Omikuji Tools Life & Calc

Standard Deviation & T-Score Calculator

Turn one score into a T-score and z-score, or paste a whole class's scores to get the mean, standard deviation, T-scores and ranks.

Features

  • T-score, z-score and approximate percentile from a score, mean and standard deviation
  • Work backwards: the score you need for a target T-score
  • Paste a class list to get n, mean, median, min, max, population and sample SD, plus everyone's z-score, T-score and rank
  • Score distribution chart; copy the table as CSV or TSV for Excel and Google Sheets
  • Switch to an IQ-style scale (mean 100, SD 15) or set your own mean and spread

Use cases

Reading a test report

See where a score sits: T-score, z-score and roughly what top percentage.

Setting a goal

Find the score needed to reach a T-score of 60.

Grading a class

Paste quiz scores and get the mean, SD and every student's T-score at once.

Statistics homework

Compare population and sample standard deviation on the same data.

Privacy

Scores and names are processed only in this browser and never sent to a server. A pasted list is saved only in this browser on this device (Clear removes it) and is never put in a share URL. Only when you shorten a share URL are the one-score inputs (score, mean, SD and scale) sent to the shortening service.

FAQ

How is the T-score calculated?

z = (score − mean) ÷ SD tells you how many standard deviations a score is from the mean. The T-score rescales it: T = 50 + 10 × z, so the mean is 50 and each SD is 10 points.

What percentile is a T-score of 60?

If scores are roughly normal, T = 60 (z = 1) is about the top 15.9% (84th percentile), 65 is the top 6.7% and 70 the top 2.3%. Real tests are often skewed, so treat it as an estimate.

Can I compare T-scores from different tests?

Only with care. A T-score shows position within the group that took that test, so the same T-score means different things when the groups differ.

Population SD or sample SD?

To place people within the whole group you have, use the population SD (divide by n, STDEV.P). The sample SD (divide by n − 1, STDEV.S) estimates the spread of a larger population from a sample and is shown for reference.

Why is there no T-score when everyone has the same score?

The standard deviation is 0, so the formula would divide by zero. With no spread there is no distance from the mean to measure. The same applies to a single score.

Is my data uploaded?

No. Everything is calculated in your browser. A pasted list stays on this device and can be removed with Clear.

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Mode
Scale

T-score = 50 + 10 × (score − mean) ÷ SD

Score → T-score

Use the values from your score report. If you have every score, switch to “Class score list” to calculate them.

“Top ~%” assumes the scores follow a normal (bell-shaped) distribution. It is only an estimate for small or skewed groups.

Score needed for a target