Linear Grade Curve Calculator
A linear grade distribution rescales an entire set of raw scores so the lowest grade maps to a minimum you choose and the highest grade maps to a maximum you choose. Every other score lands proportionally in between. If your class topped out at 88% but you want the best score to be 100%, this calculator handles the math automatically.
Grade Curve Calculator
Enter grades below — one per line. Duplicates are ignored. Set your desired minimum and maximum scaled scores, then click Calculate.
How to Use This Calculator
- Enter your raw scores in the Grades box, one score per line.
- Set Minimum — the score the lowest raw grade will be mapped to (default: 50).
- Set Maximum — the score the highest raw grade will be mapped to (default: 100).
- Click Calculate to see the adjusted score for every unique grade.
- Duplicate scores are filtered out automatically; entering them once is enough.
The minimum and maximum you set define the output range — the raw scores are stretched or compressed to fit within that window.
How the Linear Grade Curve Works
A linear distribution scales scores proportionally. The highest raw score becomes your set maximum. The lowest raw score becomes your set minimum. Everything else is interpolated along a straight line between those two endpoints.
The Formula
$$
\Large
\text{Score} = Y_0 + \frac{Y_1 - Y_0}{X_1 - X_0} \times (Z - X_0)
$$
where
$$
\Large
\begin{align}
Z &= \text{Student's Raw Score} \\
Y_0 &= \text{Scaled Max Score} \\
Y_1 &= \text{Scaled Min Score} \\
X_0 &= \text{Raw Max Score} \\
X_1 &= \text{Raw Min Score}
\end{align}
$$
Worked Example
A test is graded with scores ranging from 55% (lowest) to 96% (highest). You want to rescale to a range of 60–100%. Jimmy's raw score is 72%.
$$
\Large
\begin{align}
\text{Score} &= Y_0 + \frac{Y_1 - Y_0}{X_1 - X_0)} \times (Z - X_0) \\
&= 100 + \frac{60 - 100}{55 - 96} \times (72 - 96) \\
&= 100 + \frac{-40}{-41} \times -24 \\
&= 100 + 0.9756 \times -24 \\
&= 100 - 23.4144 \\
&= 76.5856 \\
&= 77 %
\end{align}
$$
Jimmy's score moves from 72% to 77% after the curve.
Using Excel?
Once you enter grades and press Calculate, the formula below updates with your actual values. You can copy it directly into Excel — replace ActualScore with a reference to the cell containing each student's raw score.
=SUM(scaled_max + ((scaled_min - scaled_max) / (raw_min - raw_max)) * (ActualScore - raw_max))
The scaled_min, scaled_max, raw_min, and raw_max values come from your inputs. ActualScore is the cell reference for the student's raw grade.
When to Use a Linear Grade Curve
A linear distribution is a good choice when:
- The class performed consistently but the overall range is lower than you'd like
- You want to preserve the relative differences between students (nobody swaps rank)
- You need a transparent, explainable method — students can verify their own scaled score
- You want control over both the floor and the ceiling of the scaled range
It's less appropriate when you want to give extra help to lower scores — for that, a square root curve is usually better, since it provides a larger boost to lower values.
Handling Outliers
Be careful with extreme outliers. If one student scores a 12% and the rest of the class is clustered around 65–90%, including that 12 in the calculation will skew the entire distribution — everyone else's ceiling gets inflated to compensate.
In that case: exclude the outlier from the calculation, run the curve on the remaining scores, then manually assign the outlier the same score as the next-lowest result.
Is a Linear Curve Fair?
It depends on who you ask. Students whose grades increase will call it fair; those whose scores are already near the top may see less benefit. The distribution is mathematically neutral — no student's rank changes, and relative score gaps are preserved.
The key is consistency and communication. If you apply a curve, explain how it works before returning papers. Students who understand the method are far less likely to contest results.
Frequently Asked Questions
Does every student's score go up with a linear curve?
Not necessarily. If you set the minimum above the lowest raw score, that student goes up — but students near the top may gain only a point or two. It's possible for scores near the maximum to stay nearly the same.
Can I set the minimum above 50?
Yes. The minimum and maximum fields accept any value. You could scale from 70 to 100, or 0 to 90 — whatever fits your grading policy.
What if two students have the same raw score?
They'll receive the same adjusted score. The calculator deduplicates grades in the output table, but the formula applies identically to everyone with the same raw score.
What happens if everyone gets the same score?
The calculator needs at least two distinct scores to compute a distribution. If all scores are equal, there's no range to scale and the formula can't run.
Does this change the rank order of students?
No. A linear transformation preserves rank order — if Student A scored higher than Student B before the curve, they'll still score higher after.
Can I use a maximum higher than 100?
Yes. If you want the top score to be 105 for extra credit purposes, just enter 105 in the Maximum field.
How is this different from adding a flat bonus?
A flat bonus (e.g., +10 to everyone) shifts all scores up by the same amount. A linear curve stretches the distribution — low scores move up more than high scores when the minimum floor is raised.
What's the difference between this and a square root curve?
A linear curve maps scores proportionally — the relationship between any two students' scores stays the same. A square root curve is non-linear and disproportionately boosts lower scores.
Source
The formula for this calculator came from eHow.
