Flat shift, square-root curve, or scale the top score to 100. Enter your class scores once and see what each method does to the whole distribution.
Curved class mean
flat shift of +6 · failures fall from 4 to 2
Mean before69
Below 60 after2
Top score after97
Scores
20
Mean before → after
69 → 75
Below 60 before → after
4 → 2
Top score before → after
91 → 97
Every score, before and after
#
Before
After
Grade
1
41
47
F
2
52
58
F
3
55
61
D-
4
58
64
D
5
60
66
D
6
62
68
D+
7
63
69
D+
8
65
71
C-
9
67
73
C
10
68
74
C
11
70
76
C
12
71
77
C+
13
73
79
C+
14
75
81
B-
15
77
83
B
16
79
85
B
17
81
87
B+
18
84
90
A-
19
88
94
A
20
91
97
A+
This calculator needs JavaScript to recalculate. The answer shown above was worked out when the page was built and is correct for the date in the address bar.
They are not variations on one idea. They redistribute grades in genuinely different directions, and choosing between them is a decision about who you are helping.
1. Flat shift
Add the same number of points to everyone. curved = raw + k, where k is usually chosen to bring the class mean to a target. Simple, transparent, and it preserves the gaps between students exactly. A student who was 9 points ahead is still 9 points ahead.
2. Square-root curve
curved = 10 × √raw. A 36 becomes 60, a 64 becomes 80, a 81 becomes 90, and a 100 stays 100. The lift shrinks as scores rise, so it helps the bottom of the class far more than the top — a failing student gains 24 points while a strong one gains 9. It compresses the distribution, which is either the point or the problem depending on what you were trying to measure.
3. Top score to 100
curved = raw × 100 ÷ max. Whoever scored highest gets 100 and everyone is scaled proportionally. This one helps the top most in absolute terms and does very little for the bottom: if the top score was 91, a student on 41 gains 4.1 points while the top student gains 9. It also means one exceptional student can wipe out the curve for everyone else.
Worked example — the same class, all three ways
Twenty scores, mean 69.0, four of them below 60.
Method
New mean
Lowest score
Highest
Below 60
Raw
69.0
41
91
4
Flat shift +6
75.0
47
97
2
Square root
82.4
64
95
0
Top score to 100
75.8
45
100
3
Read the last column. The square-root curve eliminates failing grades entirely; the flat shift halves them; top-score scaling barely moves them. Three defensible methods, three different classes at the end of it. That comparison is the reason this page exists — most calculators implement one method and call it "the curve".
What a curve is not
A true bell curve forces the class into a target distribution — a fixed proportion of As, Bs and Cs regardless of absolute performance — by ranking students and assigning grades by percentile. That is a different operation from anything above, it is rare outside a few professional programmes, and it is not what most instructors mean when they say they are curving. This calculator does not do it, and a tool offering "bell curve" that simply adds points is mislabelling itself.
Where this stops being reliable
Curves are statistically meaningless in small classes — with eight students, one absence changes the mean by several points and any curve derived from it is noise. Flat shifts and top-score scaling can push scores above 100, which you may or may not want to allow. The square-root curve is undefined for negative scores and does nothing useful for scores already near 100. And no curve fixes a badly-written test; it only moves the numbers the test produced.
Common questions
How does a grade curve work?
A curve adjusts raw scores upward according to a rule applied to the whole class. The three common rules are adding a fixed number of points to everyone, applying a square-root transformation, or scaling so the highest score becomes 100. They help different parts of the class and are not interchangeable.
What is a square root curve?
Take the square root of the raw score and multiply by 10. A 36 becomes 60, a 64 becomes 80, a 100 stays 100. Because the lift shrinks as scores rise, it helps struggling students most — 24 points at the bottom of the class against 9 near the top.
Can curving lower a grade?
None of the three methods here can. Flat shifts with a positive k, square-root curves and top-score scaling all leave scores the same or higher. Curving down only happens under a forced distribution, where a fixed share of the class receives each grade regardless of absolute scores — a different operation, and one this calculator does not perform.
How do I curve to a target class mean?
For a flat shift, subtract the current mean from the target and add that difference to every score. A class at 69 curved to 75 needs +6 points each. Enter your scores and a target above and the calculator works out the shift.
Is curving standard practice?
It varies enormously by institution, department and instructor. Some courses curve every assessment, some curve only when a test performs badly, and some have policies forbidding it. Where a curve is applied, the method is usually at the instructor's discretion, which is why three reasonable people can produce three different sets of grades from the same scores.
What if a curve pushes scores above 100?
Decide in advance whether to cap. Flat shifts and top-score scaling can both exceed 100 for the strongest students. Capping preserves the 100 ceiling but compresses the top of the class; not capping rewards the extra performance. Neither is wrong, but changing your mind after publishing grades is.