A T-score is a standardized score with a mean of 50 and a standard deviation of 10. It is calculated as T = 50 + 10z, where z is the z-score. T-scores avoid negative numbers, which makes them common in psychological and educational testing.

How is the z-score calculated?

The z-score is (raw score − mean) / standard deviation. It expresses how many standard deviations a value sits above or below the mean. All the other standardized scores here are derived from this z-score.

A stanine (standard nine) compresses scores onto a 1-9 scale with a mean of 5 and a standard deviation of 2. It is computed as 5 + 2z, rounded and clamped to the 1-9 range. Stanines group performance into broad bands.

What is a Normal Curve Equivalent (NCE)?

The NCE is a normalized score from 1 to 99 with a mean of 50, designed so that 1, 50, and 99 match those same percentiles. It is calculated as 50 + 21.06z and is used in standardized education reporting.

How is the percentile rank found?

The percentile rank is the area under the standard normal curve to the left of the z-score, multiplied by 100. It tells you the percentage of the population scoring at or below your raw value.

T-Score & Standard Score Converter

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Convert any raw score into standardized form

Raw test scores are only meaningful relative to a distribution. This converter takes a raw score, the mean, and the standard deviation of its distribution and produces the full family of standardized scores: z-score, T-score, stanine, Normal Curve Equivalent (NCE), and percentile rank. These are the scores used across educational and psychological assessment to make results comparable across different tests and scales.

How it works

Everything starts from the z-score:

z = (raw − mean) / standard_deviation

The z-score is then linearly rescaled into each reporting scale:

T-score = 50 + 10 × z          (mean 50, SD 10)
Stanine = round(5 + 2 × z)     (clamped to 1–9)
NCE     = 50 + 21.06 × z       (1–99 scale)

The percentile rank is the cumulative probability of the standard normal distribution up to z, expressed as a percentage. This tool approximates the normal CDF using the Abramowitz & Stegun polynomial, accurate to about 1e-7.

Example and notes

A student scores 65 on a test with a mean of 50 and standard deviation of 10. The z-score is (65 − 50) / 10 = 1.5. That gives a T-score of 65, a stanine of 8, an NCE of about 81.6, and a percentile rank of roughly 93.3 — meaning the student outperformed about 93% of peers.

Notes: a standard deviation of zero is undefined (every value equals the mean), so the tool flags that case. Stanines are intentionally coarse — many distinct percentiles collapse into the same band, which is by design.