How to use the grade curve calculator

  1. Type or paste the raw scores into the box, one per line or separated by commas, semicolons or spaces. Use a decimal point, not a decimal comma.
  2. Set the maximum possible score of the test. The default is 100.
  3. Pick a curve method. For the flat curve and the boundary shift, enter k, the number of points (or percentage points) to use.
  4. Optionally press Raise the highest score to the maximum or Raise the class mean to the target. These two buttons only fill in k for the flat curve; you can still edit it.
  5. Check the letter scale. The defaults are A at 90 percent, B at 80, C at 70 and D at 60; change them to match your school.
  6. Read the table, the statistics and the chart. Then copy the curved scores, copy the whole table, or print the page. The print layout contains only the results.

How it works

Let raw be a student's score, max the maximum possible score and highest the best score in the class. The first three methods are:

flat: curved = raw + k
scale: curved = raw × max / highest
square root: curved = √(raw / max) × max

The flat curve adds the same k points to everyone. Raising the highest score to the maximum means k = max − highest; raising the class mean to a target means k = target − mean. The scale method multiplies every score by the same factor, so the best student gets exactly 100 percent and the order and the ratios between scores are kept. The square-root curve works on the fraction of the maximum: on a 100-point test it is simply 10 × √raw, and it lifts low scores much more than high ones. The boundary shift does not change a single score. It lowers each letter cutoff by k percentage points, so with k = 5 an A needs 85 percent instead of 90.

With the cap option on, a curved score is never allowed above the maximum or below 0. This matters for the flat curve, where adding points to a high score could otherwise exceed 100 percent. The scale and square-root methods never go above the maximum anyway.

A letter is chosen from the unrounded curved percentage, curved / max × 100, and compared with the cutoffs, so a curved score displayed as 89.99 never turns into a B by rounding. The statistics use the n scores entered: the mean, the median (the average of the two middle scores for an even n), the highest and lowest score and the sample standard deviation with n − 1 in the denominator. Displayed values are rounded half up to the chosen number of decimals; the change column is rounded separately from the curved scores.

Examples

Examples 1 to 4 use the scores 55, 62, 70, 78, 85 and 91 on a 100-point test. Their mean is 73.5 and the median is 74. With the default scale the letters are F, D, C, C, B, A.

Example 1: flat curve with k = 5. The new scores are 60, 67, 75, 83, 90 and 96, and the mean becomes 78.5. The letters are D, D, C, B, A, A. Raising the highest score to the maximum gives k = 100 − 91 = 9, and raising the mean to 80 gives k = 80 − 73.5 = 6.5.

Example 2: scale to the highest score. The factor is 100 / 91, so the scores become 60.44, 68.13, 76.92, 85.71, 93.41 and 100, with a mean of 80.77.

Example 3: square-root curve. The scores become 74.16, 78.74, 83.67, 88.32, 92.20 and 95.39, with a mean of 85.41. The letters are C, C, B, B, A, A. A 55 turns into 10 × √55 = 74.16, a gain of more than 19 points, while a 91 gains about 4.4.

Example 4: boundary shift of 5 points. The cutoffs become A 85, B 75, C 65 and D 55. The scores are unchanged, but the letters go from F, D, C, C, B, A to D, D, C, B, A, A. The 55 is now a D because it meets the lowered D cutoff of exactly 55.

Example 5: a different maximum. On a 50-point test with scores 34, 40 and 45, the square-root curve gives 41.23, 44.72 and 47.43, while scaling to the highest score gives 37.78, 44.44 and 50.

Which curve should you use?

The flat curve is the simplest to explain and is fair when the whole test was slightly too hard, because every student gains the same. Its drawback is that, with the cap on, the top students run into the maximum and the differences between them shrink. Scaling to the highest score keeps the ratios, but it depends on one student: one unusually high score shrinks the boost for everyone, and a single perfect score removes it completely. The square-root curve helps weaker students most and compresses the scale, so use it only when low scores are clearly a sign of a hard test and not of missing knowledge. Shifting the boundaries is the most transparent option, because the points stay as earned and only the meaning of the letters changes. Many teachers prefer it for that reason.

Common mistakes

  • Entering a decimal comma. Write 87.5, not 87,5; the comma is treated as a separator.
  • Forgetting the maximum. On a 40-point test, a score of 36 is 90 percent, so set the maximum to 40.
  • Comparing letters after rounding. The tool uses the unrounded percentage; if you round by hand first, a few borderline students can end up in a different grade.
  • Curving twice. Do not feed curved scores back in unless you really want a second curve.

Frequently asked questions

Is curving grades the same as grading on a bell curve?

No. In everyday use, curving means adjusting scores or cutoffs after a test. Grading on a bell curve means fixing the share of each letter in advance from a normal distribution. This calculator does the first and does not force any share of grades.

Can a curve lower a score?

With a positive k, the scale method or the square-root curve, no score goes down. A negative k lowers every score, and with the cap on the result never falls below 0.

What if one student scored above the maximum?

The page stops and names the score, because a value above the maximum is usually a typing error. Correct it or raise the maximum possible score, for example when the test had bonus points.

Why is the scale method unavailable when the highest score is 0?

It divides by the highest score, and division by zero has no result. If nobody scored a point, choose another method.

How is the standard deviation calculated?

It is the sample standard deviation: the square root of the sum of squared differences from the mean, divided by n − 1. With one score it is not defined, so the tool shows a dash.

Is my data stored or sent anywhere?

No. The calculation runs in your browser. Your scores and settings are kept only in your own browser's local storage so they are still there when you return; nothing is uploaded to a server.

Related tools