Linear Grade Distribution

This online grade curve 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 maximum. 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 a 88%, but you want to have the lowest score a 50% and the highest score a 100%. This page will allow you to enter your grades and it will rescale them to fit in that range.

Using the Grade Curve 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.


Using Excel?

Here's the formula if you want to punch it into Excel. Once you enter grades above and press the Calculate button the values will replace with what you entered.

=SUM(scaled_max + ((scaled_min - scaled_max) / (raw_min - raw_max)) * (ActualScore - raw_max))

The scaled_min, scaled_max, raw_min and raw_max are whatever the values you want them to be. ActualScore should be a reference to the field with the student's raw score.

Linear Distribution Equation

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

\text{Score} = Y_0 + \frac{Y_1 - Y_0}{X_1 - X_0} \times (Z - X_0)


Z &= \text{Student's Raw Score} \\
Y_0 &= \text{Scaled Max Score} \\
Y_1 &= \text{Scaled Min Score} \\
X_0 &= \text{Raw Max Score} \\
X_1 &= \text{Raw Min Score}

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 the max was a 96%.

\text{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 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 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 part of the scale it would scale everyone else up unfairly; and that's actually unfair, not a student's view of unfair. I'd toss the 12, calculate with a 67 as minimum, and then the 12 would manually scale to the same score as the 67.


The formula for this calculator came from eHow.

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