Test Curve Calculator

Raw average {{ resultsReady ? formatScore(computation.values.raw_average) : '—' }} Average shift {{ resultsReady ? formatDelta(computation.values.average_change) : '—' }} Scores changed {{ resultsReady ? computation.values.affected_count : '—' }}

Raw scores:

Paste one score per line or labelled CSV, up to 500 score rows.

Maximum raw score:

Use the same point total students were originally graded against.

points

Curve method:

The formula trail explains the selected method before any score is posted.

Points to add:

points

Percentage points to add:

Target class average:

Target curved range:

to points

Multiplier and offset:

× raw + points

Score cap:

The cap may be lower than, but not higher than, the maximum raw score.

points

Rounding rule:

Out-of-range score handling:

This policy affects only score rows below zero or above the declared maximum.

Grade-band minimums:

Example: A,90 then B,80. Thresholds classify results but do not change curved scores.

Curve audit

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Calculation method:

Review the method, cap, rounding, and score-row handling before using the curved values.

{{ row.label }}: {{ row.value }}; {{ row.note }}

Student	Raw	Curved	Change	Band	Copy
{{ row.label }}	{{ formatScore(row.raw_score) }}	{{ formatScore(row.curved_score) }}	{{ formatDelta(row.change) }}	{{ row.raw_band }} → {{ row.curved_band }}

A test curve changes the rule that maps raw points to reported points. It can compensate for an assessment that was harder than intended, align a class average with a stated target, or explore the effect of a proposed grading policy. It cannot show by itself that the policy is fair or that the test measured the intended knowledge.

Different curves answer different questions. Adding points gives every accepted score the same point change. Scaling the highest score to the maximum preserves score ratios. A square-root curve raises lower percentages more strongly than higher ones, while linear rescaling stretches the observed class range onto a chosen range. Those methods can produce very different rank gaps and grade-band movement even when their new averages look similar.

Practical differences between common test curve families
Curve family	What stays consistent	Main caution
Fixed or percentage-point lift	Every accepted score receives the same point increase	High scores may cluster at the cap
Target-average lift	The same offset is applied to the class	The target may be reached only before capping and rounding
Scale to top	Ratios between accepted scores	One unusually high or low top score controls the factor
Square root	Score order for nonnegative values	Lower percentages receive a larger relative lift
Linear rescale	Observed minimum and maximum map to chosen endpoints	Outliers define the whole mapping
Multiplier plus offset	A declared linear rule	It may lower scores or create many capped scores

Caps and rounding are policy decisions, not cosmetic details. A cap can compress several different raw scores into the same reported score. Whole-number rounding can move a student across a grade threshold, and floor or ceiling rules introduce a consistent downward or upward bias compared with nearest-value rounding.

Grade bands classify the curved percentages after the score calculation. They do not change the scores. A threshold of 90 means 90% and above belongs to that band; the next lower threshold receives values below 90% until the following boundary.

Before adopting a curve, examine the score distribution, assessment design, accommodations, institutional policy, and the effect on individual students. A transparent formula helps explain the change, but it does not replace academic judgment or a review of flawed questions.

How to Use This Tool:

Start with the same maximum score and raw-score source used for the original grading, then choose one curve policy to inspect.

Paste Raw scores as one number per line or labelled CSV. Up to 500 score rows are accepted.
Enter Maximum raw score, choose Curve method, and set the parameters for that method. The formula trail identifies the active rule.
Choose a Score cap, Rounding rule, and how scores below zero or above the maximum should be handled. Exclusion skips those rows; clamping changes them to the nearest valid endpoint before curving.
Review the accepted and skipped counts, average change, capped count, grade-band moves, and each score row. Correct malformed rows or unintended policy settings before posting grades.

Interpreting Results:

The curved average summarizes the class, but the score ledger shows who was affected and by how much. Review the lowest and highest curved scores, individual changes, cap hits, and grade-band moves together.

Skipped rows means a line was nonnumeric or was outside the allowed range under the exclusion policy. A clean average can still be misleading if valid students were skipped.
Scores capped counts unrounded curve results above the cap. Several cap hits indicate compression near the top.
Grade bands changed counts students whose band label changed after curving and rounding. Confirm the entered thresholds match the grading policy.
A target-average method applies the offset needed to reach the target before caps and rounding. The final curved average may differ when either rule changes individual scores.

Technical Details:

Each accepted raw score is transformed by the selected curve, restricted to zero through the score cap, and then rounded. Percentages are derived from the rounded score and the declared maximum before grade bands are assigned.

Formula Core

Let x be an accepted raw score, f(x) the selected curve, C the score cap, and R the chosen rounding rule. The reported score y is:

y = R (\min (C, \max (0, f (x))))

The active transformation uses the following exact rule. M is maximum raw score, μ is the accepted raw-score average, and x_min and x_max are the observed endpoints.

Exact formulas for each supported test curve method
Method	Curve before cap and rounding
Fixed-point lift	$f (x) = x + p$
Percentage-point lift	$f (x) = x + \frac{q}{100} M$
Target-average lift	$f (x) = x + (\frac{t}{100} M - μ)$
Scale highest to maximum	$f (x) = x \frac{M}{x_{\max}}$
Square-root curve	$f (x) = M \sqrt{\frac{x}{M}}$
Linear min/max rescale	$f (x) = L + \frac{(x - x_{\min}) (H - L)}{x_{\max} - x_{\min}}$
Multiplier plus offset	$f (x) = a x + b$

When all accepted scores are equal, linear rescaling returns the chosen high endpoint for every row because an observed span of zero cannot be divided. Scale-to-top requires at least one accepted score above zero.

Rule Core

Ordering and boundary rules for score parsing, capping, rounding, and grade bands
Stage	Exact behavior
Row parsing	Blank lines are ignored. A header is recognized from common score or student labels, and the numeric score column is selected from the header or the last numeric field.
Out-of-range input	Scores below 0 or above M are either excluded or clamped to the inclusive interval 0 to M.
Cap	The unrounded curve result is clamped to the inclusive interval 0 to C. The cap must be no greater than M.
Rounding	No rounding, nearest hundredth, nearest tenth, nearest whole, floor whole, or ceiling whole is applied after the cap. A non-whole cap followed by ceiling rounding can display the next whole point.
Percentage	Curved percent is 100 × y ÷ M.
Grade band	Thresholds are sorted highest to lowest; the first band whose minimum is less than or equal to the curved percentage wins. Values below every entered minimum receive Below lowest band.

Grade-band minima accept 0% through 100%, including both endpoints, and labels must be unique without regard to letter case. The source accepts at most 500 score rows, 20,000 characters of score text, and 2,000 characters of grade-band definitions. Averages use the final rounded scores, while the capped count compares the unrounded curve result with the cap.

Privacy and Policy Limits:

Score calculations run in the browser and the entered roster is not sent to a calculation service. Even so, student names and grades may be sensitive records.

Use anonymous labels when names are not necessary, especially on shared devices or during demonstrations.
Follow school policy for educational records, grade changes, accommodations, and approval of curve methods.
Review malformed and excluded rows before relying on class statistics.
Treat the result as a transparent simulation of the selected rule, not a recommendation that the rule is equitable.

Test Curve Calculator

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Curve audit

Calculation method:

How to Use This Tool:

Interpreting Results:

Technical Details:

Formula Core

Rule Core

Privacy and Policy Limits: