Same information, friendlier numbers
A z-score says how many standard deviations a value sits from its mean, with a sign and decimals: z = 1.5. The T-score rescales that onto a metric with mean 50 and standard deviation 10: T = 50 + 10z. Nothing is added and nothing is lost; each T maps back to exactly one z, and through it to one percentile. The rescale exists for readers, not for maths: T-scores land in a 20-to-80 band for almost all real data, carry no minus signs, and need no decimals to be readable, which is why clinical and educational reports (bone-density scans report T-scores; so do many school assessments) prefer them.
A mark of 85 on a test with mean 70 and SD 10 gives z = 1.5, hence T = 50 + 15 = 65, the 93.32nd percentile. Read off the ladder: z = 0 is T = 50, z = 1 is T = 60, z = −2 is T = 30. On the IQ-style metric (mean 100, SD 15) the same performance is 100 + 15 × 1.5 = 122.5. Three numbers, one performance, and converting between them is always the same two steps: back to z, then out to the new scale.
The other T in the room
Capital T also names Student's t distribution and the t statistic, and the collision causes real confusion in search results and textbooks. The T-score on this page is a rescaled score, fixed at mean 50 and SD 10, with no distribution and no hypothesis attached. The t statistic is a ratio built from sample data that follows the t distribution under a null hypothesis. If your source mentions degrees of freedom, it means the statistic; if it mentions a mean of 50, it means this score.
Comparing T-scores across tests with different reference groups. A T of 65 means "1.5 SD above the mean of the norming group". If two tests normed on different populations, the same T is not the same performance.
Frequently asked questions
What is the formula for a T-score?
T = 50 + 10z, where z = (x - mean)/SD. Mean maps to 50, each standard deviation is worth 10 points.
What T-score is average?
50 exactly, by construction. Scores from 40 to 60 cover the middle band within one standard deviation of the mean.
Is a T-score the same as a t statistic?
No. A T-score is a rescaled measurement (mean 50, SD 10). A t statistic is a hypothesis-test ratio with degrees of freedom. The names collide; the objects do not.