Grade Curve Calculator
Paste a whole class or type one score, pick a curve, and this grade curve calculator shows every score before and after with the spread drawn underneath. Seven methods are built in, from adding flat points to fitting a bell curve. If the grade you are working out has not been curved at all, start with the standard grade calculator.
Paste your scores, pick a curve, and every score is recalculated as you type. Nothing here is a rule: your school decides whether a curve is allowed and which one it uses.
For the methods that need a class average, fill in the class figures below.
Class statistics, before and after
How the spread moves
Every score, before and after
Runs in your browser. Nothing is sent or stored. Each method is ordinary arithmetic and the formula for the one you picked is shown with the result, so you can check it by hand. Whether a curve is applied at all, and which one, is set by your instructor or your department, so treat any number here as an estimate until the grade is published.
Free to use, no sign-up, and every calculation happens in your browser.
How to use this grade curve calculator
The calculator opens on a whole class, because that is where a curve is decided. If you are a teacher working out what a curve would do to a set of results before they go in the gradebook, stay on this tab. Switch to the one-score tab if you are a student working out what a curve did to your own result.
- Put the raw test scores in. Paste them from a spreadsheet or type them separated by commas, spaces or new lines. Anything that is not a number is ignored.
- Pick a curve. Seven are built in. Three of them need no settings at all; the other four ask for one or two numbers.
- Read the three figures. The curved average, how far it moved, and how many scores were counted. Underneath, every score appears before and after, and the chart shows what happened to the shape of the class.
The cap at 100 is on to begin with. Turn it off and you will see the raw arithmetic, including any score that lands above 100, which is a real outcome of some methods rather than a bug.
Seven ways to curve a grade, and what each one does
A curve is any rule that turns a set of raw scores into a set of adjusted ones. The rules below are not variations on a theme. They are different arithmetic, and on the same class they produce answers more than seventeen points apart.
Flat points added to every score
The simplest one: pick a number and add it to everybody.
A five-point flat curve moves a 38 to 43 and an 88 to 93. Every score moves by the same amount, so the gaps between students are exactly what they were. It is the only method here that leaves the spread of the class untouched.
A percentage increase on every score
Multiply instead of add.
A ten percent increase gives a 38 an extra 3.8 points and an 88 an extra 8.8. That is the opposite of what people expect a curve to do: the higher scores gain more, in points, than the lower ones, and the class spreads out rather than tightening.
Scale the top score to 100
Find the highest score, treat it as a perfect score, and scale everything to match.
If the best score in the room was 88, everything is divided by 88 and multiplied by 100. This is the method that most obviously depends on one person: if the top score had been 95 rather than 88, everyone else would gain less.
Linear rescale to a new range
Also called a linear curve or linear scaling. Stretch the whole class onto a range you choose, so the lowest score lands on your new floor and the highest on your new ceiling.
Rescaling 38 to 88 onto 60 to 100 puts the bottom of the class exactly on a pass and the top exactly on 100. It is the most interventionist option on this page, and it guarantees that somebody scores 100.
The square root curve
Take the square root of the score and multiply by ten.
A 49 becomes a 70; an 81 becomes a 90; a 100 stays a 100. This is the method sometimes called the Texas curve, and its appeal is that it gives the largest lift where the scores are lowest and almost none at the top. On the class in the example below, it adds 23.6 points to a 38 and 5.8 points to an 88.
The cube root curve
The same idea, turned up.
A 64 becomes 86.2 where the square root would have made it 80. The cube root lifts harder everywhere and compresses the class more, which is either the point or the problem depending on what the scores were meant to show.
The bell curve, using mean and standard deviation
The only method here that is genuinely statistical. Each score is converted to a z-score, which is how many standard deviations it sits from the class average, and then rebuilt on a distribution you specify.
Set the target average to 80 and the target standard deviation to 10, and the class comes out centered on 80 with a predictable spread, whatever it looked like before. Rank order never changes: the best score before is the best score after. This is what people mean by fitting grades to a normal distribution, though the arithmetic only shifts and stretches the class. If the scores were not bell shaped to begin with, they are not bell shaped afterwards.
Fitting scores to a bell shape is the method with the most baggage attached to it, and the section below on whether your school curves at all is mostly about this one.
Square root and cube root are the same curve
These two get written as separate methods everywhere, and they are not. Both are the same power curve with a different exponent:
Set n to 2 and you have the square root curve. Set it to 3 and you have the cube root. That is why both leave a perfect score alone, since one raised to any power is still one, and why the cube root always lifts more than the square root between zero and 100. Seeing them as one family also makes the trade-off obvious: the larger n gets, the more the bottom of the class rises and the less a raw score tells you about the student.
