The formula, rearranged for the unknown
Your overall grade is a weighted average of your current average and your final exam score: Overall = currentAverage × (1 − finalWeight) + finalScore × finalWeight. To find the final score needed for a specific desired overall grade, solve for finalScore: finalScore = (desiredOverall − currentAverage × (1 − finalWeight)) ÷ finalWeight.
A worked example — an achievable target
With a current average of 72%, a final exam worth 30% of the overall grade, and a target overall of 80%: neededFinalScore = (80 − 72×0.70) ÷ 0.30 = (80 − 50.4) ÷ 0.30 ≈ 98.67%. That's a demanding but reachable score — it tells you exactly how much margin for error you have (in this case, almost none) going into the final.
A worked example — an unreachable target
With a current average of 60%, a final worth only 20% of the overall grade, and a target overall of 95%: neededFinalScore = (95 − 60×0.80) ÷ 0.20 = (95 − 48) ÷ 0.20 = 235% — a result well above the maximum possible 100%. This means the target isn't reachable at all with this current average and final weight, no matter how the final exam goes; a needed score over 100% (or under 0%, if the target is already guaranteed) is the formula's way of telling you the target is out of reach or already secured.
Why the final exam's weight matters as much as your current average
A low-weight final (say 10-15% of the overall grade) can only move your overall grade a little, no matter how well or poorly you do on it — which is exactly why the second example's target was unreachable despite a two-thirds gap between current average and target. A high-weight final (40%+) gives you much more room to change your outcome in either direction. Always check your course's actual final-exam weighting before assuming a strong final can rescue a weak current average, or that a weak final can't hurt a strong one.
Using this before the exam, not after
This calculation is most useful done before the final, while you can still adjust your study effort based on the result — a comfortably achievable needed score suggests your current preparation is likely sufficient, while a needed score near or above 100% signals you should either study substantially harder or recalibrate your target grade expectations.