T-Score Calculator From Raw Score to the 50 ± 10 Metric
Standardize any test score to the T metric used across psychology and education — with the z-score and percentile shown alongside.
What is a T-score?
A standardized score with mean 50 and SD 10
A T-score expresses where a score sits within its norm group on a scale with mean 50 and standard deviation 10. According to the APA Dictionary of Psychology, it is computed by rescaling the z-score — T = 50 + 10z — so typical scores land between 20 and 80 and negative values disappear. Most psychological and educational test norms report T-scores.
The conversion has two steps. First the raw score is standardized: the z-score measures how many standard deviations it lies above or below the norm-group mean. Then the z-score is rescaled to the T metric, which simply moves the mean to 50 and stretches one standard deviation to 10 points. Because the rescaling is linear, the percentile is unchanged — a T-score of 65 and a z-score of 1.5 describe exactly the same position in the distribution.
T = 50 + 10 × z, where z = (x − μ) / σInterpretation follows the normal model: T-scores between 40 and 60 (within one SD of the mean) cover the middle two-thirds of the norm group and count as the average range. On many clinical scales, such as the ASEBA and MMPI families, T-scores from 65 upward are flagged as borderline and 70 or more (two SD above the mean) as clinically elevated — always check the convention of the specific instrument.
Three unrelated numbers share the name, and mixing them up is the most common mistake. The psychometric T-score computed here rescales a z-score to the 50 ± 10 metric. A bone-density T-score from a DXA scan is different: it reports how many standard deviations your bone mineral density lies below the young-adult reference mean, with no 50 + 10 rescaling. According to the NIH's National Institute of Arthritis and Musculoskeletal and Skin Diseases, values down to −1.0 are normal, −1.0 to −2.5 indicates low bone mass, and −2.5 or lower indicates osteoporosis — your DXA report states this number directly, and its interpretation belongs with your physician. Finally, a t-statistic is a hypothesis-testing quantity; for that, use our t-statistic calculator and convert it to a p-value with the p-value calculator.
Accuracy and scope
Results are for informational purposes. A T-score is only as meaningful as its norm group — the mean and SD must come from a reference population that fits the person being scored (right age band, right test version). The percentile assumes scores are approximately normally distributed, which most published norms are constructed to satisfy. This tool does not interpret medical bone-density values.