T-Score Calculator
Or fill in the three fields below instead.
- 65.00
- T-score
- 1.5000
- Underlying z
- 93.32%
- Percentile
- Above average
- Interpretation
The T-score calculator converts a z-score, or a raw value with its mean and standard deviation, to the T-score scale used in psychological and educational assessment. T-scores have a mean of 50 and a standard deviation of 10, which removes the negative numbers and decimals that make z-scores awkward to report.
How it works
T = 50 + 10z
- 50
- the mean of the T-score scale
- 10
- the standard deviation, so one z equals ten T points
This is a linear rescaling and nothing more. It changes no information, a T-score and its z-score describe exactly the same position, but a range of roughly 20 to 80 is easier to read and report than −3 to +3.
- T = 50 is the mean. T = 60 is one standard deviation above; T = 40 one below.
- Scores above 70 or below 30 are two standard deviations out, which many clinical instruments treat as a threshold of interest.
- The conventional interpretation bands are shown alongside the result.
Do not confuse this with the t-statistic from Student’s t-test. They share a letter and nothing else. A t-statistic tests a hypothesis and depends on degrees of freedom; a T-score locates one value on a scale.
Examples
From a z-score
z-score
1.5
Result
T-score 65.00 · 93.32nd percentile
50 + 10 × 1.5. One and a half standard deviations above the mean.
From a raw value
Raw
68
Mean
50
SD
12
Result
z 1.5000 · T-score 65.00
The raw fields take precedence when all three are filled, computing z first and then rescaling.
Frequently asked questions
Is a T-score the same as a t-test statistic?
No, and the shared letter causes real confusion. A T-score is a rescaled z-score locating one value on a mean-50 scale. A t-statistic comes from Student’s t-distribution, tests a hypothesis, and depends on degrees of freedom. They are unrelated.
Why rescale at all if no information changes?
Readability. Reporting a child’s result as "T = 35" is easier to communicate than "z = −1.5", and it avoids the negative signs and decimals that get transcribed incorrectly. Clinical instruments standardised on it for that practical reason.
What counts as a significant T-score?
Convention treats 70 and above, or 30 and below, as clinically notable. Two standard deviations from the mean, roughly the top and bottom 2 percent. The exact threshold depends on the instrument, and no calculator can tell you what a specific test considers meaningful.
Can a T-score be negative?
Arithmetically yes, at z below −5, but it never happens with real data. Five standard deviations below the mean is about one in three million, which is why the scale is built to avoid negatives in practice.