Flat points
Add the same number of points
Each raw score receives a fixed increase. The displayed result is capped at 100%.
Formula result = raw + points
Example 72 + 5 = 77%
Parameter Points to add
Grading tools
Grade Curve Calculator
Compare common ways to curve a grade and see how the same raw score changes under each method.
Compare methods
02Methods
How each grading curve works
Square root curve
Transform the raw percentage
The square root transformation gives lower scores a larger numerical increase.
Formula result = 10 × √raw
Example 72 → approximately 84.9%
Parameter None
Open the full Square Root Curve Calculator →Scale highest score to 100
Multiply every score by one factor
All scores are multiplied by the same factor based on the highest score.
Formula result = raw × (100 / highest score)
Example 72 × (100 / 90) = 80%
Parameter Highest score in class
Add top-score gap
Add the same gap to every score
The difference between the highest score and 100 is added to every score.
Formula result = raw + (100 − highest score)
Example 72 + (100 − 90) = 82%
Parameter Highest score in class
03Worked comparison
One raw score, four different results
Raw score: 64% · Points added: 5 · Highest score: 80%
| Method | Arithmetic | Result |
|---|---|---|
| Flat points | 64 + 5 | 69% |
| Square root | 10 × √64 | 80% |
| Scale highest to 100 | 64 × (100 / 80) | 80% |
| Add top-score gap | gap = 100 − 80 = 20; 64 + 20 | 84% |
04Definition
What is a grade curve?
Curving a grade broadly means applying a defined adjustment or mathematical transformation to a raw grade. The phrase alone does not identify the formula; the specific method and any required parameter must be stated.
05Reference
Which grade curve should I use?
Match the calculation to the grading policy that was actually specified.
| If the instructor says | Use |
|---|---|
| “Add 5 points” | Flat points |
| “The highest grade becomes 100 and everyone is scaled proportionally” | Scale highest score to 100 |
| “Add the difference between the highest score and 100” | Add top-score gap |
| “Use a square root curve” | Square root method |
| “Bell curve,” “normal distribution,” or “z-score” | A different distribution-based method; not calculated here |
Check our calculation methodology, caps and validation rules. For the specialist method, see the searchable square root curve table and printable chartor review the formula and worked examples.
When Should You Curve a Test?
Start with the assessment and the published grading policy. A low average alone does not identify the cause or tell you which adjustment to use.
| Situation | What to review before adjusting grades |
|---|---|
| A flawed question or marking error | Review the affected responses and apply a consistent correction under your policy. Regrading or removing an item may be more appropriate than transforming the whole test. |
| The class average is unexpectedly low | Check answer keys, question difficulty, time limits and coverage of taught material. If the scores reflect learning gaps, consider feedback or reassessment rather than assuming a curve solves them. |
| The instructor specifies a curve | Use that exact method and its stated parameters. Compare several low, middle and high scores before applying it to the class. |
How can you curve grades fairly?
Explain the reason, formula, cap and rounding rule, then apply the agreed policy consistently. Preserving rank order alone does not establish fairness: square root curving changes score gaps, while capping can make different scores tie at 100%.
Compare the effects: 25% → 50% gains 25 percentage points, while 81% → 90% gains 9. Whether that adjustment is appropriate depends on what the assessment was intended to measure.
How much should you add?
Enter the approved adjustment in percentage points. Adding 5 to 72% gives 77%. On a 50-point test, adding 5 earned marks instead equals 10 percentage points; normalize the scores before using this calculator.
For highest-score methods, enter the actual class high as a percentage. With a high of 90%, a raw 72% becomes 80% by proportional scaling or 82% by adding the top-score gap.
Will a curve reach a target class average?
These four methods do not automatically choose an adjustment to reach a target average. Without caps, adding 5 percentage points moves a mean of 65% to 70%; if some scores hit 100%, the increase can be smaller.
For a square root curve, calculate each score before averaging. Curving the class mean gives a different result: scores of 25% and 81% curve to 50% and 90%, averaging 70%, while curving their raw mean of 53% gives about 72.8%.
Check the square root curve for a whole classCheck the original scores first
Use percentages consistently, apply the curve once, and round only at the end. Keep an unadjusted copy so you can explain each result and check it against the instructor’s policy.
See common square root curve mistakes06Questions
Grade Curve Calculator FAQ
What is a grade curve calculator?
It compares a raw grade with the result of a specified grading adjustment or transformation.
How do you calculate a curved grade?
Apply the exact formula or point adjustment stated by the instructor to the raw grade.
What is a flat grade curve?
A fixed number of points is added to every raw score, usually with results capped at 100%.
How does scaling the highest score to 100 work?
Multiply each raw score by 100 ÷ highest score.
Is scaling to the highest score the same as adding points?
No. Scaling multiplies scores by a factor; adding points applies the same numerical increase.
What is a square root grading curve?
It transforms a raw percentage with 10 × √raw grade.
Is a grade curve the same as a bell curve?
No. A bell curve uses the class distribution; many grade curves use fixed arithmetic transformations.
Can a curved grade go above 100?
Some uncapped formulas can. This calculator caps flat-point and top-score-gap results at 100%.