Quick answer
The standardised T-score is T = 50 + 10z, where z = (x − μ) ÷ σ. A raw score of 85 with mean 70 and SD 10 has z = 1.5 and T = 65.
Enter the raw score, mean and standard deviation. The calculator returns the T-score and z-score. Use this t-score (standardized) calculator to check your own figures.
Related tools: Z-Score Calculator: Standardize a value using a mean and standard deviation. Standard Deviation Calculator: Sample or population standard deviation with variance and mean. Mean Median Mode Range Calculator: Mean, median, mode and range of a data set.
How to use the T-Score (Standardized) Calculator
- Enter raw score.
- Enter mean.
- Enter standard deviation (above 0).
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Raw score | A number | — |
| Mean | A number | — |
| Standard deviation | A number | > 0 |
Formula and method
Formula
z = (x − μ) ÷ σ; T = 50 + 10z
IEEE-754 double precision; shown to at most 6 decimal places.
The T-score scale used in psychological and bone-density testing; it is not the t statistic of a t-test.
Worked examples
This example is verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Raw score = 85; Mean = 70; Standard deviation = 10.
| Result | Value |
|---|---|
| T-score | 65 |
| z-score | 1.5 |
The first line is the headline result (t-score). Below it the t-Score (Standardized) Calculator lists z-score, which describe the same case from other angles. IEEE-754 double precision; shown to at most 6 decimal places.
Why T-scores
T-scores avoid negatives and decimals by rescaling to mean 50 and SD 10, used in psychology and educational testing. A T of 65 is 1.5 SD above average, about the 93rd percentile.
Not a t-statistic
This T-score is unrelated to the t-statistic from t tests or the T-score in bone-density tests, which have their own definitions. σ must be positive.
How the result changes with raw score
Holding every other input at the first worked example, this table changes only raw score. It shows how sensitive the answer is to that one value; each row was produced by running this calculator.
| Raw score | T-score | z-score |
|---|---|---|
| 42.5 | 22.5 | -2.75 |
| 85 | 65 | 1.5 |
| 170 | 150 | 10 |
| 340 | 320 | 27 |
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Standard deviation: entering "0" shows "Standard deviation must be greater than 0." beside that field and no result.
Choosing between the T-Score (Standardized) Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Z-Score Calculator](/statistics/z-score-calculator/) | value, mean and standard deviation | Z-score |
| [Standard Deviation Calculator](/statistics/standard-deviation-calculator/) | data set and data type | Population standard deviation (σ) |
| [Mean Median Mode Range Calculator](/statistics/mean-median-mode-range-calculator/) | data set | Mean |
| [Median Calculator](/statistics/median-calculator/) | data set | Median |
| [Relative Standard Deviation Calculator](/statistics/relative-standard-deviation-calculator/) | data set and data type | Relative standard deviation |
Background: descriptive statistics
Population statistics divide by n and sample statistics divide by n − 1 (Bessel's correction), because a sample tends to understate variability. Use the population version when your data is every value in the group, and the sample version when it is a subset.
Defaults differ between tools, and so do quartile conventions, which can give slightly different values for small data sets; this page states the method it uses.
Assumptions and limitations
- σ > 0
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for standard deviation to confirm this.
Frequently asked questions
What T-score is average?
An average person has a T-score of 50, which corresponds to z = 0.
What is T for z = −1?
T = 50 + 10 × (−1) = 40.
Is T-score the same as a t-value?
No. This standardised T-score (mean 50, SD 10) is unrelated to the t-value from a t-test.
What does the T-Score (Standardized) Calculator calculate?
Convert a raw score to a standardized T-score (mean 50, SD 10). It returns T-score and z-score.
What formula does the T-Score (Standardized) Calculator use?
z = (x − μ) ÷ σ; T = 50 + 10z. The T-score scale used in psychological and bone-density testing; it is not the t statistic of a t-test.
What do I need to enter in the t-Score (Standardized) Calculator?
You enter Raw score, Mean and Standard deviation.
How is the result rounded or limited?
IEEE-754 double precision; shown to at most 6 decimal places. σ > 0.
What is an example of a t-Score (Standardized) result?
With raw score 85, mean 70 and standard deviation 10, the t-score is 65.
Related calculators
- Z-Score Calculator — Standardize a value using a mean and standard deviation.
- Standard Deviation Calculator — Sample or population standard deviation with variance and mean.
- Mean Median Mode Range Calculator — Mean, median, mode and range of a data set.
- Median Calculator — Median of a data set.
- Relative Standard Deviation Calculator — Relative standard deviation (RSD) as a percentage.
- Variance Calculator — Sample or population variance.
Sources
- NIST/SEMATECH e-Handbook of Statistical Methods (itl.nist.gov/div898/handbook)
- Standard textbook definitions (e.g. Moore, McCabe & Craig, Introduction to the Practice of Statistics)
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.