Linear Grade Distribution

This calculator allows a teacher to enter a series of grades and rescale them onto a linear grade distribution. A linear grade distribution takes the lowest grade, sets it equal to your set minimum; and takes the highest grade and sets it to your set maxiumum. Any other grades are scaled between these two points. For example, let’s say you give a test and the lowest score is a 30% and the highest is an 88%, but you want to have the lowest score a 50% and the highest a 100%. This page will allow you to enter your grades and it will rescale them to fit in that range.

Using the Calculator

Enter the grades in the box below, one per line. If you have more than one of a grade, you only have to enter it once, although it doesn’t change anything if you leave duplicates in. The calculator filters out duplicates. Enter the minimum and maximum grades for your distribution and press the Calculate button.

Linear Distribution Equation

If you would rather compute the linear grade distribution by hand, here is the formula that this page uses.

\(\large \mbox{Score} = Y_0 + \frac{Y_1 – Y_0}{X_1 – X_0} \times (Z – X_0)\)


Z &= \mbox{Student’s Raw Score} \\
Y_{0} &= \mbox{Scaled Max} \\
Y_{1} &= \mbox{Scaled Minimum} \\
X_{0} &= \mbox{Raw Max} \\
X_{1} &= \mbox{Raw Minimum}

Let’s say you gave a test and want scores to be distributed between 60 and 100%. Jimmy scores a raw 72%. The overall minimum score was a 55% and max was 96%.

\(\begin{align} \large  \mbox{Score} &= Y_0 + \frac{Y_1 – Y_0}{X_1 – X_0} \times (Z – X_0) \\
&= 100 + \frac{60 – 100}{55 – 96} \times (72 – 96) \\
&= 100 + \frac{-40}{-41} \times -24 \\
&= 100 + 0.9756 \times -24\\
&= 100  – 23.4144 \\
&= 76.5856 \\
&= 77\%

After scaling, Jimmy now has a 77% instead of his previous 72%.

Is a linear grade distribution curve fair?

Fair depends on who you ask. I’d bet that if you asked all of your students whether this curve type is fair the ones that had their grades go up would all consider it fair while the ones with lower grades after the curve would find it unfair.

The times that I’ve used this curve the scaled minimum was never below the raw minimum so everyone went up a bit. I’ve also left really low outliers out of the calculation and then manually changed them to the desired minimum grade.

For example, one student makes a 12% but the next lowest is a 67%. If the 12 was considered as part of the scale it would scale everyone else up unfairly; and that’s actual unfair, not a student’s version of unfair. I’d toss the 12, calculate with the 67 as minimum, and then the 12 would manually scale to the same score as the 67.


The forumla for this calculator came from eHow.

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