Grading Curve Calculator
Choose an arithmetic transformation for a score list. Inspect the formula, compare original and final distributions, and export every result with any cap changes made explicit.
Scores and chosen transformation
Paste up to 10,000 numeric scores, separated by commas, spaces or newlines. Use decimals, not labels, percentages or fractions. Input numbers support six decimal places and absolute values up to 1,000,000. Values outside zero to the maximum remain valid arithmetic inputs.
The maximum is a reference value until you enable the upper cap. There is no lower floor: negative results remain negative. Target-mean mode adds the same offset to every score; capping can reduce the achieved mean. A zero or negative multiplier is allowed in linear mode. These are user-chosen arithmetic operations, not grade recommendations.
Applied formula
raw = (1) × score + (5); final = raw
Formula coefficients and scores above round to six decimals. Exact multiplier: 1/1; exact offset: 5/1. Calculations use those exact fractions. Small nonzero results can round to zero.
Final scores below zero: 0. Final scores above the stated maximum: 0. These counts describe the output; they do not assign categories or performance judgments.
Before and after distribution
Blue: original · Teal: final
Ten equal-width bins cover zero, the stated maximum, and every original and final score. Both distributions share these boundaries. Each bin includes its lower endpoint and excludes its upper endpoint; bin 10 also includes the final upper endpoint. Tables scroll horizontally on narrow screens; the compact mobile chart shows every bin.
Inspect bin ranges and counts
| Bin | Range | Original | Final |
|---|---|---|---|
| 1 | [0, 10) | 0 | 0 |
| 2 | [10, 20) | 0 | 0 |
| 3 | [20, 30) | 0 | 0 |
| 4 | [30, 40) | 0 | 0 |
| 5 | [40, 50) | 0 | 0 |
| 6 | [50, 60) | 0 | 0 |
| 7 | [60, 70) | 1 | 1 |
| 8 | [70, 80) | 1 | 1 |
| 9 | [80, 90) | 1 | 1 |
| 10 | [90, 100] | 2 | 2 |
Range labels use up to 16 decimals. The TXT summary includes exact boundary fractions.
Every calculated score
| Row | Before | Raw transform | Final | Change | Cap applied |
|---|---|---|---|---|---|
| 1 | 60 | 65 | 65 | 5 | No |
| 2 | 70 | 75 | 75 | 5 | No |
| 3 | 80 | 85 | 85 | 5 | No |
| 4 | 90 | 95 | 95 | 5 | No |
| 5 | 95 | 100 | 100 | 5 | No |
Rows retain input order. Highlighted rows had the upper cap applied. The table pages through 50 scores at a time; exports include all scores.
CSV contains before/raw/final/change values, cap flags and exact raw/final fractions. The readable formula uses rounded coefficients; exact coefficients appear in the summary.
Arithmetic worksheet using the selected formula and optional upper cap. No recommendation of grades or judgment of student performance. Calculations use exact fractions; score displays round to six decimals. Scores stay in your browser and are not automatically saved.
Common questions
- How does the additive curve work?
- The worksheet adds your chosen offset b to each score: y = x + b. Adding 5 to 60 and 80 produces 65 and 85. You choose the offset; the calculator does not recommend one.
- How does a target-mean transformation work?
- It calculates offset = target mean − original mean, then adds that offset to every score. Scores 60 and 80 average 70; choosing target 80 adds 10 and gives 70 and 90. The offset is calculated as an exact fraction before display rounding.
- How does the linear transformation differ?
- The linear option uses y = a × x + b, with your supplied multiplier a and offset b. A zero multiplier gives a constant result; a negative multiplier reverses order. These choices are permitted arithmetic operations, not grading recommendations.
- Does the maximum automatically limit scores?
- No. The maximum is a reference until you select the upper cap. With the cap enabled, final = min(raw transformed score, maximum). The worksheet shows raw and final scores and flags each capped row. It does not apply a lower floor, so negative values remain negative.
- Why does the final mean differ from the target?
- The target-mean formula reaches the target before capping. An upper cap can reduce the achieved mean. For example, transforming 60 and 80 to target 100 gives raw scores 90 and 110. A cap of 100 changes the final scores to 90 and 100, with a final mean of 95.
- How are the before and after charts compared?
- Both distributions use the same ten equal-width bins spanning zero, the stated maximum and all original and final scores. Bins include the lower boundary and exclude the upper boundary, except the last bin also includes its upper boundary. The bin table and exported summary show ranges and counts.
- What are the input and export limits?
- Paste up to 10,000 numeric scores. Input values support six decimal places and absolute values up to 1,000,000; the maximum must be positive. Results use exact fractions internally and score displays round to six decimals. CSV exports every row with before, raw, final and change values, cap flags and exact fractions. The table displays 50 rows per page.
- Does this judge performance or recommend grades?
- No. It applies only the arithmetic transformation you select and does not rank students, assign letter grades or classify proficiency. Scores remain in the browser and are not automatically saved. Export the results before leaving.
Arithmetic worksheet using the selected formula and optional upper cap. No recommendation of grades or judgment of student performance. Calculations use exact fractions; score displays round to six decimals.