Letter Grade Scales: How a Fraction Becomes an A−

A test score starts life as a fraction — 45 out of 50 — and ends life as a letter stapled to your transcript. Between the two sits a surprisingly opinionated piece of machinery: the grading scale. Understanding how it works turns "I got a 90" into "I got an A−, and the A was two points away."

A percentage is just a fraction with better manners

The first step is always the same: divide points earned by points possible and multiply by 100. Forty-five out of 50 is 90%; 43 out of 48 is 89.6% after rounding to one decimal. The percentage is the objective part of grading — it does not care which school, teacher, or country you are in. Everything after this step is convention.

The 13-step plus/minus ladder

Most colleges use a thirteen-rung ladder. Each letter grade owns a band of percentages, and the bands are: A+ starts at 97, A at 93, A− at 90, B+ at 87, B at 83, B− at 80, C+ at 77, C at 73, C− at 70, D+ at 67, D at 63, D− at 60, and F below 60. Notice the pattern: whole letters open on a 3-point boundary (93, 83, 73, 63), pluses land on 7s, and minuses on round 10s.

The bands explain a familiar frustration: an 89.6% is a B+ even though it rounds to 90, because thresholds are floors, not targets. Rounding happens on the percentage; the letter lookup uses the rounded value against a fixed cut.

Plain scales and custom curves

Plenty of schools keep it simple: A from 90, B from 80, C from 70, D from 60, F below — five letters, no modifiers. And many teachers define their own cut points entirely, often to bake a curve into the scale itself rather than fudging scores at the end of term. A custom scale is just a list of pairs — A:92, B:84, C:70, D:60 — where each letter declares the percentage floor it starts at. Custom scales are friendlier than ad-hoc curves because the rules are published before you take the test.

The lesson: the syllabus is part of the exam. The same 45/50 is an A− on one scale and a B on another, and neither is wrong — they are different policies wearing the same arithmetic.

The half-point rounding trap

Converting a threshold back into points introduces one wrinkle worth knowing. If an A starts at 93%, then on a 50-point test the A boundary sits at 46.5 points — a score that cannot exist if tests are graded in whole points. The practical requirement is the next whole point up: 47. This is why "points to the next letter" sometimes looks off by half a percent from the raw threshold. Percentages are continuous; points are not. When the gap matters — say, deciding whether to argue a half-point question — check whether your teacher awards partial credit in halves.

Reading a grade backwards is the most useful skill the scale teaches. Score 45/50 and you are at 90% — an A−. The A band starts at 93%, which is 46.5, so 47 points. Two points. That number is gold: it tells you whether the difference was one multiple-choice question (study one topic) or nine points of structure (change how you prepare). Grades are backward-looking; the points-to-next-letter figure is the forward-looking part.

Letters are not the final stop, either. Each letter converts to grade points — A = 4.0, B+ = 3.3, and so on — and grade points multiplied by credit hours become quality points, the currency of GPA. So the fraction you earned on one Tuesday quiz eventually propagates all the way into a cumulative average that admissions offices will read years later. Small cut points, long shadows.

Try it yourself

The Test Grade Calculator does the whole chain at once: enter points earned and possible, pick the plus/minus ladder, the plain scale, or paste your teacher's custom scale, and see the percentage, the letter, and exactly how many points the next letter up would have taken. For the course-long version of the same math, the Final Grade Calculator shows what you need on a final to hit a target letter — and the final exam math explainer walks through that formula step by step.