How to use it
If you know the group's mean and standard deviation — most score reports, exam statistics and research papers print both — keep the first mode, enter your score and read the z-score, percentile and T-score. Add the number of test takers to estimate your rank. If you have every score instead (a class's results, say), switch to the list mode: the calculator works out the mean and the population standard deviation for you and also gives your exact rank in the list.
The formulas
z = (score − mean) ÷ standard deviation
T-score = 50 + 10 × z
The z-score says how many standard deviations a score lies above (positive) or below (negative) the mean. The T-score rescales it so the mean becomes 50 and one standard deviation is 10 points. The percentile is the share of a normal distribution below that z-score, read from the standard normal curve.
Worked example
A test has a mean of 60 and a standard deviation of 10, and you scored 80. Then z = (80 − 60) ÷ 10 = 2, the T-score is 50 + 10 × 2 = 70, and the percentile is about 97.7: roughly 97.7% of test takers scored lower and 2.3% scored higher. Among 1,000 test takers that is around 23rd place. With the same 80 points on a test where the mean was 75 and the standard deviation 5, z = 1 and the T-score is 60 — a good score, but a much less exceptional one.
T-scores and hensachi
In Japan, the T-score is known as hensachi (偏差値) and is the standard way to compare results on mock entrance exams and to describe how hard a school is to get into. A hensachi of 50 is exactly average, 60 is about the top 16%, and 70 is about the top 2.3%. Because it is relative, a hensachi only means something within one test's population: 60 on a mock exam taken by top students is harder to reach than 60 on one taken by everyone.
Reading the table
The table under the result lists T-scores from 30 to 75 with their z-scores and percentiles. About 68% of scores fall between T-scores of 40 and 60 (within one standard deviation), and about 95% between 30 and 70. These shares hold only for roughly bell-shaped data; very easy or very hard tests bunch scores near one end, and then the percentile is only an approximation. The rank estimate rests on the same assumption, so treat it as a ballpark figure.
To compute the standard deviation of a data set step by step, use the standard deviation calculator; for a plain percentage score, the test grade calculator.
Frequently asked questions
What is a good z-score?
It depends on the purpose, but a z-score of 1 puts you above about 84% of a normal distribution, 2 above about 97.7%, and 3 above about 99.9%. Negative z-scores are below average.
What is the difference between a z-score and a T-score?
They carry the same information on different scales. The z-score is centered on 0 with a standard deviation of 1; the T-score is 50 + 10 × z, so it is centered on 50 and is rarely negative. The Japanese hensachi uses the T-score scale.
Should I use the population or the sample standard deviation?
For ranking scores within a test, use the standard deviation of everyone who took it — the population figure, which is what the list mode calculates. Score reports normally print that value already.
Can a T-score be above 100?
Only with an extreme score: a T-score of 100 needs a z-score of 5, which almost never happens in a large group. Very high values usually come from small groups or tests where most people scored poorly.
Last updated: October 14, 2026