keisoku

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.

Input

Paste all the scores from your class or test at once. Values can be separated by line breaks, commas, or spaces.

pts

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.ScoreT-scoreRank
17249.674 / 7
26544.225 / 7
38862.112 / 7
45435.677 / 7
59164.441 / 7
66040.346 / 7
77753.553 / 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.