Grade Curve Calculator
Pick one rule (added points, 10 × √score or a bell curve) and this grade curve calculator applies it to every score, showing each letter before and after.
12 scores, add 5 points: class average 68 → 73
68 → 73
Class average before and after, 12 scores. Lowest 30 → 35, highest 95 → 100. 5 scores change letter.
Method: one curve rule applied to every score, chosen by the teacher · Examples: Lone Star College and university grading guidesLast verified Oct 19, 2026
Every score, before and after
| # | Before | After | Change | Letter |
|---|---|---|---|---|
| 1 | 30 | 35 | +5 | F |
| 2 | 50 | 55 | +5 | F |
| 3 | 56 | 61 | +5 | F → D |
| 4 | 60 | 65 | +5 | D |
| 5 | 64 | 69 | +5 | D |
| 6 | 68 | 73 | +5 | D → C |
| 7 | 72 | 77 | +5 | C |
| 8 | 75 | 80 | +5 | C → B |
| 9 | 78 | 83 | +5 | C → B |
| 10 | 82 | 87 | +5 | B |
| 11 | 86 | 91 | +5 | B → A |
| 12 | 95 | 100 | +5 | A |
Show the math
| Rule | Every score + 5 points |
|---|---|
| Average before | 68 (12 scores) |
| Average after | 73, no score above 100 |
| Largest safe setting | +5 points: keeps every score at or under 100 and the order unchanged |
| Letters | the default scale |
Grade curve at a glance
- Flat curve
- Add the same number of points to every score
- Percentage curve
- Raise every score by the same percentage (50 becomes 55 with 10%)
- Top-score curve
- Add the gap between the top score and the maximum to every score
- Target-average curve
- Shift every score by the same amount so the class average reaches a target
- Bell curve rescale (a common teacher method)
- New score = target average + (score − class average) × target spread ÷ class spread
Sources: University of Edinburgh, Registry Services (Student Systems), Lone Star College, Virtual Teaching Assistance Center, University of Warwick, Department of Physics, University of Maryland, Baltimore County (instructor course page)
How the square root curve calculator works: 10 × √score
The square-root curve gives each student 10 × the square root of their percent score, so 49 becomes 70, 64 becomes 80 and 81 becomes 90, while 100 stays 100. Scores well below 100 gain the most, a score of 100 or less never passes 100, and the order never changes. It is a common teacher method, not an official standard; a University of Washington math course used it as √(70N) out of 70.
Source: University of Washington, Department of Mathematics (instructor course page)
Good to know
- Choose a number of points that keeps every score at or under 100 instead of leaning on the cap. On scores of 96, 97 and 98, +5 with the cap makes three 100s and ties three students who were apart; +2 keeps them apart. The calculator shows the largest safe add.
- Adding the top score's gap is a flat curve sized by your best student. In Lone Star College's example the top is 180 of 200, so everyone gets 20 points; one near-perfect paper means almost no curve for the rest of the class.
Common questions
What is grading on a curve?
In the strict sense, it means grading each student by where they stand relative to the class, usually on the normal (bell) curve, as a Cal State Fullerton psychology instructor's page explains. Teachers also say “curve” for one simpler fix applied to every score, such as adding 5 points so 50 becomes 55.
Sources: California State University, Fullerton (instructor teaching page, Psych 101), University of Edinburgh, Registry Services (Student Systems)
How to curve a test with one simple rule
Pick one rule, apply it to every score and check that none passes the maximum. You can add the same points (5 points: 50 becomes 55), add the gap between the top score and the maximum (Lone Star College: 200 − 180 = 20), or use the square-root curve, 10 × √score.
Sources: University of Edinburgh, Registry Services (Student Systems), Lone Star College, Virtual Teaching Assistance Center, University of Washington, Department of Mathematics (instructor course page)
How to curve grades fairly, by one university's scaling policy
The University of Southampton's scaling policy sets two tests: the students' rank order after the curve must be the same as before, and scores should not be curved just to reach a desired average. Every curve here keeps the order unless the cap ties scores. The target-average and bell curves do set an average, so use them to correct a test that came out harder than usual, as one physics department shifts a paper to its group's usual average, not to hit a number picked in advance.
Sources: University of Southampton, University of Warwick, Department of Physics
Can a curved score go above 100?
Your school's rules decide. Exeter's and Southampton's scaling policies (two UK universities) say no: one allows no score above 100 or below 0, the other allows adding points only if none then goes over 100. If a curve would push a score past the maximum, the calculator warns and shows the largest add that keeps every score at or under it; a score that was already above the maximum keeps its starting score.
Does a curve change the class average?
Yes. Adding the same points to every score raises the class average by those points unless some scores are stopped at the maximum; in one physics department's example, a paper averaging 68% was shifted up to 73%.
What is a top-score curve?
Every score gets the gap between the top score and the maximum. In Lone Star College's example the top score is 180 out of 200, so everyone gets 20 points.
Source: Lone Star College, Virtual Teaching Assistance Center
Can a bell curve lower a score?
Yes. The UMBC course page that uses this rescale notes it can lower some grades, especially ones far above the class average; that happens when the spread you set is smaller than the class's own spread. The calculator says how many scores go down.
