FreeTools by FunnyTools.win 繁中

Normalized Score Converter

🔒 Local only Education & Statistics Tools

Linearly convert a raw score to a target mean and standard deviation.

Standardize a raw score to z, then map it to a target mean and standard deviation. This is a linear standard-score conversion; it does not make a skewed distribution normal.

Tool area

Formula and calculation

z = (X − M) / SD; Y = Mₜ + z × SDₜ

First compute z on the original scale, then use target mean Mₜ and target SD SDₜ to obtain Y. Both SDs must be positive.

Educational applications

Useful for teaching and transformations under a shared reference framework. Scores from tests with different constructs, reliability, or norms are not automatically interchangeable after rescaling.

APA / research reporting tip

Example: “Scores were standardized using the original M = 70 and SD = 8, then transformed to a scale with M = 50 and SD = 10.” Report the converted value.

How to use

  1. Enter the raw score, original mean, and original SD.
  2. Set the target mean and target SD.
  3. Calculate z and the converted score.

Use cases

  • Place different test results on a common scale.
  • Model a mean-50, SD-10 score.
  • Teach the effect of linear standardization.

FAQ

Does this normalize the distribution?
It performs linear standardization and does not change distribution shape. Percentile-based normalizing requires the full distribution.
Can this produce T scores?
Yes. Set target mean to 50 and target SD to 10.
Can converted scores be extreme?
Yes. A linear transformation has no fixed bounds.

Related tools

Z Score CalculatorConvert a raw score into standard deviations from the mean.Calculator🔒 Local onlyUse NowNewestT Score CalculatorConvert a z score to a T score with mean 50 and SD 10.Calculator🔒 Local onlyUse NowNewestPercentile Rank CalculatorCalculate percentile rank from counts below and equal to a score.Calculator🔒 Local onlyUse NowNewestGrade Average CalculatorCalculate simple and weighted averages from grade entries.Calculator🔒 Local onlyUse NowNewestWeighted Average CalculatorCalculate a weighted mean from values and weights.Calculator🔒 Local onlyUse NowNewestClass Rank Percentile CalculatorEstimate class-rank percentile from rank and class size.Calculator🔒 Local onlyUse NowNewest

Privacy & local processing

🔒 This tool runs entirely in your browser. No data is uploaded to any server.

All input and calculations stay in your browser and are not uploaded to FreeTools.

Trust & usage note

This tool runs mainly in your browser. Your input is not actively uploaded to a server. Avoid entering highly sensitive data. Results are for reference only.

Disclaimer

This tool is for teaching and preliminary estimates. It does not replace formal statistical software or professional judgment. Verify the data, research design, and assumptions before reporting results.

Last updated:

Embed this tool