Grade Curve Calculator
Curve a whole class of test scores with a flat curve, a curve to the top score, a square-root curve or a bell curve.
To curve grades, apply the same rule to every student’s score. The most common method scales scores so the highest becomes 100%: multiply each score by 100 ÷ the highest score. For example, if the top score is 88%, every score is multiplied by 100 ÷ 88 = 1.136, so a 72% becomes 81.82%.
- Scale to top: score × (100 ÷ highest score).
- Flat curve: add the same number of points to every score.
- Square root: 10 × √percent. Bell curve: target mean + z × target SD.
How to Use the Grade Curve Calculator
- Paste the class scores into the box, separated by commas, spaces or new lines (points or percentages).
- Set the points possible (100 for percentages, or the test total).
- Choose a curving method and its setting, such as the points to add or the target average.
- Read the table with each student’s original and curved grade, the change and the new letter grade.
Grade Curving Methods and Formulas
1. Curve to the highest score (scale)
The top score becomes 100% (or another target) and everyone is raised by the same proportion. Low scores gain fewer points than high scores.
2. Flat curve
Everyone gets the same number of points. Teachers often add the difference between 100 and the top score.
3. Raise the class average
A flat curve sized so the class average lands on a target such as 75% or 80%.
4. Square-root curve
Gives the biggest boost to low scores and little to high scores. 100% stays 100%.
5. Bell curve (normal distribution)
Grades are set by each student’s position relative to the class. This calculator uses the population standard deviation. Letters can also be given by z-score bands: A at +1.5 SD or more, B from +0.5, C from −0.5, D from −1.5 and F below that.
Worked Example: Five Scores, Four Curves
Scores of 58%, 65%, 72%, 80% and 88% (class mean 72.6%, SD 10.61):
| Original | Flat +12 | Scale to top (× 100/88) | Square root | Bell (mean 75, SD 10) |
|---|---|---|---|---|
| 58% | 70% | 65.91% | 76.16% | 61.24% |
| 65% | 77% | 73.86% | 80.62% | 67.84% |
| 72% | 84% | 81.82% | 84.85% | 74.43% |
| 80% | 92% | 90.91% | 89.44% | 81.97% |
| 88% | 100% | 100% | 93.81% | 89.51% |
The flat curve and the scale curve both bring the top score to 100%, but the flat curve helps the lowest score more. The square-root curve lifts the bottom of the class the most.
Which Curve Should You Use?
| Goal | Method |
|---|---|
| Top student should get 100% | Scale to the highest score, or flat curve by (100 − top score) |
| Same boost for everyone | Flat curve |
| Class average should hit a target | Raise the class average |
| Help struggling students most | Square-root curve |
| Grade by rank within the class | Bell curve |
Tips for Curving Test Grades Fairly
- Decide the rule before you look at names. Apply one method to the whole class.
- Explain the method to students. Flat and scale curves are the easiest to understand.
- Check for an outlier. One very high score makes a scale-to-top curve small; consider using the second-highest score as the target.
- Cap at 100% unless your policy allows extra credit.
- Keep the letter scale consistent. Use the same grade scale for curved and uncurved work.
For a step-by-step guide with more examples, read how to curve test grades. To see where a student ranks in the class, use the percentile calculator, and to grade a test before curving, use the easy grader.
Frequently Asked Questions
How do you curve grades?
Pick a method, then apply it to every score. The most common is curving to the highest score: divide 100 by the top score and multiply every score by that number, so the top student gets 100%.
What is the fairest way to curve a test?
A flat curve (adding the same points to everyone) is the easiest to explain and keeps the gaps between students the same. Curving to the top score is also popular because the best student ends at 100%.
How does a bell curve work for grades?
Each score is turned into a z-score (how many standard deviations it is from the class average). The new grade is the target average plus z times the target spread, or letters are given by z-score bands.
What is a square-root curve?
Take the square root of the percentage and multiply by 10. It helps low scores the most: 49% becomes 70%, 64% becomes 80%, and 100% stays 100%.
Can curving lower a grade?
A flat or scale-to-top curve never lowers a grade. A bell curve can, because students above the average may be pulled toward the target average if the target spread is smaller than the class spread.
How many points should I curve a test?
Many teachers add enough points to bring the top score to 100%, or to bring the class average to a target such as 75–80%. Choose a rule before you look at individual students to keep it fair.
Should curved grades go above 100%?
Most teachers cap curved grades at 100%. Leave the cap off only if your grading policy allows extra credit.
Add This Grade Curve Calculator to Your Website
Teachers and schools can add this grade curve calculator to their own page. Copy the code and paste it into an HTML or embed block on your class site, LMS page, LibGuide or Google Site. It is free and needs no sign-up. See all free calculator widgets.
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