How to Calculate a Test Score Percentage

A test percentage is the reverse-looking formula that is actually the easy one: part divided by whole, times 100. The pain starts when a course has several wholes — a quiz out of 20, a paper out of 40, a final out of 100 — and each whole is a different share of the grade. This page does the single test first, then the weighted course, because skipping to the average is how a strong final gets diluted by a short quiz or, worse, the reverse.

One test

Percent = (points earned / points possible) × 100

42 out of 50. 42/50 = 0.84 = 84%.

18 out of 20. 90%. The 18 is not “18%.” It is 18 marks. The percent sign arrives only after the division.

7 out of 8. 87.5%. People round this to 88% in conversation. A syllabus that says “87.5 and above” cares about the half. Know the rounding rule before you round.

Bonus marks. If the teacher allows 55 out of 50, the ratio is 110%. That can be a legitimate score under that policy. It is not a reason to change the denominator to 55. The whole was 50; you exceeded it.

The X is what percent of Y tool is this calculation with X = earned and Y = possible. Zero possible marks is not a test. Do not divide by it.

Dropping a lowest score

Four quizzes, out of 10 each: 10, 8, 7, and 4. If the lowest is dropped, you average 10, 8, and 7.

• As percents those are 100, 80, and 70.
• Mean = 83.3%.
• If you forget to drop the 4, the mean of the four percents is 72.5%.

Dropping happens before the average, on the scores the policy names. If the quizzes were worth different points, convert each to a percent first or, more safely, add earned points and divide by possible points among the quizzes you keep. Those two methods match when every quiz has the same total. They do not match when one “quiz” is out of 30 and another out of 10 and you average the percents while thinking you averaged the points. Decide which policy is written down.

Weights

A course states:

• Homework: 20% of the grade, and you scored 90% on it
• Midterm: 30%, you scored 70%
• Final: 50%, you scored 80%

Course percent = 0.20 × 90 + 0.30 × 70 + 0.50 × 80

= 18 + 21 + 40 = 79%

The simple average of 90, 70, and 80 is 80%. One point, in this example, because the scores were not wildly different. Change the final to 50% and the homework to 100%:

Weighted = 0.20 × 100 + 0.30 × 70 + 0.50 × 50 = 20 + 21 + 25 = 66%

Unweighted mean of 100, 70, and 50 = 73.3%. Now the shortcut flatters you by 7 points, which is the difference between letter grades in plenty of scales. The final was half the course and it was the weak paper. An unweighted mean pretends the homework was a third of the course. The syllabus said a fifth.

Check that the weights sum to 1 (or 100%). A syllabus that lists 20, 30, and 40 has forgotten 10%. Do not quietly rescale unless the instructor tells you the remainder is unused. Ask.

Points hiding inside weights

Sometimes homework is “20 points of the course” and you scored 18 of those, the midterm is 30 points and you scored 21, the final is 50 and you scored 25. Then you do not need percents at all: 18 + 21 + 25 = 64 out of 100, which is 64%. I got 66 a moment ago with slightly different inputs; the method is the point. Adding raw marks works when the points available already are the weights. Averaging percents is what you do when each component was graded on its own scale and the syllabus supplies the weights separately. Using both methods on the same numbers without converting is double bookkeeping.

Curves and letter cuts

A curve that “adds 5%” might mean 5 percentage points (74 becomes 79) or 5% relative (74 × 1.05 = 77.7). Those are not equal. Percentage points versus percent change is the language to bring to that argument. A cut score (“70% is the pass”) is a threshold on the percent, not a percent change from last year’s class average. Being 2 points under a 70% cut is 68%, which is 2 percentage points short, and it is also about 2.9% relatively short of the cut (2/70). Only the points version tells you how many marks to find on a 100-point scale: 2 marks.

What you need on the next paper

Sometimes the useful question is forward, not backward. The course is 79% with the final still unwritten, and the final is 40% of the grade. The other 60% is already locked at 85%.

Course = 0.60 × 85 + 0.40 × final.

You want the course to reach 80.

0.60 × 85 = 51, so 51 + 0.40 × final = 80, and final = (80 − 51) / 0.40 = 72.5%.

A 70% on the final would leave the course at 51 + 28 = 79. You do not “need a 70 because the course is already about 80.” The weight decides. If you instead average the locked 85 with the final as if they were equal, you will study for the wrong target. Write the equation with the weights visible. The percentage calculator can compute 40% of a guessed final; it will not build the equation. That line is the homework.

When to use the calculator

Use it to convert an awkward fraction (83 out of 120 is 69.166…%) and to check a weighted sum you did in a notes app. Type each contribution as “weight percent of score” only if you are careful: 20% of 90 is 18, which is exactly the contribution in the first example, and then you must add contributions, not average them again.

Do not use a single “what percent is this of that” for a whole course unless you have already collapsed the course into one earned total and one possible total. The collapse is the actual work. The division at the end is the easy line. Zero points available is not a score you can percent; it is a missing assignment, and the syllabus says whether that missing work is a zero or a hole in the average. Those are different denominators. Read that sentence before you divide.