade. Treat the current grade as the average of the completed portion, not points already weighted across the entire course.
Open calculator →Final Grade Calculator
Project the overall course grade from completed coursework, a final exam score and its weight. Enter a known or hypothetical exam score; use Required Grade to solve backwards from a target.
Open calculator →