One class, seven curves
These are the twelve scores the calculator starts with, from a class that averaged 62.75 on a hard exam. Every figure below comes from running that same class through each method.
| Method | New average | Change | A 38 becomes | An 88 becomes | Spread |
|---|---|---|---|---|---|
| No curve | 62.8 | 0 | 38.0 | 88.0 | 13.9 |
| Add 5 points | 67.8 | +5.0 | 43.0 | 93.0 | 13.9 |
| Increase by 10% | 69.0 | +6.3 | 41.8 | 96.8 | 15.3 |
| Top score to 100 | 71.3 | +8.6 | 43.2 | 100.0 | 15.8 |
| Square root | 78.7 | +16.0 | 61.6 | 93.8 | 8.9 |
| Linear onto 60 to 100 | 79.8 | +17.0 | 60.0 | 100.0 | 11.1 |
| Bell, target 80 and 10 | 80.0 | +17.3 | 62.2 | 98.2 | 10.0 |
| Cube root | 85.1 | +22.4 | 72.4 | 95.8 | 6.5 |
The last column is the one to look at, because it is the one a single-method calculator cannot show you. A flat five points leaves the spread at 13.9, exactly where it started. A ten percent increase and a scale to the top score both make the class wider, at 15.3 and 15.8. The root curves pull it in hard, to 8.9 and 6.5. Two curves can move the average by a similar amount and do completely different things to the distance between students.
Where the square root curve puts its help. Same class, score by score:
| Raw | Curved | Lift |
|---|---|---|
| 38 | 61.6 | +23.6 |
| 51 | 71.4 | +20.4 |
| 62 | 78.7 | +16.7 |
| 74 | 86.0 | +12.0 |
| 88 | 93.8 | +5.8 |
The bottom of the class gets four times the lift the top does. If what you want is to rescue a failing group without handing the strongest students a free ten points, that shape is the reason to pick it.
When a curve lowers a grade
Curving is talked about as though it can only help. It does not always. Two things are worth knowing before you apply a curve: a curve pointed below the class average takes points off every score, and the cap at 100 can quietly hide what a method really produced.
A bell curve set below where the class already is. Take a class that did well, averaging 88.25. The twelve scores are 72, 79, 83, 85, 87, 88, 90, 91, 93, 95, 97 and 99. Paste those in, pick the bell curve and set the target average to 75. Every one of the twelve scores comes down: a 72 lands at 53.1 and a 99 lands at 89.5. Nothing went wrong in the arithmetic. A z-score curve moves the class to wherever you point it, and if you point below the class average, that is down. The rule is simple enough to check before you apply it: if the target average is lower than the real one, the curve is a deduction.
A cap that hides an overflow. Fit that same class to a target average of 85 with a standard deviation of 15, and two scores come out above the ceiling: the 97 reaches 102.7 and the 99 reaches 106.7. With the cap on, they both read 100, which looks tidy and quietly erases the gap between them. The calculator tells you how many scores hit the cap for exactly that reason, and turning the cap off shows you what the method really produced.
Whether your school curves at all
Before any of this matters, the question is whether your course uses a curve, and that is a syllabus question rather than a math one. Curving is not a default.
The teaching blog of Johns Hopkins University, The Innovative Instructor, sets out the definition plainly. Writing in 2013, Michael J. Reese described it this way:
Curving defines grades according to the distribution of student scores… Often called norm-referenced grading, curving assigns grades to students based on their performance relative to the class as a whole.
That last phrase is the whole argument. Under a norm-referenced scheme your grade depends on the people sitting around you as much as on what you knew. The same publication returned to the subject in 2016. Writing there, Macie Hall put the case against it by quoting Adam Grant:
By limiting the number of students who can excel, other students who may have mastered the course content are unfairly punished.
The practical version for a student is short. Find the grading section of your syllabus. If it describes a fixed distribution or a set number of each grade, you are in a norm-referenced course and the calculator above is modeling something real. If it lists percentage cutoffs and says nothing about distribution, your grade is measured against the standard rather than against the room. That is criterion-referenced grading, the opposite of the norm-referenced scheme above, and under it a curve is at your instructor’s discretion rather than a rule.
