Calculator
The page uses a single-column layout overall, while the calculator fields adapt to 3, 2, or 1 columns by screen size.
Formula used
1) Linear rescaling
Scale Score = Smin + ((X - Xmin) / (Xmax - Xmin)) × (Smax - Smin)
Use this when a raw score must be stretched into a new reporting range such as 0–100, 200–800, or 1–9.
2) Raw score to z-score
z = (X - μ) / σ
This standardizes a score relative to its group mean and standard deviation, showing how far the value sits above or below average.
3) Z-score to target scale
Scale Score = Mtarget + z × SDtarget
This converts a standardized result into a familiar score system. The percentile is estimated from the normal distribution of the z-score.
How to use this calculator
Step-by-step use
- Select the scoring mode.
- Enter the required raw score, z-score, or range values.
- Set target mean, target deviation, or target scale limits.
- Choose rounding and optional clamping settings.
- Press Calculate scale score to show results above the form.
Helpful notes
- Use Linear rescaling for direct range conversion.
- Use Raw score to standard scale when mean and deviation are known.
- Use Direct z-score to scale when a z-score already exists.
- Export buttons save the current visible report as CSV or PDF.
Example data table
Sample conversion using raw mean = 50, raw standard deviation = 10, target mean = 100, and target standard deviation = 15.
| Raw Score | Mean | SD | Z-Score | Estimated Percentile | Scale Score |
|---|---|---|---|---|---|
| 35 | 50 | 10 | -1.50 | 6.68% | 77.50 |
| 45 | 50 | 10 | -0.50 | 30.85% | 92.50 |
| 50 | 50 | 10 | 0.00 | 50.00% | 100.00 |
| 60 | 50 | 10 | 1.00 | 84.13% | 115.00 |
| 70 | 50 | 10 | 2.00 | 97.72% | 130.00 |
FAQs
What is a scale score?
A scale score is a transformed value placed on a reporting scale. It lets scores be compared more consistently than raw totals, especially across versions, sections, or reporting periods.
When should I use linear rescaling?
Use linear rescaling when you only need to map one score range into another. It is ideal for grading bands, rubric conversion, and simple score normalization.
When is the standard score mode better?
Choose standard score mode when you know the raw mean and standard deviation. It preserves relative standing in the distribution before converting into a new score scale.
Does percentile equal percent correct?
No. Percent correct describes how many items were answered correctly. Percentile estimates the percentage of scores at or below a given point in a reference distribution.
What does reverse raw score mean?
Reverse scoring flips the direction of the raw scale. It is useful when lower original values should become higher converted values in the final reporting scale.
Why use clamping?
Clamping forces the final score to stay within a chosen band. This can be helpful when your reporting system does not allow values outside a defined scale.
Are these results official test-equated scores?
Not necessarily. Official scaled scores may use proprietary equating models, anchor items, or historical calibration. This calculator applies transparent statistical transformations you define.
Can I export the results?
Yes. After calculation, the page shows CSV and PDF buttons. They export the current visible report summary so you can save or share the output easily.