GradeDuck

Grade Curve Calculator

Paste a class’s scores, pick a curve, and see every score before and after, with the new mean, median, spread, and letter grades.

Reviewed by Matias Mardones · Updated · How we calculate

Class mean after the curve
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Mean before –
Average change –
Scores that went down –

StatisticBeforeAfter
LetterBeforeAfter

Every score, before and after

#BeforeAfterChangeLetter beforeLetter after

What curving a grade does

A curve is a rule that changes every score on a test the same way. Teachers usually reach for one when a test came out harder than intended: a confusing question, a topic that didn’t land, a class average far below the usual. Students use the same math to see where a curve might leave them. Everything here runs in your browser, so a class list never leaves your computer.

Scores go in as percentages. If your test was out of 40 points, convert first (or score it with the EZ grader). Standard deviation here is the population SD, dividing by the number of scores, since the class is the whole group being curved.

The four methods and their formulas

Flat curve

Curved = Score + c

Everyone gets the same number of points. You choose c so the top score reaches a target (often 100) or so the class mean does. The gaps between students don’t change at all, which makes it the easiest curve to explain.

Square root curve

Curved = 10 × √Score

No settings. A 64 becomes 80 and a 100 stays 100. It never lowers a score between 0 and 100, and it helps low scores far more than high ones, so it also shrinks the spread.

Linear scale

Curved = New mean + (Score − Mean) × (New top − New mean) ÷ (Top − Mean)

This pins two points: the class mean moves to your new mean, and the top score moves to your new top. Everything else slides along a straight line between them. If the multiplier is above 1, the spread widens, and that can push the lowest scores down.

Bell curve (z-score)

z = (Score − Mean) ÷ SD  →  Curved = New mean + z × New SD

Each score keeps its position relative to the class, measured in standard deviations, and gets rebuilt on the mean and SD you choose. It’s the most flexible method, and the only one here that routinely lowers high scores.

Two worked examples

Both use the class already loaded in the calculator: 45, 52, 60, 64, 68, 72, 75, 80, 88, 96. The mean and median are both 70, and the SD is 14.89. On the percent scale that’s one A, two B’s, two C’s, one D and four F’s.

Flat +5 vs. square root. To bring the mean to 75, a flat curve adds 5 to everyone: the 45 becomes a 50 and the 96 becomes a 101, which the cap holds at 100. The square root curve is far kinder to the bottom: the 45 becomes 67.08, the 60 becomes 77.46, and the 96 becomes 97.98. The class mean jumps to 83.18, and the four F’s turn into a D+, a C-, a C+ and a B-.

Bell curve to a mean of 75 and an SD of 10. The 96 sits about 1.746 SDs above the mean, so it becomes 75 + 1.746 × 10 = 92.46. That’s lower than the student’s raw score, an A turned into an A-. The 88 slips to 87.09, while the 45 rises to 58.21. With relative letters (A at +1.5 SD, B at +0.5, C at −0.5, D at −1.5), the class splits into one A, two B’s, four C’s, two D’s and one F, no matter how hard the test was.

Comparing the methods

MethodCan it lower a score?Effect on the spread
Flat curveOnly if the shift is negativeUnchanged
Square rootNo, for scores 0–100Narrower; low scores gain most
Linear scaleYes, low scores if it stretchesWider or narrower, your choice
Bell curveYes, high or low scoresSet to the SD you pick

Square root curve at a glance:

Raw score253649506064708190100
Curved50607070.7177.468083.679094.87100

Can grades be curved down?

Yes, and it’s the part people miss about bell curves. A curve that targets a mean and SD doesn’t care whether the class did well. If everyone scored between 85 and 98, a bell curve with a mean of 75 drags the whole class down. Relative letters work the same way: with cutoffs set by SD, roughly the same share of the class lands in each letter whether the test was easy or brutal. Many teachers only curve up for that reason. If that’s your rule, tick “Never lower a score” and the tool keeps the higher of each student’s raw and curved score.

Before you curve

  • Small classes. In a class of 12, one very low or very high score moves the mean and SD a lot, so a bell curve can swing wildly. Flat and square root curves don’t depend on the rest of the class.
  • Extra credit. Scores above 100 are fine to enter. The cap applies to curved scores only, and “Never lower a score” keeps a raw 104 at 104.
  • Letter cutoffs. The percent letters use the standard plus/minus scale (93 for an A, 90 for an A-), the one on the methodology page. The distribution table groups them into whole letters.
  • School policy. Some schools limit or forbid curving, and many gradebooks have their own curve tools (Canvas has a Curve Grades option). Check before you post anything.

Once the curved test is in the gradebook, students can see what it does to their class grade with the grade calculator, or what’s left to earn on the last exam with the final grade calculator.

Frequently asked questions

How do you curve grades?

Pick a rule and apply it to every score. The simplest is a flat curve: add the same points to everyone, for example enough to bring the top score to 100. Other options are the square root curve (10 × √score), a linear scale to a new mean and top score, or a bell curve that sets a new mean and standard deviation.

What is a square root curve?

Each score becomes 10 times its square root. A 64 becomes 80, a 49 becomes 70, and a 100 stays 100. It lifts every score between 0 and 100, and it lifts the low ones the most, so a 36 gains 24 points while a 90 gains about 5.

How do I curve grades with a mean and standard deviation?

Turn each score into a z-score, (score − class mean) ÷ class SD, then rebuild it as new mean + z × new SD. In a class with a mean of 70 and an SD of 14.89, a 96 has a z of about 1.746; with a target mean of 75 and SD of 10, it becomes 75 + 17.46 = 92.46.

Can grades be curved down?

Yes. A flat curve with a negative shift, a linear scale that stretches the spread, or a bell curve with a lower mean or smaller SD than the class has will all lower some scores. Relative letter grades can also hand out fewer A’s than the raw percentages would. Tick “Never lower a score” to rule that out.

Which curve is the fairest?

It depends on what went wrong. If one question was broken, a flat curve treats everyone equally. If the whole test ran hard, a square root curve helps the students who struggled most. A bell curve is about rank, not mastery, so it’s the hardest to defend in a small class. Check your school’s grading policy first.

Does the curve change who ranks first?

No. All four methods here keep the order of the scores. A higher raw score always ends up with an equal or higher curved score. Capping at 100 can make top scores tie, but it never flips anyone’s order.