How to Calculate a T Score from a Z Score
T scores are z scores in a friendlier costume: the same information, rescaled to a mean of 50 and a standard deviation of 10 so that nobody has to read negatives or decimals. The conversion is one line — T = 50 + 10z — and it runs in both directions.
The conversion: T = 50 + (10 × z). A z of 1.5 becomes T = 65; z of −0.8 becomes T = 42; z of 0 becomes T = 50 exactly. Backwards: z = (T − 50) / 10, so T = 73 means z = 2.3, the 98.93rd percentile.
The conversion table
- z = −2 → T = 30 (2.28th percentile) · z = −1 → T = 40 (15.87th) · z = −0.5 → T = 45 (30.85th)
- z = 0 → T = 50 (the mean, 50th percentile) · z = 0.5 → T = 55 (69.15th)
- z = 1 → T = 60 (84.13th) · z = 1.5 → T = 65 (93.32nd) · z = 2 → T = 70 (97.72nd) · z = 2.5 → T = 75 (99.38th)
Test publishers (MMPI, many cognitive and personality inventories, educational assessments) report T scores because "T = 70" communicates elevation to a clinician faster than "z = 2.00, 97.7th percentile" — and because a scale centred at 50 makes the clinical cutoffs (65, 70) memorable. The price is one extra conversion whenever real statistics must be done: probabilities, combinations and intervals all live on the z scale, so T is converted back first. Nothing is gained or lost in either direction — the percentile never changes — which is the mark of a pure rescaling. The z score vs t score page compares the scales' uses in full.
Two namesakes that are NOT this T score
The t distribution (lowercase t, Student's t) is a probability distribution for inference with estimated σ — utterly unrelated to the T-score scale, despite sharing a letter and a century. If degrees of freedom are anywhere in the problem, it is the distribution, and the t distribution table is the tool. The DEXA bone-density T-score compares a patient's bone density with a young-adult reference mean, in reference-standard-deviation units — structurally a z-like score against a fixed reference population (its sibling, the DEXA Z-score, compares against age-matched peers). Same arithmetic shape, different reference group; the osteoporosis thresholds (T ≤ −2.5) belong to that field's conventions. Keeping the three apart is mostly a matter of asking "T relative to what, for what purpose?"
Also asked as: how do you calculate a t score · how to convert z score to t score · t score from z score · z score to t score conversion.
Related questions
Frequently asked questions
What T score is average?
50, by construction — the scale is built so the reference group's mean lands there, with 40–60 covering the ordinary middle (z from −1 to 1, the 16th to 84th percentiles).
Can a T score be negative?
In principle the formula allows it below z = −5, which essentially never occurs in real test data — real T scores live roughly between 20 and 80. If you compute a negative T, the z was almost certainly mis-entered; check it on the percentile converter.