Working backwards to the grade you need
Most grade arithmetic runs forwards: you have the scores, you want the total. This one runs backwards. You have a target, you know what the last assessment is worth, and you want to know what you have to get on it.
It is one rearrangement of one equation, and the only real difficulty is being honest about the answer when it comes out impossible.
The forward version first
If the final is worth a fraction w of the grade, everything before it is worth 1 − w. So:
final grade = current × (1 − w) + final score × w
A current standing of 82 with a final worth 30% of the grade, if you score 92 on that final: 82 × 0.70 + 92 × 0.30 = 57.4 + 27.6 = 85.
Rearranged
Set the left side to the target you want and solve for the final score:
needed = (target − current × (1 − w)) ÷ w
In words: work out what your existing work already contributes, subtract that from the target to get the shortfall, then divide the shortfall by the final's weight. Dividing by the weight is the whole reason a small final needs a big score — a final worth 30% has to cover the shortfall three and a third times over.
A worked example
Current standing 82, final worth 30%. What is already banked: 82 × 0.70 = 57.4. That figure does not change, whatever happens on the final.
Now try three targets against it.
- Target 80:
(80 − 57.4) ÷ 0.30 = 22.6 ÷ 0.30 = 75.33. Comfortable. - Target 85:
(85 − 57.4) ÷ 0.30 = 27.6 ÷ 0.30 = 92. Demanding but possible — and it checks out against the forward calculation above, which landed on exactly 85. - Target 90:
(90 − 57.4) ÷ 0.30 = 32.6 ÷ 0.30 = 108.67. Not possible.
Notice how fast the required score climbs: five points of target cost roughly seventeen points of final score, because every point of target has to be paid for out of 30% of the grade.
When the answer is above 100
A required score of 108.67 is not a number to act on. It is a statement that the target is out of reach from where you stand: even a perfect final leaves you short. A tool that prints "108.67%" and stops has technically answered and practically misled.
The useful response is to say the target is unreachable and let you reset it. Work out the ceiling instead — what a perfect final would actually give you. With 57.4 banked and a 30% final: 57.4 + 100 × 0.30 = 87.4. That is the best available outcome, and it is a far more actionable number than 108.67.
And when it comes out negative
The mirror case. A current standing of 95 with a final worth 20%, targeting 75: banked is 95 × 0.80 = 76, so (75 − 76) ÷ 0.20 = −5.
A negative requirement means the target is already secured. Scoring zero on the final still leaves you at 76, which clears 75. Worth knowing, though it is rarely the situation anyone is checking.
Two things that will make the answer wrong
- A current standing that does not cover the rest of the grade. The formula assumes your current figure is the weighted average of everything except the final, covering the full remaining
1 − w. If there is other work still outstanding, or if the current figure is only an average of what has been marked so far rather than of everything due, the sum is measuring something else. - A final weight of zero. The formula divides by the weight, so there is no answer. Which is correct in substance: if the final counts for nothing, no score on it can change your grade.
And the arithmetic cannot see the rules. Attendance requirements, a minimum you must score on the exam itself regardless of the total, rounding conventions at the grade boundaries — those live in the course documentation, not in the formula, and they can overturn its answer.
Doing it without the paper
The free Final Grade Needed tool takes your current percentage, the final's weight as a percentage and your target, and returns the score you need — in your browser, keeping nothing. It also reports whether the target is reachable rather than leaving you to notice: over 100% it says so plainly, and a negative requirement is reported as already achieved. That second output is the one worth reading first.