Linear Grade Distribution Calculator
This online grade curve calculator makes it a little easier to get your students' grades where you think they should be using a linear redistribution curve.
This online grade curve calculator lets you enter a set of grades and rescale them onto a linear grade distribution. A linear grade distribution takes the lowest grade and sets it equal to your chosen minimum, takes the highest grade and sets it to your chosen maximum, and scales every other grade proportionally in between.
For example, say you give a test and the lowest score is a 30% and the highest is an 88%, but you want the lowest score to become a 50% and the highest to become a 100%. Enter your grades below and it'll rescale them to fit that range.
Using the Grade Curve Calculator
Enter the grades in the box below, one per line. If you have more than one student with the same grade, you only have to enter it once — duplicates are filtered out automatically. Enter the minimum and maximum grades for your distribution and press Calculate.
Linear Distribution Equation
If you'd rather compute the linear grade distribution by hand, here is the formula this page uses.
\[Score = Y_0 + \frac{Y_1 - Y_0}{X_1 - X_0} \times (Z - X_0)\]where
\[\begin{align} Z &= \text{Student's Raw Score} \\ Y_0 &= \text{Scaled Max Score} \\ Y_1 &= \text{Scaled Min Score} \\ X_0 &= \text{Raw Max Score} \\ X_1 &= \text{Raw Min Score} \end{align}\]Let's say you gave a test and want scores distributed between 60% and 100%. Jimmy scores a raw 72%. The overall minimum score on the test was a 55% and the max was a 96%.
\[\begin{align} Score &= Y_0 + \frac{Y_1 - Y_0}{X_1 - X_0} \times (Z - X_0) \\ &= 100 + \frac{60 - 100}{55 - 96} \times (72 - 96) \\ &= 100 + \frac{-40}{-41} \times -24 \\ &= 100 + 0.9756 \times -24 \\ &= 100 - 23.4144 \\ &= 76.5856 \\ &= 77\% \end{align}\]After scaling, Jimmy now has a 77% instead of his previous 72%.
Using Excel?
Here's the formula if you want to punch this into a spreadsheet instead.
=SUM(scaled_max + ((scaled_min - scaled_max) / (raw_min - raw_max)) * (ActualScore - raw_max))scaled_min, scaled_max, raw_min, and raw_max are whatever values you want them to be. ActualScore should be a reference to the cell with the student's raw score.
Is a linear grade distribution fair?
Fair depends on who you ask. If you asked all of your students whether this curve type is fair, the ones whose grades went up would call it fair while the ones with lower grades after the curve would call 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, say one student makes a 12% but the next lowest is a 67%. If the 12 were included in the scale, it would scale everyone else up unfairly — and that's actually unfair, not just a student's perception of unfair. I'd toss the 12, calculate with the 67 as the minimum, and then manually set the 12 to the same score as the 67.
Source
The formula for this calculator came from eHow.