Grade curve calculator

This grade curve calculator applies six common curving methods to a whole set of test scores at once. Paste the scores, choose how you want to curve – by a flat number of points, to a target class average, to the highest score, with the square root rule or onto a bell curve – and compare each original score with its curved score.

Source: Wikipedia – Standard score (z-score: z = (x − μ) ÷ σ, and rescaling to a new mean and standard deviation). Updated: 6 October 2026.

Scores of the class

One score per line, or separated by commas or spaces. Use a decimal point for half points (87.5). Up to 400 scores.

Maximum possible score

points

100 for percentages; otherwise the number of points the test was out of. No curved score goes above it.

Curving method

Target class average

points

Used by “Raise the class average” and by the bell curve.

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Result

Class average: Class average 67 → 75 (+8 points, 10 scores)
Curve applied: Every score changed by +8 points (target average 75 − class average 67)
Class statistics: Number of scores: 10
Average (mean): 67 before, 75 after the curve
Lowest and highest score: 41 and 90 before, 49 and 98 after
Standard deviation of the original scores: 14.85
Original and curved scores: Original score Curved score Change
90 98 +8
85 93 +8
78 86 +8
74 82 +8
70 78 +8
66 74 +8
61 69 +8
57 65 +8
48 56 +8
41 49 +8; A curve changes scores, not what students learned. Whether and how to curve is the instructor’s decision and should follow the course syllabus.

Original score	Curved score	Change
90	98	+8
85	93	+8
78	86	+8
74	82	+8
70	78	+8
66	74	+8
61	69	+8
57	65	+8
48	56	+8
41	49	+8

How it is calculated

Curving a test means adjusting every score by the same rule so that the results better fit the intended difficulty. The simplest curve adds the same number of points to everyone; others rescale the scores to the top result or to a target mean and standard deviation. This grade curve calculator shows what each method does to your class.

The six methods and their formulas

Method	Formula	Effect
Raise the class average	score + (target average − class average)	everyone gets the same bonus; the mean lands on the target
Flat curve to the top score	score + (maximum − highest score)	the best paper gets full marks; same bonus for all
Scale to the top score	score × maximum ÷ highest score	the best paper becomes 100%; higher scores gain more points
Fixed points	score + points	for a flawed question worth a known number of points
Square root curve	√(score ÷ maximum) × maximum	low scores gain the most; 100% stays 100%
Bell curve	target mean + (score − mean) ÷ SD × target SD	sets both the average and the spread

Worked example

Ten scores out of 100 are preloaded: 90, 85, 78, 74, 70, 66, 61, 57, 48 and 41. Their average is 670 ÷ 10 = 67.

Raise the average to 75: 75 − 67 = 8, so every score goes up 8 points. 90 becomes 98, 41 becomes 49, and the new average is 75.
Flat curve to the top score: 100 − 90 = 10 points for everyone. 90 becomes 100, 41 becomes 51; the average rises to 77.
Scale to the top score: every score is multiplied by 100 ÷ 90. 85 becomes 94.44 and 41 becomes 45.56 – a gain of 9.44 points at the top but only 4.56 at the bottom.
Square root curve: 10 × √score on a 100-point test. 64 would become 80, 81 would become 90; in the example 41 becomes 64.03 and 90 becomes 94.87.

Curving with the mean and standard deviation (bell curve)

The bell-curve method first expresses each score as a z-score – how many standard deviations it lies above or below the class mean – and then places it on a new scale with the mean and standard deviation you choose:

curved score = target mean + (score − class mean) ÷ class SD × target SD

The example scores have a mean of 67 and a standard deviation of 14.85. With a target mean of 75 and a target SD of 10, the top score of 90 becomes 75 + (90 − 67) ÷ 14.85 × 10 = 90.49, and the lowest score of 41 becomes 57.49. The order of the students never changes; only the centre and the spread do. The calculator uses the population standard deviation (dividing by the number of scores), because the class is the whole group being graded.

Which curve should I use?

The test was simply too hard overall: raise the average, or use the flat curve.
One question was broken: add its points back as fixed points.
You want to help struggling students most without pushing anyone over 100%: the square root curve.
Your department prescribes a mean and spread for the course: the bell curve.

Scores are never curved above the maximum or below zero. When that limit bites, the calculator tells you how many scores were affected – the class average then ends up a little below the target.

From curved score to letter grade

Once the scores are curved, convert them with the scale in your syllabus – the grade calculator does that for points and percentages, and the average calculator gives you median and mode as well. The list of scores contains no names; it is stored in the page address so you can bookmark the curve or send it to a colleague.

Frequently asked questions

How do you curve a grade?

Pick a rule and apply it to every score. The most common one adds the difference between the highest score and the maximum to everyone: if the best score is 90 out of 100, each student gets 10 points.

How do I curve grades to a certain average?

Subtract the class average from the average you want and add the difference to every score. With an average of 67 and a target of 75, everyone gets 8 points.

What is the square root curve?

Take the square root of the percentage score and multiply by 10: 64% becomes 80% and 81% becomes 90%. Low scores gain more than high ones, and nobody can exceed 100%.

How does curving with the standard deviation work?

Each score is converted to a z-score, (score − mean) ÷ standard deviation, and then mapped to a new mean and standard deviation. A student one standard deviation above the class mean ends up one target standard deviation above the target mean.

Can a curve lower a grade?

A bell curve or a negative number of fixed points can, because scores above the old mean may be pulled toward the new one. Adding points or the square root curve never lowers a score.

Does curving change the ranking of students?

No. All six methods keep the order of the scores. Only ties created by the maximum cap can make two different scores equal.

What happens to scores that would go over 100%?

They are capped at the maximum possible score. The calculator reports how many scores were capped.

Which standard deviation does the calculator use?

The population standard deviation, which divides by the number of scores. For a class graded as a whole this is the appropriate measure.

Sources and legal basis

As of: 6 October 2026 · Editorial policy

Original score	Curved score	Change
90	98	+8
85	93	+8
78	86	+8
74	82	+8
70	78	+8
66	74	+8
61	69	+8
57	65	+8
48	56	+8
41	49	+8

Original score	Curved score	Change
90	98	+8
85	93	+8
78	86	+8
74	82	+8
70	78	+8
66	74	+8
61	69	+8
57	65	+8
48	56	+8
41	49	+8