T-Score Calculator
A score of 70 on a test with mean 50 and standard deviation 10 has a T-score of 70, which is about the top 2.3% if scores are normally distributed.
How to use
- Choose Score to T-score, then enter the raw score, the mean and the standard deviation of the whole group.
- Add the number of test takers to get an estimated rank. It is optional.
- To find the score you need for a target T-score, switch to T-score to score and enter the T-score, mean and standard deviation.
How it works
T = 50 + 10 × (score − mean) ÷ standard deviation. It is the z-score rescaled so that the mean is 50 and one standard deviation is 10 points.
The percentile assumes a normal distribution. A T-score of 60 is the top 15.87%, and 70 is the top 2.28%. Real score distributions are often skewed, so treat the percentage as an estimate.
Use the population standard deviation of the whole group, as reported with the test. T-scores are used in psychological and educational testing, and in Japan the same value is called hensachi.
T-score and percentile
Assuming a normal distribution.
| T-score | Top share |
|---|---|
| 40 | 84.13% |
| 45 | 69.15% |
| 50 | 50.00% |
| 55 | 30.85% |
| 60 | 15.87% |
| 65 | 6.68% |
| 70 | 2.28% |
| 75 | 0.62% |
| 80 | 0.13% |
FAQ
What does a T-score of 50 mean?
The score equals the group mean. Above 50 is above average and below 50 is below average.
Can a T-score be above 100 or below 0?
Yes, if the score is more than 5 standard deviations from the mean. It is very rare in a normal distribution.
What is the difference between a T-score and a z-score?
They carry the same information. A z-score has mean 0 and SD 1, and a T-score is 50 + 10z.
Is my data sent anywhere?
No. The calculation runs in your browser.