What this calculator does
Curve a set of test scores and see each student's grade before and after. When a test turns out harder than planned, a teacher may curve the scores. That means adjusting every result by the same rule, so grades better reflect what students actually learned.
There's no single correct curve. This calculator applies four of the most common methods to a list of scores you paste in. It shows each score before and after.
The simplest methods add points. They add either enough to lift the highest score to 100, or enough to move the class average to a target. The square-root curve lifts low scores more than high ones, while 0 and 100 stay where they are. The most statistical method rescales the whole set of scores to a chosen average and standard deviation (a measure of how spread out scores are). That's what people usually mean by curving to a bell curve.
Where it's used
Why this math matters outside the classroom:
- Adding points. When the top score is 88, adding 12 points to every score raises the top score to 100.
- Square-root curve. The 10√x curve turns a 64 into an 80 and an 81 into a 90, helping lower scores more than higher ones.
- Target average. Teachers rescale scores so the class average and spread match chosen values while keeping students in the same order.
- Comparing methods. A before-and-after table shows how each curve changes the class average and the spread of scores.
How to use it
- Paste the scores, as percentages, separated by commas, spaces or new lines.
- Pick a curve method and enter its target: the new top score, the target average, or the target average and standard deviation.
- For the methods based on the average, choose whether to keep curved scores between 0 and 100.
- Compare the original and curved averages. Then check the table for each student's change.
What the inputs mean
- Scores (percent)
- Each score as a percentage of the test, such as 74 or 81.5. The table keeps the same order, so you can match rows to students.
- Top score becomes
- What the highest score should become. It's usually 100, but some teachers raise the top score to 95 or 98.
- Target average
- The class average you want after the curve, in percent.
- Target standard deviation
- How spread out the curved scores should be. About 10 points is common. A smaller value bunches scores closer to the average.
- Keep curved scores between 0 and 100
- When this is on, any curved score above 100 is held at 100, and any below 0 is held at 0. This can leave the average slightly off the target.
Formula and method
Top score: curved = x + (target − highest score) Square root: curved = 10 × √x Shift: curved = x + (target average − average) Scale: curved = target average + target SD × (x − average) ÷ SD
x is one student's original score. √ is the square root. SD is the standard deviation, roughly the typical distance of a score from the class average.
The two methods that add points move every score up by the same amount. So the gaps between students, and the standard deviation, stay the same. Raising the top score to 100 is easy to explain. But one unusually high score can mean almost no curve for everyone else.
The square-root curve works on a 0–100 scale. A 49 becomes 10 × 7 = 70 and a 64 becomes 80, while 100 stays 100. Low scores gain the most, and the order of students never changes.
The scaling method first turns each score into a z-score, (x − average) ÷ SD. That says how many standard deviations the score sits above or below the class average. Then it places that z-score on the new average and SD.
The SD here is the population SD, because the class is the whole group being graded. It isn't a sample from a larger group.
Worked example
Ten students score 52, 61, 68, 70, 74, 77, 79, 83, 85 and 88. The teacher raises the top score to 100.
- Original average: 737 ÷ 10 = 73.7.
- Points to add: 100 − 88 = 12.
- Each score gains 12, so 52 becomes 64 and 88 becomes 100.
- Curved average: 857 ÷ 10 = 85.7. The standard deviation stays at about 10.66, because every score moved by the same amount.
Result: The class average rises from 73.70 to 85.70. With the scaling method and a target of 75 with SD 10 instead, the 52 becomes about 54.64 and the 88 about 88.42.
Understanding the result
The 'Average points added' result shows how generous the curve is overall. The table shows that some methods help low scorers more than high scorers.
Curves that add points keep the spread, so the curved SD matches the original. The square-root curve narrows the spread, and the scaling method sets it to your target.
If the curved average isn't exactly the target, some scores were held at 0 or 100. Turn off the limit to see the scores without it.
Assumptions and limitations
- Scores are percentages on a 0–100 scale. Curves that add points also work on raw points, though.
- The list holds the whole class, so the population standard deviation is used.
- Every student is curved by the same rule.
- A curve is a policy choice, not a statistical fact. This calculator shows the math, not which method is fair for a given class.
- Very small classes give shaky averages and standard deviations. So scaling methods can behave unexpectedly.
- Letter grades aren't assigned here. The test grade calculator applies letter cut-offs to a single score.
Frequently asked questions
Which curve method is the fairest?
It depends on the goal. Adding a flat amount keeps the gaps between students and is easy to explain. The square-root curve helps the students who struggled most. Scaling to a target average and SD is the closest to grading on a bell curve. But it fixes how many students land far above or below the average.
Can a curve lower someone's score?
The top-score method refuses to, and the square-root curve never lowers a score between 0 and 100. Shifting or scaling can lower scores if the target average is below the current one. A high scorer can also be pulled down by a smaller target SD.
Why does the square-root curve stop at 100?
Because 10 × √100 = 100. The method was designed for percentages. It keeps 0 at 0 and 100 at 100, and bends the scores in between upward. Scores above 100 or below 0 don't fit that design, so they're rejected.
Why population standard deviation and not sample?
The sample formula divides by n − 1, where n is the number of scores. It's meant for guessing the spread of a larger group from a sample. Here the class is the complete set of scores being curved. So dividing by n describes it exactly.
How this calculator is checked
Method: Standard curving methods: additive shifts, the 10√x transform, and a linear z-score rescaling using the population standard deviation. The calculation is covered by automated tests with known reference values and edge cases. Last updated 2026-10-18. Found a problem? Tell us.
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