# How does the grade curve work?

Curves a test score three ways: a flat curve that adds points, a scale that multiplies, or a linear curve that maps the class’s lowest and highest scores onto a new range.

- Page: https://www.acalculator.org/education/grade-curve-calculator
- JSON spec: https://www.acalculator.org/education/grade-curve-calculator.json
- Version: e637649bf889

## Default answer

Example with the default inputs (Curve Flat (add points), Your score (points) 75, Points possible 100, Highest score in the class 92, Curve the top score to 100%): Your curved grade is 83.00%.

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| m | Curve | Flat adds the same points to everyone; scale multiplies; linear stretches the low-to-high range. |
| s | Your score (points) | The points you scored on the test. |
| t | Points possible | The most points the test allows; 100 when scores are percents. |
| h | Highest score in the class | The top score anyone got, in points. |
| l | Lowest score in the class | The lowest score anyone got, in points. |
| ty | Curve the top score to | The percent the highest score becomes; usually 100%. |
| by | Curve the lowest score to | The percent the lowest score becomes. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| curved | Curved grade | Your grade after the curve, as a percent to 2 decimal places. |
| raw | Raw grade | Score ÷ points possible × 100, before the curve, to 2 decimal places. |
| curvedPoints | Curved score (points) | The curved percent of the points possible. |
| added | Points added | Curved points minus your points. |
| rule | Rule | The curve as a formula on percents. |

## Method

Raw % = score ÷ points possible × 100, and top % the same for the highest score. Flat: curved % = raw % + (target − top %). Scale: curved % = raw % × target ÷ top %. Linear: curved % = new low + (target − new low) ÷ (top % − low %) × (raw % − low %).

## Assumptions

- Every score is on the same test, out of the same points possible; your score is at most the highest score.
- A curve can give more than 100% if you set the target above 100%; nothing is capped.
- Values are taken exactly as typed; percents are shown to 2 decimal places, halves away from zero.

## Worked examples

1. m = flat, s = 75, t = 100, h = 92, ty = 100% gives curved = 83.00%, raw = 75.00%, curvedPoints = 83, added = 8. Source: CompSci.rocks, Should you grade on a curve? (flat curve: subtract the highest score from a perfect score and add the difference to everyone; linear distribution: Score = Y₀ + [(Y₁ − Y₀)/(X₁ − X₀)] × (Z − X₀), 72% with scores 55 to 96 curved to 60 to 100 is about 77%), https://compsci.rocks/blog/curve-grades/ (retrieved 2026-10-05).
2. m = linear, s = 72, t = 100, h = 96, l = 55, ty = 100%, by = 60% gives curved = 76.59%, curvedPoints = 76.585366, added = 4.585366. Source: CompSci.rocks, Should you grade on a curve? (flat curve: subtract the highest score from a perfect score and add the difference to everyone; linear distribution: Score = Y₀ + [(Y₁ − Y₀)/(X₁ − X₀)] × (Z − X₀), 72% with scores 55 to 96 curved to 60 to 100 is about 77%), https://compsci.rocks/blog/curve-grades/ (retrieved 2026-10-05).
3. m = scale, s = 34, t = 40, h = 38, ty = 100% gives curved = 89.47%, raw = 85.00%, curvedPoints = 35.789474. Source: CompSci.rocks, Should you grade on a curve? (flat curve: subtract the highest score from a perfect score and add the difference to everyone; linear distribution: Score = Y₀ + [(Y₁ − Y₀)/(X₁ − X₀)] × (Z − X₀), 72% with scores 55 to 96 curved to 60 to 100 is about 77%), https://compsci.rocks/blog/curve-grades/ (retrieved 2026-10-05).
4. m = linear, s = 156, t = 200, h = 194, l = 0, ty = 100%, by = 23.5% gives curvedPoints = 170.030928, curved = 85.02%. Source: Texas A&M, Math 467 grades page (a linear curve: scores × 0.79 + 47 raise the top score 194 to 200 and the median 156 to 170), https://people.tamu.edu/~fulling/m467/s09/grades.html (retrieved 2026-10-05); CompSci.rocks, Should you grade on a curve? (flat curve: subtract the highest score from a perfect score and add the difference to everyone; linear distribution: Score = Y₀ + [(Y₁ − Y₀)/(X₁ − X₀)] × (Z − X₀), 72% with scores 55 to 96 curved to 60 to 100 is about 77%), https://compsci.rocks/blog/curve-grades/ (retrieved 2026-10-05).

## FAQ

### How does a flat curve work?

Find how far the top score is from 100% and add that to everyone. If the top score is 92%, everyone gets 8 points: a 75% becomes 83%.

### What is the difference between a flat curve and a scale?

A flat curve adds the same points to everyone. A scale multiplies, so the top score lands on 100% and every score keeps its ratio to it: with a top of 95%, 85% becomes 85 × 100 ÷ 95 = 89.47%. A scale adds fewer points to low scores.

### How does a linear curve work?

It stretches the range of scores. The lowest score is moved to a new low (say 60%) and the highest to a new high (say 100%), and every score in between keeps its place. With scores from 55% to 96%, a 72% becomes 60 + 40 ÷ 41 × 17 = 76.59%.

### Does a curve ever lower a score?

Not when the target is at least the top score’s percent, which is the usual case. A linear curve can lower some scores only if the new low is below the old lowest percent or the target is below the old top percent.

### Can a curved grade be over 100%?

Only if you set the target for the top score above 100%. With a target of 100%, the top score becomes exactly 100% and no one goes over.

### What about the square root curve?

It is a fourth rule: 10 × √(raw %), so 64% becomes 80%. The square root curve calculator does it.

## Sources

- CompSci.rocks, Should you grade on a curve?: the flat curve (subtract the highest score from a perfect score and add the difference to every score) and the linear distribution, Score = Y₀ + [(Y₁ − Y₀)/(X₁ − X₀)] × (Z − X₀), with 72% on scores from 55 to 96 curved to 60 to 100 giving about 77%. Retrieved 2026-10-05. https://compsci.rocks/blog/curve-grades/
- Texas A&M University, Math 467 grades page: a linear curve that multiplies scores by 0.79 and adds 47, raising the top score 194 to 200 and the median 156 to 170. Retrieved 2026-10-05. https://people.tamu.edu/~fulling/m467/s09/grades.html