T-Score (Standard Score) Calculator
Paste a set of test or class scores and instantly get each entry's T-score, the mean, standard deviation, and rank. Enter any score to see exactly what T-score and rank it corresponds to.
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Input
Paste all the scores from your class or test at once. Values can be separated by line breaks, commas, or spaces.
Even if left blank, the T-score for each entry is shown below.
Result
T-score for a raw score of 80
55.89
Ranked 3 of 7
Data points
7
Mean
72.43 pts
Std. deviation
12.86
Highest
91 pts
Lowest
54 pts
Variance
165.39
T-score for each entry
| No. | Score | T-score | Rank |
|---|---|---|---|
| 1 | 72 | 49.67 | 4 / 7 |
| 2 | 65 | 44.22 | 5 / 7 |
| 3 | 88 | 62.11 | 2 / 7 |
| 4 | 54 | 35.67 | 7 / 7 |
| 5 | 91 | 64.44 | 1 / 7 |
| 6 | 60 | 40.34 | 6 / 7 |
| 7 | 77 | 53.55 | 3 / 7 |
How it works
- The T-score (called hensachi in Japan) is calculated as T = (score − mean) / standard deviation × 10 + 50. By design the mean of the data maps to a T-score of 50, scores above the mean exceed 50, and scores below it fall under 50.
- T-scores are widely used in Japanese exams and entrance tests to express where a student stands relative to the whole group, regardless of how easy or hard the test was.
- Scores can be pasted all at once using line breaks, commas, or spaces as separators. Any token that cannot be read as a number is ignored automatically.
- The standard deviation and variance treat the entered data as the entire population (population variance: the sum of squared deviations divided by the number of data points n). This is the conventional method for T-scores and differs from the unbiased sample variance (dividing by n − 1).
- Entering a score in the optional field shows that score's T-score and its equivalent rank within the existing data (ties share the same rank). Leaving it blank still lists the T-score of every data point in the table.
- Ranks are ordered so that higher scores are placed higher (1st), and identical scores are treated as the same rank. When every score is identical the standard deviation is 0, so all T-scores are shown as 50.
What hensachi is, for readers outside Japan
Hensachi, usually translated as "deviation score," is the standardized score Japanese students see on school tests and especially on mock exams for high school and university entrance. It uses the same scale as the T-score familiar from statistics and psychology: the group mean is set to 50 and each standard deviation is worth 10 points. A hensachi of 60 therefore means one standard deviation above average, regardless of how hard the test was or what the maximum score was. Schools and prep programs in Japan are often ranked by the hensachi typically needed to get in, which is why the number carries so much weight there.
A five-student walkthrough
Take five scores: 50, 60, 70, 80 and 90. The mean is 70, so the deviations from the mean are −20, −10, 0, +10 and +20. Squaring and adding them gives 400 + 100 + 0 + 100 + 400 = 1,000. Divide by the number of students (5) to get a variance of 200, and take the square root for a standard deviation of about 14.14. The student with 90 gets 20 ÷ 14.14 × 10 + 50 ≈ 64.14, and the student with 50 gets about 35.86. Paste the same five numbers into the calculator and the table shows exactly these values.
Same raw score, different hensachi
The score measures distance from the mean relative to the spread. On a test where everyone bunches together, a few extra points move your hensachi a lot.
- Test with mean 60 and standard deviation 10: (80 − 60) ÷ 10 × 10 + 50 = 70.
- Test with mean 70 and standard deviation 5: (80 − 70) ÷ 5 × 10 + 50 = 70.
- Test with mean 60 and standard deviation 20: (80 − 60) ÷ 20 × 10 + 50 = 60.
Small groups and skewed results
With n people, the highest possible deviation score is 50 + 10 × √(n − 1). In a group of 7 the ceiling is about 74.49; in a group of 10 it is exactly 80. If everyone has the same score, everyone gets 50. At the other extreme, if 1 person out of 100 scores 100 and the rest score 0, that one person's hensachi is about 149.5, so values above 100 are possible.
Converting hensachi to a percentile (55 is roughly the top 31%, 65 roughly the top 6.7%, 45 roughly the top 69%) only works when scores are close to a normal distribution. For a small class or a test where many people hit the maximum or score zero, trust the rank column instead.
Practical tips
- Work backward from a target: required score = mean + (target − 50) ÷ 10 × standard deviation. With the default sample data (mean about 72.43, standard deviation about 12.86), a hensachi of 60 requires about 85.29, so 86 points or more.
- Scores from different mock exams are not directly comparable when different groups of students took them.
- Decide whether absent students count as zero before you paste the data; including or excluding them changes both the mean and the standard deviation.
Frequently asked questions
- What formula is used to calculate the deviation score?
- The deviation score (hensachi) is calculated as (score − mean) ÷ standard deviation × 10 + 50. A score equal to the mean gives exactly 50, above the mean is over 50, and below the mean is under 50.
- What do deviation scores of 50, 60, and 70 mean?
- A score of 50 is exactly the average. 60 is one standard deviation above the mean and 70 is two standard deviations above, which under a normal distribution roughly corresponds to the top 16 percent and top 2 percent.
- Does it use the population or sample standard deviation?
- It treats the entered data as the whole population and uses the population variance (sum of squared deviations divided by n), which is the standard method for deviation scores. Note this differs from the unbiased variance that divides by n−1.
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