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The Linear Grade Curve

The linear curve is the workhorse of grade adjustment: it stretches or shifts the score range so the class lands where you want it, while keeping every student in the same relative order. It's the easiest method to explain and the hardest to argue with.

What is a linear curve?

A linear curve applies a straight-line transformation to every score. In its simplest form it adds a constant; in its more useful form it rescales the range so the lowest score lands on a target minimum and the highest stays at the maximum, mapping everyone in between proportionally. Because the relationship is linear, the gaps between students shrink or grow by the same factor — nobody jumps ahead of anyone they trailed.

The linear curve formula

curved = (score − min) / (max − min) × (top − target) + target

Here min and max are the lowest and highest raw scores, target is the minimum you want the bottom score to reach, and top is your maximum grade. A common variant simply adjusts the whole class to hit a chosen target mean, or lifts the top score up to 100% and shifts everyone with it.

A worked example

Suppose raw scores range from 48 to 86 and you want the lowest to become 60 while the highest reaches 100:

• 48 → 60  (the new floor)
• 67 → 80  (mapped proportionally through the middle)
• 86 → 100  (the new ceiling)

Every student moves up, the spacing between them scales uniformly, and the ranking is untouched. That predictability is exactly why linear curves are so easy to defend to students and administrators alike.

When should you use a linear curve?

• The test was a bit harder than planned and you want a clean, across-the-board correction.
• You want maximum transparency — a straight-line rule is trivial to explain.
• There are no extreme outliers that would distort the rescaling.

If a single very low score is dragging the floor, or you specifically want to help strugglers more than top scorers, a square root curve is a better fit. If you need consistent distributions across large sections, consider bell curve grading.

Linear vs. flat curve

A flat curve adds the same number of points to everyone — simple, but top students can hit the ceiling and lose the benefit. A linear curve rescales instead of shifting, so it can stretch the range to fill the whole scale without clipping at the top. For the full comparison, read our pillar guide on how to curve grades.

Apply a linear curve in seconds

Choose how you want to anchor the curve — add fixed points, adjust to the highest grade, or reach a target mean — paste your scores, and review the impact before you commit. Export a CSV straight into your gradebook.

Try the Linear Curve Calculator →

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