A fair curve is one rule, chosen before you look at names, applied to every student, that never lowers a score. If you can’t explain it in one sentence, pick a simpler one.
We ran one made-up class of 10 through each method. Flat points gave everyone the same gain. Scaling to the highest score favored high scorers. A square-root curve favored low scorers. Moved cutoffs changed letters and left scores alone. A bell curve fit worst, because 10 students are too few.
When a curve is the right call, and when it is not
A curve fits one problem: the test came out harder than you meant, so the scores say more about the test than about your students. Use one when most of the class scored well below its usual level, on material you did teach.
A curve is the wrong fix when:
- One question was broken. Give everyone the point or remove the question.
- You did not get to the material. Teach it and test it again. A curve raises grades, not what students know.
- A few students failed and the rest did fine. A curve lifts the students who were fine. The ones who struggled still need help.
- Your school says no. The US has no national grading standard, and a 2005 U.S. Department of Education overview says classroom teachers typically decide grades. Your school or department may still have a rule, so check first.
One test, one class: the same scores under each method
Made-up example. These 10 scores are invented, on a test out of 100. Letters use the 10-point scale in Florida law for public school grades 6-12: A from 90, B from 80, C from 70, D from 60, F below 60. That is one state’s scale, so use your own.
| No curve | Flat +8 | Scale to highest | Square root | Moved cutoffs | Bell curve |
|---|---|---|---|---|---|
| 92 A | 100 A | 100.0 A | 95.9 A | 92 A | A |
| 85 B | 93 A | 92.4 A | 92.2 A | 85 A | B |
| 81 B | 89 B | 88.0 B | 90.0 A | 81 B | B |
| 78 C | 86 B | 84.8 B | 88.3 B | 78 B | C |
| 74 C | 82 B | 80.4 B | 86.0 B | 74 C | C |
| 70 C | 78 C | 76.1 C | 83.7 B | 70 C | C |
| 66 D | 74 C | 71.7 C | 81.2 B | 66 C | C |
| 61 D | 69 D | 66.3 D | 78.1 C | 61 D | D |
| 55 F | 63 D | 59.8 F | 74.2 C | 55 D | D |
| 41 F | 49 F | 44.6 F | 64.0 D | 41 F | F |
Scale and square-root scores are rounded to one decimal, and each letter comes from the unrounded score. The moved cutoffs are our example: A from 85, B from 75, C from 65, D from 55. The bell curve column uses made-up shares, explained below.
Here is what each method does to the whole class. The order of the students never changes.
| Method | A | B | C | D | F | Class average | Moved up a letter |
|---|---|---|---|---|---|---|---|
| No curve | 1 | 2 | 3 | 2 | 2 | 70.3 | 0 |
| Flat +8 | 2 | 3 | 2 | 2 | 1 | 78.3 | 5 |
| Scale to highest | 2 | 3 | 2 | 1 | 2 | 76.4 | 4 |
| Square root | 3 | 4 | 2 | 1 | 0 | 83.4 | 9 |
| Moved cutoffs | 2 | 2 | 3 | 2 | 1 | 70.3 | 4 |
| Bell curve | 1 | 2 | 4 | 2 | 1 | 70.3 | 2 |
Adding flat points
Add the same number to every score. The most you can add without passing 100 is 100 minus the top score. Here that is 100 − 92 = 8.
Everyone gains 8, so the gap between any two students stays the same. That makes this the easiest curve to explain. Five students move up a letter. The student with 41 reaches 49 and still has an F.
Scaling to the highest score
Divide each score by the top score, then multiply by 100. Here, 74 ÷ 92 × 100 = 80.4.
The student with 92 gains 8.0. The student with 41 gains 3.6. The higher the score, the bigger the gain.
One student also controls the whole curve. If the top score had been 100, nobody would gain a point.
Watch the 55. It lands on 59.8, just under the D line, so it stays an F unless you round to whole numbers first. Set your rounding rule before you curve. How to Set Up a Gradebook Students Can Check covers that.
Using a square-root curve
Take the square root of the score and multiply by 10: 10 × √score. For an 81, that is 10 × √81 = 10 × 9 = 90.0.
This works on scores out of 100, so turn anything else into a percent first. A 34 out of 40 is 85%, and 10 × √85 rounds to 92.2.
In this class, the lower the score, the bigger the gain. The student with 92 gains 3.9. The student with 41 gains 23.0.
That is a big lift. Nine of the 10 students move up a letter, two of them jump two letters, and nobody has an F. The class average goes from 70.3 to 83.4. If that is more than the test deserves, use a smaller fix.
Moving the letter-grade cutoffs
Leave every score alone and lower the lines. Our example lowers each line by 5 points. Four students move up a letter, and the class average stays at 70.3.
Each score still shows what the student earned, which suits a final course grade. On one test, your gradebook may not let you change the scale.
Cutoffs already differ between schools. C starts at 73 in the Johns Hopkins School of Nursing table and at 70 at the University of the Incarnate Word.
The weak spot is the edge. The 74 misses the new B line by one point, and students will know you drew that line after seeing the scores.
Bell curves in small classes
A strict bell curve hands out letters by rank, in fixed shares. Take this made-up set: 10% A, 20% B, 40% C, 20% D, 10% F. In our class of 10, that means 1 A, 2 B, 4 C, 2 D and 1 F.
Those shares fall apart in a small class:
- One student is 10% of the class. Two students tied at 92 would not fit in one A slot.
- Someone must get the F. If the lowest score were 80, that student would still fail.
- Shares stop dividing. With one student absent, 10% of 9 is 0.9 of a student.
Ten scores are too few to show a bell shape. For a class this size, pick one of the methods above.
How to explain a curve to students
Tell students before they see new scores: why you curved, the rule in one sentence, that no score went down, and whether the curve covers this test only.
Show raw and curved scores side by side, so students can check the math. You could say: “This test ran harder than I planned, so I added 8 points to every score. No score went down.”
Try it on your own test
GradeCat has no curve tool yet, so use a spreadsheet for the methods that change scores. With raw scores in cells A2 to A11:
- Flat points:
=MIN(A2+8,100) - Scale to highest:
=ROUND(A2/MAX($A$2:$A$11)*100,1) - Square root:
=ROUND(10*SQRT(A2),1)
You can try moved cutoffs here. On the Grading Scale page, choose Make my own scale, change the minimums and press Save scale. In that browser, your scale then appears in the Grading scale menu of the Test Grade Calculator, where you can print a chart.
The Test Grade Calculator does not curve anything, and it will not accept a score above the total.
Sources
- U.S. Department of Education overview, 2005
- Florida Statutes, Section 1003.437 (2026)
- Johns Hopkins School of Nursing grading policy
- University of the Incarnate Word grading scale
Tools for this guide
- Test Grade Calculator: Turn questions wrong into a score, with a chart you can print.
- Grading Scale: See how percents turn into letter grades, and set your own scale.
More guides
- How to Set Up a Gradebook Students Can Check
- Rubric Grading: Why 2 out of 4 Need Not Mean 50%
- Zero, 50% or Missing: How Each Changes a Grade
- Weighted Grades in Excel and Google Sheets
- Standards-Based Report Cards: What a 1 to 4 Means
This guide is general information. Your school's rules come first. Found a mistake? Tell us.