Grade Curve Calculator (curve test scores by mean & standard deviation)

Understanding the grade curve calculator — concept and principle

This calculator curves a set of class scores in one of three ways, by a target mean and standard deviation, by a flat number of points, or by lifting the top score to the maximum, and shows your own curved score. Students use it to understand how a curve affects them; teachers use it to compare curving methods.

Keep your place, move the curve: with the default inputs the result is 76.9 curved (+2.9 points).

How it is calculated

First the class mean μ and population standard deviation σ of the raw scores are found.

Mean and SD method: z = (x − μ) ÷ σ; new score = target mean + z × target SD.
Flat curve: every score + (target mean − μ).
Top-score method: every score + (maximum − highest score).
All curved scores are kept between 0 and the maximum.

The principle

A z-score says how many standard deviations a score lies above or below the class average. Keeping each student's z-score and rebuilding the scores around a chosen mean and spread changes the scale but keeps the ranking and relative gaps. A flat curve just shifts everyone up by the same amount, so the spread stays the same. The top-score method gives everyone the points the best student needed to reach full marks. Because scores are capped at the maximum, a few very high scores can make the curved mean differ slightly from the target.

Worked example

Default inputs: scores 58, 62, 65, 70, 71, 74, 76, 78, 81, 85, 88, 93; your score 74; target mean 78 and SD 10; maximum 100.

Mean μ = 901 ÷ 12 = 75.08; σ = 10.16.
Your z = (74 − 75.08) ÷ 10.16 = −0.11.
Curved = 78 + (−0.1066 × 10) = 76.9, so 2.9 points are added.
Lowest curved = 78 + (58 − 75.08) ÷ 10.16 × 10 = 61.2; highest = 95.6.
Curved class mean = 78; scores in the list = 12.

Each point is the calculator re-run with only “Target mean” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

Target mean	Your curved score
19.5	18.4
39	37.9
58.5	57.4
78	76.9
97.5	96.4
117	100
156	100

How to read the result

With a mean-and-SD curve, a target SD larger than the raw SD spreads the scores out, and a smaller one squeezes them together. Here the target SD (10) is a little smaller than the raw one (10.16), so the curve slightly narrows the spread, and scores far above the mean gain the least. Your position in the class does not change with any linear curve; only the numbers do.

Common mistakes

Using the sample standard deviation when the method uses the population one, or the reverse.
Expecting a curve to raise every score; a mean-and-SD curve can lower some.
Forgetting the cap at the maximum.
Assuming your teacher uses one of these methods; many use their own rules.

Keep in mind: Your teacher's own curving rule always takes precedence. This is an illustration of common methods.

Frequently asked questions

How does curving with a z-score work?

Each score keeps its distance from the mean in standard deviations, and is placed around a new mean and spread.

Can a curve lower my grade?

Yes, with a mean-and-SD curve if your score is well above the mean and the target spread is smaller.

What is a flat curve?

Adding the same number of points to every score.

Sources: OpenStax, Introductory Statistics, sections 2.7 (standard deviation) and 6.1 (z-scores)

Checked 9 Nov 2026. Linear standardisation of scores (z = (x − μ) ÷ σ, new score = target mean + z × target SD) and flat additive curves — standard descriptive statistics.

Your numbers