Source: University of Maryland, Baltimore County (instructor course page)
More details
| What | Value | Source |
|---|---|---|
| How the result is worked out | One rule applied to every score, such as adding the same points or raising every score by a percentage | University of Edinburgh, Registry Services (Student Systems) |
| A scaling rule must cover | Every raw score, from 0 to 100 | University of Southampton |
| A target-average shift, worked example | A paper averaging 68% shifted up to the group's usual 73% | University of Warwick, Department of Physics |
| Square-root curve (a common teacher method) | New score = √(score × maximum), which is 10 × √score on a 100-point test | University of Washington, Department of Mathematics (instructor course page) |
| A bell-curve rescale can lower a score far above average (UMBC) | Yes | University of Maryland, Baltimore County (instructor course page) |
| What 'grading on the curve' means (a Cal State Fullerton psychology instructor's page) | Grading each student by where they stand relative to the class; the curve is usually the normal (bell) distribution | California State University, Fullerton (instructor teaching page, Psych 101) |
| No curved score above 100 or below 0 (a UK university's scaling guidance) | Yes | University of Exeter |
| Curving must keep the students' rank order (a UK university's scaling policy) | Yes | University of Southampton |
| Adding points that push a score past 100 breaks that rank-order rule (same policy) | Yes | |
| What curving is for (same policy) | Fixed standards (criterion-referenced), not reaching a desired class average | |
| Lowest percent for an A (default scale) | 90% | South Carolina Department of Education |
| Lowest percent for a D (default scale) | 60% |
Common values
Each row curves a made-up class list out of 100 unless it says otherwise, with no curved score above the maximum. Letters are on the default scale (A from 90%, B from 80%, C from 70%, D from 60%, F below 60%).
| Scores and curve | Class average, before → after | Lowest and highest, before → after; letters changed |
|---|---|---|
| 12 scores averaging 68, add 5 points | 68 → 73 | 30 → 35, 95 → 100; 5 |
| 12 scores averaging 68, target average 70 | 68 → 70 | 30 → 32, 95 → 97; 2 |
| 12 scores averaging 68, square-root curve | 68 → 81.7 | 30 → 54.77, 95 → 97.47; 10 |
| Quiz out of 20 (top score 17), top-score gap | 13.4 → 16.4 | 9 → 12, 17 → 20; 8 |
| Hard test (45 to 80), add 10 points | 64.6 → 74.6 | 45 → 55, 80 → 90; 9 |
| Hard test (45 to 80), top-score gap | 64.6 → 84.6 | 45 → 65, 80 → 100; 10 |
| Hard test (45 to 80), raise 20% | 64.6 → 77.5 | 45 → 54, 80 → 96; 9 |
| Hard test (45 to 80), bell curve to average 75, spread 15 | 64.6 → 75 | 45 → 46.61, 80 → 97.31; 7 |
| Top scores 96, 97, 98, add 5 points (capping ties them) | 85.2 → 89 | 60 → 65, 98 → 100; 1 (3 stopped at 100) |
| Top scores 96, 97, 98, add 2 points (the largest safe add) | 85.2 → 87.2 | 60 → 62, 98 → 100; 0 |
Grade distribution calculator results: letters before and after the curve
How many of the calculator's scores get each letter before and after the curve, on the default scale (A from 90%, B from 80%, C from 70%, D from 60%, F below 60%). It starts on a made-up example class with 5 points added to every score and follows the scores and curve you enter; scale edits change only the calculator's own table.
| Letter | Before the curve | After the curve |
|---|---|---|
| A (90–100%) | 1 (8%) | 2 (17%) |
| B (80–89%) | 2 (17%) | 3 (25%) |
| C (70–79%) | 3 (25%) | 2 (17%) |
| D (60–69%) | 3 (25%) | 3 (25%) |
| F (0–59%) | 3 (25%) | 2 (17%) |
How it works
The curve you pick is applied to every score in the list, and every method keeps the students' order. Flat, percent, top-score and square-root curves raise every score by a fixed rule; the target-average and bell curves set the class average you choose (the bell also sets the spread), which is closer to grading on the curve in the strict sense. Capping at the maximum can tie students who were apart, so when a curve would push a score past the maximum, the calculator says so and gives the largest setting that keeps every score inside the range.
Flat: new score = old score + the points you add. Percent: new = old × (1 + the percent ÷ 100). Top score: new = old + (maximum − top score), a gap never below 0. Square root: new = 10 × √old, out of 100. Target average: new = old + (your target − the class average). Bell: new = your target + the spread you set × (old − the class average) ÷ the class's spread.
- Paste the scores and set the test's maximum (100 for percents).
- Pick a curve and its setting (points to add, percent, target average, or target average and spread).
- The tool curves each score and shows the change and the letter before and after.
- With the square-root curve, a 49 becomes 70 (10 × 7), a 64 becomes 80 and an 81 becomes 90; 100 stays 100.
- If a score would pass the maximum, the result says so and gives the largest add (or percent, target or spread) that keeps every score inside the range. With the cap ticked, scores stop at the maximum, which can tie students who were apart; a score already above the maximum keeps its starting score, because the cap never lowers one.
A flat curve: add 5 points
- Add 5 points to every score
- 50 → 55
- 30 → 35
Every score up 5 points, none above 100
Related: grade percentage calculator
What this doesn't account for
- Your school's or department's own curving rules
- Curves that taper near 0 and 100, and bell curves that hand out letters by fixed shares of the class (this tool rescales the scores; the letters still come from the scale)
- Rounding curved scores to whole numbers
Sources
- Mark Scaling by Linear or Percentage Adjustment
- Scaling Policy (Quality Handbook, last updated August 2023)
- Chapter 5 – Annex 1: Post-hoc Mark Scaling Guidance (TQA Manual)
- Add a Curve Using Adjusted Grade
- Mark Scaling in Physics (October 2025)
- South Carolina Uniform Grading Policy (May 14, 2019)
- Mathematics 504 (course page, 2003)
- Three Systems for Grading
- Generic Grade Description
Verified by
Checked by CountOnTools against its official sources on Oct 19, 2026. How we verify
Before and after this step
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