The basic formula
Grade percent equals (points earned divided by points possible) times 100. Take 37 out of 45: 37 divided by 45 is 0.8222, times 100 gives 82.2 percent. Take 128 out of 150: 128 divided by 150 is 0.8533, times 100 gives 85.3 percent.
Partial credit works the same way. If a 100-point exam has you at 73 points with a 5-point bonus problem, your earned total is 78, and 78 divided by 100 times 100 is 78 percent. Bonuses simply add to the numerator.
Reading your letter grade
Most US courses use a familiar scale, but the exact cutoffs are set by your syllabus and can vary. A common version is: 90 to 100 is an A, 80 to 89 is a B, 70 to 79 is a C, 60 to 69 is a D, and below 60 is an F. Some courses use plus and minus grades inside those bands, and some shift the bands up or down. Always check the syllabus before assuming where you stand.
Borderline math is where the formula earns its keep. At 89.4 percent on a 90 percent A cutoff, you need to know exactly how many more points lift you over. Here is the clean way: multiply your target percent by the total possible course points to get the target point total, then subtract the points you already have. Say you have 447 of 500 so far (89.4 percent) with a 100-point final ahead. To finish at 90 percent of 600, you need 540 points, so you need 93 on the final.
Weighted grades: when categories count differently
Many courses weight categories: homework 20 percent, quizzes 30 percent, final exam 50 percent, for example. A 95 percent homework average does not carry the same punch as a 95 percent final. The method: convert each category percent to a decimal, multiply by its weight, and add.
Worked example. Homework average 92 percent at 20 percent weight: 0.92 times 0.20 equals 0.184. Quiz average 85 percent at 30 percent weight: 0.85 times 0.30 equals 0.255. Final exam 78 percent at 50 percent weight: 0.78 times 0.50 equals 0.390. Add them: 0.184 plus 0.255 plus 0.390 equals 0.829, or 82.9 percent. A B, despite the strong homework scores.
If your syllabus gives weights as points instead of percents (homework 200 points, final 400 points), the weighting is automatic: add all earned points, add all possible points, divide, times 100. That is the same as the basic formula applied to the whole course.
What does "curved" mean?
A curve adjusts raw scores so the class distribution matches the instructor's target. The most common simple curve adds a fixed number of points to everyone: if the highest score was 88 and the instructor wants the top to be 100, everyone gains 12 points. Your 74 becomes an 86.
Another common approach scales scores: multiply every score by (100 divided by the top score). With a top score of 88, the multiplier is 1.136, so a 74 becomes 84.1. Either way, a curve moves everyone by the same rule; it never changes who is ranked where, only the numbers attached to the ranks. Ask your instructor which method they use before assuming anything.
Tracking your grade during the semester
Keep a running total: points earned so far divided by points possible so far, times 100. That is your current grade if the course stopped today. Then project: for each remaining assignment, plug in a realistic score and see where the final lands. Students who track this weekly catch slumps early, when there is still time to fix them.
Quick sanity checks along the way: a zero on a big assignment hurts far more than a zero on a small one, because the denominator is bigger. Dropping the lowest quiz score, if your syllabus allows it, removes both its earned and possible points from the totals. For the underlying part-of-whole math, see our guide on finding what percent one number is of another.