Grade Curve Calculator
Paste a class's test scores and curve them the way teachers commonly do: add points, scale the top score to 100%, move the average, square root, stretch or bell curve. Advanced adds letter grades, class stats, a histogram and the raw score each grade needs.
Separate scores with commas, spaces or new lines. Add names if you like: “Ana 78”.
Usually 100%. Some teachers use 95% so the top student isn't pushed to a perfect score.
Each grade starts at the % shown. Change any of them to match your school.
Whether to curve, and how, is up to the teacher and the school. This tool shows what each method does to the scores.
How your curve is worked out
One rule is applied to every score in the class, then the results are capped, rounded and graded.
- 1
Look at the class
10 scores · top 80%
average 62% - 2
Find the factor
100 ÷ 80
= × 1.25 - 3
Curve each score
66 × 1.25
= 82.5% (B) - 4
The new class
62% → 77.5%
A needs 72 raw
Read more: every formula, a worked example and how the methods compare
A grade curve applies one rule to every score in the class. Some rules add the same points to everyone, some multiply, and some reshape the spread. Pick the one your teacher or school uses; the calculator applies it to every score and then caps, rounds and grades the results.
The formula
raw % = raw points ÷ points possible × 100
add points: curved = raw % + points added
add the gap: curved = raw % + (100 − top score %)
top score to 100: curved = raw % × 100 ÷ top score %
class average to a target: curved = raw % × target ÷ class average (or raw % + target − class average)
square root: curved = 10 × √(raw %)
stretch: curved = new lowest + (raw % − lowest) × (new highest − new lowest) ÷ (highest − lowest)
bell curve: z = (raw % − class average) ÷ class SD, curved = target average + z × target SD
raw % needed for a grade = the same rule run backwards from the grade's cut-off
Worked example
The class scored 66, 80, 42, 58, 74, 50, 61, 70, 55 and 64 out of 100. They add up to 620, so the class average is 620 ÷ 10 = 62%. The top score is 80.
To make the top score 100%, every score is multiplied by 100 ÷ 80 = 1.25. The 66 becomes 66 × 1.25 = 82.5%, the 42 becomes 52.5% and the 80 becomes 100%. The curved scores are 82.5, 100, 52.5, 72.5, 92.5, 62.5, 76.25, 87.5, 68.75 and 80, and the new class average is 62 × 1.25 = 77.5%.
On the common US scale (A 90, B 80, C 70, D 60) the grades go from no A, 1 B, 2 C, 3 D and 4 F to 2 A, 3 B, 2 C, 2 D and 1 F. Run backwards, an A after the curve needs 90 ÷ 1.25 = 72 raw points, a B needs 80 ÷ 1.25 = 64, a C needs 56 and a D needs 48.
The spread grows by the same factor: the standard deviation goes from √116.2 = 10.78 to 10.78 × 1.25 = 13.47 points. The median goes from (61 + 64) ÷ 2 = 62.5 to (76.25 + 80) ÷ 2 = 78.13.
The same class with other methods
| Method | Rule | 66 becomes | New average |
|---|---|---|---|
| Add 5 points | +5 | 71 | 67 |
| Add the gap to the top | +(100 − 80) = +20 | 86 | 82 |
| Top score to 100% | × 1.25 | 82.5 | 77.5 |
| Class average to 75%, multiply | × 75 ÷ 62 | 79.84 | 75 |
| Class average to 75%, add | +13 | 79 | 75 |
| Square root | 10 × √66 | 81.24 | 78.43 |
| Stretch to 50–100% | 50 + (x − 42) × 50 ÷ 38 | 81.58 | 76.32 |
| Bell curve, 75% with SD 10 | 75 + (x − 62) ÷ 10.78 × 10 | 78.71 | 75 |
Which method does what
- Adding points moves everyone up by the same amount. The gaps between students stay the same.
- Scaling (multiplying) gives higher scores more points than lower ones and widens the spread.
- Square root helps low scores the most: 36% becomes 60%, but 90% only becomes 94.87%.
- Stretching pins the lowest and highest scores to new values and spaces the rest in between.
- Bell curve sets both the average and the spread. It can pull top scores down, which is why many teachers add "never lower a score".
The class SD here is the population standard deviation (dividing by the number of students), because the class is the whole group, not a sample. Letter-grade cut-offs vary between schools and teachers, so edit the scale in Advanced to match yours.
Common questions
How do you curve grades?
Pick a method, then apply the same rule to every score. The most common are adding the same points to everyone, scaling so the top score becomes 100%, moving the class average to a target, the square root curve (10 × √score) and the bell curve, which sets a new average and spread.
How do I curve a test so the highest score is 100?
Divide 100 by the top score and multiply every score by that factor. If the top score is 80, the factor is 100 ÷ 80 = 1.25, so a 66 becomes 82.5. Or add the gap to everyone: 100 − 80 = 20 points each, so a 66 becomes 86.
What is the square root curve?
Take the square root of the percentage and multiply it by 10. A 64% becomes 10 × 8 = 80%, a 49% becomes 70% and a 100% stays 100%. Low scores gain the most, and nobody goes over 100%.
How does a bell curve work for grades?
Each score is turned into a z-score: how many standard deviations it sits from the class average. The curved score is the target average plus z times the target spread. With a class average of 50, a spread of 20 and a target of 75 with a spread of 10, a 70 (z = 1) becomes 85.
Can a curve lower my grade?
Adding points, scaling up and the square root curve never lower a score. A bell curve or a linear stretch can lower top scores if the target is below where they already were. Many teachers only use a curve when it helps, so this calculator has a "Never lower a score" option.
What raw score do I need for an A after the curve?
Work the curve backwards from the grade cut-off. If every score is multiplied by 1.25 and an A starts at 90%, you need 90 ÷ 1.25 = 72% before the curve. Advanced shows this for every grade on your scale.
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Made by Zulu Calculator, part of AlphaZulu LLC. Formulas are shown in full and rule figures are checked against official sources; see how we build calculators.