Square Root Curve


A square root curve is designed to be easy to use and has the advantage of helping the lower scores more than the higher scores, if that’s an advantage to you. It’s also dead simple to do.

Let’s look at a couple of examples. Jimmy gets a raw score of 75 on a test.

\(\Large \begin{align} \mbox{Score} &= 10 \times \sqrt{\mbox{Raw Score}} \\ &= 10 \times \sqrt{75} \\ &= 10 \times 8.66 \\ &= 86.60 \\  &= 87\% \end{align}\)

Sue does very poorly and makes a raw score of 25.

\(\Large \begin{align} \mbox{Score} &= 10 \times \sqrt{\mbox{Raw Score}} \\ &= 10 \times \sqrt{25} \\ &= 10 \times 5 \\ &= 50 \\  &= 50\% \end{align}\)

You’ll notice that Jimmy’s score went up 12 points but Sue’s score went up 25 points. While Sue still has a poor grade, her grade did go up more than Jimmy’s.

Square Root Curve Calculator

If you have a set of grades to calculate, and don’t want to do it by hand, you can use the following form to calculate the grades of your students on a square root curve by entering their grades in the box below. You only need to enter one of each grades if there are multiples of the same score. Duplicates are stripped out.

Should you use it?

Using the square root curve, or any curve, is a question you have to answer for yourself.

One of my favorite administrator lines ever is “grades are totally at the teacher’s purview.” Of course it was to a student that went in to dispute their grade, so not a fun situation. But it did tell me that even though the student earns their points, a teacher has the option of working the numbers as they see fit. If you see fit to curve a set of grades, or not, that’s your decision.

Personally, I’ve used a square root curve a couple of times. I prefer to use a linear grade distribution instead, scaling the top grade to a 100 and the low grade to a 50; assuming that there are grades under a 50.

And Thanks

Thanks goes out to Dave Richeson at DivisByZero.com for the start for this calculator. His post goes over several curve types, including my personal favorite the gravity curve, and also discusses why you would curve an exam.

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2 thoughts on “Square Root Curve

  1. I am trying to use the square root calculator that I have used before but the place to put in the total # of questions is missing.

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