Curving in a spreadsheet
If you would rather do this in Excel or Google Sheets, every method here is one formula. With raw scores in column A starting at A2:
| Method | Formula to paste in B2 |
|---|---|
| Add points | =A2+5 |
| Percent increase | =A2*1.1 |
| Top score to 100 | =A2/MAX($A$2:$A$13)*100 |
| Linear onto 60 to 100 | =60+(A2-MIN($A$2:$A$13))*40/(MAX($A$2:$A$13)-MIN($A$2:$A$13)) |
| Square root | =10*SQRT(A2) |
| Cube root | =100*(A2/100)^(1/3) |
| Bell, target 80 and 10 | =80+((A2-AVERAGE($A$2:$A$13))/STDEVP($A$2:$A$13))*10 |
Two things to watch. Use STDEVP rather than STDEV if the scores are the entire class rather than a sample of it. That is the population standard deviation, which is what the calculator above uses, and the two give different answers. And wrap anything in MIN(100, ...) only if you actually want the cap, because hiding an overflow in a spreadsheet is harder to spot than hiding one here.
Where to go next
A curve is applied to scores that already exist. The steps on either side of it live elsewhere on the site.
- Turning a set of right and wrong answers into a score is the step before this one, and scoring a test out of the questions missed is where that happens. A curve is applied after it, not instead of it.
- The bell curve method runs off the class average, and averaging a set of scores is how you get that figure.
- Banding a class by standard deviation instead of changing its scores is a different job, and the bell curve grade calculator does it: the cutoff for each letter, how many students land in each band, and the class drawn against the normal curve.
Frequently asked questions
What does grading on a curve mean?
It means your grade is set by comparing you with the rest of the class rather than against a fixed standard. Johns Hopkins’ teaching blog defines curving as assigning grades based on performance relative to the class as a whole, which is also called norm-referenced grading. In everyday use the phrase has drifted, and people say a test was curved when an instructor simply raised everyone’s score. Both meanings are on this page: the bell curve method is the strict one, and the other six are adjustments.
How do you calculate a curved grade?
Pick the rule first, because there is no single formula. Adding flat points is raw plus the number. A square root curve is ten times the square root of the raw score, so a 49 becomes a 70. A bell curve converts each score to a z-score, which is the distance from the class average measured in standard deviations, then rebuilds it on the average and spread you want. The calculator above shows the formula for whichever method you have selected, next to the result.
Can a curve lower my grade?
Yes, and two of the methods here can do it. A bell curve pointed at a target average below the class average brings every score down. Take the strong class on this page, which averages 88.25: fit it to a target of 75 and all twelve scores fall, with a 72 landing at 53.1. A linear rescale does the same if you set the new floor and ceiling below the scores the class already has. A norm-referenced course with a fixed number of each grade can also cost you a grade you would have earned on a fixed scale. Adding points, raising by a percentage and the root curves cannot lower anything.
Which curving method should I use?
It depends on what went wrong. If one question was unfair, add flat points, because it leaves every gap between students exactly as it was. If the whole paper was too hard at the bottom end, a square root curve puts the help where the low scores are and barely touches the top. If you need the class centered on a particular average, the bell method is the only one that lands there on purpose. If you want the strongest work to define the top of the scale, scale the top score to 100 and accept that one student now sets everyone else’s result.
What is the formula for a bell curve grade?
Two steps. First find the z-score: subtract the class average from the raw score and divide by the standard deviation. Then rebuild it: multiply the z-score by the standard deviation you want and add the average you want. A score sitting one standard deviation above its class average ends up one target standard deviation above the target average, whatever the raw numbers were. Rank order is preserved exactly, so the method redistributes scores without reordering anybody.
Can you curve grades in Excel?
Every method on this page is a single spreadsheet formula, and the table above lists all seven for Excel and Google Sheets. The one thing to get right is the standard deviation. Use STDEVP when the scores are the whole class and STDEV when they are a sample: the two return different numbers, and the bell curve result moves with them.
What happens if a curved score goes above 100?
Some methods produce scores above 100, and a bell curve with a generous target does it readily. Fit the strong class on this page to a target average of 85 with a standard deviation of 15, and it produces 102.7 and 106.7. The calculator caps at 100 by default and tells you how many scores hit the cap, because a cap quietly removes the difference between two students who were not actually equal. Turn the cap off to see what the arithmetic produced before the ceiling was applied.
Can I curve a single score instead of a whole class?
Yes. Switch to the one-score tab and enter your raw result. Four methods work from that alone: adding points, a percentage increase and the two root curves. The other three need to know something about the class, so fill in the average, the standard deviation, the top score or the bottom score, whichever your method asks for. If your instructor has told you the curve but not the class figures, the flat and root methods are the ones you can check yourself.
How much does a curve help your grade?
It depends entirely on the method, and the range is wide. On the twelve-score class above, a flat five points adds exactly 5 to everyone. A square root curve adds 23.6 points to a 38 and 5.8 points to an 88. A cube root curve moves the class average by 22.4 points. And a bell curve pointed below the class average subtracts instead. Ask which method is being used before assuming a curve helps you at all.