Test Grade Calculator

percentage = points earned ÷ points possible × 100; letter = the highest cutoff the percentage reaches (F below the lowest); points to the next letter = (next cutoff − percentage) × points possible ÷ 100

pointsEarned

What the paper came back with. There is no ceiling on it: a 50-point test that offers five points of extra credit really can score 55, and the page prints 110% rather than refusing the input

pointsPossible

What the test was out of, so 50 for a fifty-point paper. It has to be greater than zero, since the percentage is points earned divided by this number — with zero there is no share to take

cutoffs

The four percentages your syllabus or school uses for A, B, C and D. They are inputs rather than constants because there is no authoritative set: 90/80/70/60 and 93/85/75/65 are both in use, and this page does not know which one is in front of you

letter

The highest cutoff the score reaches, or F if it reaches none of them. A score sitting exactly on a line takes that letter, so 18 out of 20 with an A line at 90% is an A rather than a B

points above the cutoff

The score minus what your own letter's cutoff works out to in points — 43 against a B line of 40 gives 3, in points rather than in percent, because points are the unit written on the paper. F is the exception: it is worth no cutoff of its own, so the row reads the score itself

Use this calculator right after a test comes back, when the question is what the letter is under your school's lines and how much room there was. The two point rows answer the question a percentage cannot: whether the 3 points above the B line were comfortable or whether the B was scraped. It is also the honest way to check a grade you think was computed against different cutoffs — enter your syllabus's lines and see whether the letter changes. If what you have is a GPA and the form wants a letter, that is the GPA to letter grade page; if you want to know what the final exam has to score to lift the semester, that is the final grade page.

1. 43 out of 50 with the usual cutoffs: 86% and a B

   1. 43 ÷ 50 × 100 = 86%
   2. 86 is below the A line of 90 and at or above the B line of 80, so the letter is B
   3. The A line in points: 90% of 50 = 45. 45 − 43 = 2 points short of it
   4. The B line in points: 80% of 50 = 40. 43 − 40 = 3 points above it

   All three rows are whole numbers, so the panel can be checked against the paper by hand. Note what the two rows do together: 2 points short of the next letter and 3 points above your own line adds up to the 5-point gap between the two cutoffs, which is a useful way to see that nothing has been dropped.

2. 18 out of 20: exactly on the A line reads A

   1. 18 ÷ 20 × 100 = 90%
   2. 90 is exactly the A line, and a score on the line takes that letter
   3. Nothing above to reach, so the row reads 0 points needed
   4. The A line in points is 90% of 20 = 18, so the score is 0 points above it

   The boundary itself is worth seeing once. A cutoff written as a percentage and a score written as a fraction rarely land on each other this neatly, and the page has to decide which side the exact hit falls on; it takes the higher letter, which is the convention every syllabus with a 90 line assumes. Note that both gap rows read 0 here, for different reasons: one has nothing left to reach, the other has nothing above the line.

3. The same 86% under 93/85/75/65: still a B, but barely

   1. The score is the same 43 out of 50, so the percentage is still 86%
   2. 86 is below the A line of 93 and above the B line of 85, so the letter is still B
   3. The A line in points: 93% of 50 = 46.5, which is 3.5 points away
   4. The B line in points: 85% of 50 = 42.5, which the score is 0.5 above

   This is the example that shows the cutoffs are really inputs. Nothing about the score changed — only the lines did — and the margin collapsed from 3 points to 0.5 with the next letter moving from 2 points away to 3.5. A page with 90/80/70/60 written into it would print the first pair of numbers here and look exactly as convincing.

4. An A line of 105%: a perfect paper reads B

   1. 50 ÷ 50 × 100 = 100%
   2. 100 is below the A line of 105, so the highest cutoff reached is the B line of 80
   3. To reach A: (105 − 100) × 50 ÷ 100 = 2.5 points, which a full paper cannot supply
   4. The B line in points is 40, so the score is 10 points above it

   The cutoffs are not clamped to 100%, because a syllabus that sets the A line above a perfect paper exists — it means nobody gets an A, and the page should report that rather than quietly improve the line to something more reasonable. Forcing the cutoffs into 0–100 would turn this into an A and lose the point of the input.

The four cutoffs must decrease strictly — A above B above C above D — and the page refuses a set where two are equal, because then the lower of the two letters could never be reached. Only four letters and F exist here: there is no A−, no E, and no B+ row, so a school that reports those cannot be reproduced by four numbers. The letter is not rounded before it is compared, so a percentage of 89.5 against a 90 line is a B, while a teacher who rounds first would call it an A. F has no cutoff of its own — it is everything below the D line — so the row that measures how far above your cutoff you are reads the raw score when the letter is F, which can look like a positive margin on a failing grade. Nothing here converts the letter into grade points or into a GPA figure; the GPA to letter grade page does that in the other direction. The defaults are placeholders for a syllabus, not a claim about one.

How do I turn a test score into a letter grade?

Divide the points earned by the points the test was out of, multiply by 100, and read the result against your cutoffs. 43 out of 50 is 86%, which is below a 90 A line and above an 80 B line, so it is a B. The calculator also prints the two cutoffs converted into points on that paper — 45 for the A line, 40 for B — which is what makes the near misses obvious.

My school uses different cutoffs. Can I change them?

Yes — all four are inputs, and 90/80/70/60 is only a placeholder. Enter your syllabus's numbers and every row updates; the letter, the points to the next letter and the margin above your line are all computed from what you type. That is deliberate: there is no authoritative set of cutoffs to hard-code, since 90/80/70/60 and 93/85/75/65 are both in everyday use and some schools put an A+ row on top of either.

What does the page do when the score is below the D line?

It reads F, which is the one letter with no cutoff of its own — it is everything under the D line. Because of that, the row that normally says how far above your cutoff you are falls back to the score itself: 29.5 out of 50 reads 29.5, not a negative number. That is a property of how F is defined rather than a sign that the margin was computed wrongly, and the row above it still shows the 0.5 points needed to reach D.

Can a score be more than 100%?

Yes, if the paper offers extra credit. The points earned field has no ceiling, so 55 out of 50 reads 110% and takes the A line if the score reaches it. Refusing the input would be the wrong call: bonus questions are real, and a page that rejected them would force you to edit the score before you could see the letter — which is exactly the arithmetic you came here to avoid.

Why are the last two rows in points rather than percent?

Because that is the unit on the paper. Saying that an A is 4 percentage points away does not tell you whether one more question would do it; saying that it is 2 points away on a 50-point test does. The conversion is the cutoff times the total, divided by 100 — for the 43-out-of-50 example, the A line of 90% works out to 45 points, so 2 more were needed.

• Measures of the Location of the Data — Introductory Statistics 2e, section 2.3 (defines quartiles and percentiles as cut points located between ordered values, and notes that several formulas for the k-th percentile are in circulation — the same reason a grade cutoff has to be an input rather than a constant) — OpenStax, Rice University
• Measures of Location — e-Handbook of Statistical Methods, section 1.3.5.1 (the weighted arithmetic mean, which is what a semester total does with the percentages this page produces) — National Institute of Standards and Technology (NIST)
• GB/T 3358.1-2009, Statistics — Vocabulary and symbols, Part 1 (the Chinese national vocabulary standard for general statistical terms; its record page notes that no online full text is offered, so it is cited as the vocabulary source rather than as a readable page) — State Administration for Market Regulation, China