Z-score Calculator

Value

Mean

Standard deviation

Result

z-score2
Percentile97.73%
Above you, %2.28%
Deviation2 σ выше среднего
How unusualв пределах обычного
Within ±z, %95.45%

One ruler for any dataset

How many standard deviations a value sits from the mean, the percentile it corresponds to, and how unusual that makes it.

A z-score converts any value into standard deviations from the mean. That makes otherwise incomparable things comparable: an IQ score and a height, a maths grade and a running time.

The percentile follows immediately — the share of values below yours. The empirical rule says 68 percent of data falls within one deviation, 95 within two and 99.7 within three, and the calculator reports the share for your figure.

What this calculator shows

The z-score and the matching percentile
What share of values sit above yours
How unusual the result is by the sigma rule

What to keep in mind

The percentile assumes a normal distribution; for skewed data it will be misleading.
The standard deviation must exceed zero — with no spread there is nothing to standardise against.

FAQs

What does a negative z-score mean?

The value is below the mean. The sign gives direction, the magnitude gives distance. Zero means it sits exactly on the mean.

What is the three-sigma rule?

For a normal distribution, 68.3 percent of values lie within one deviation, 95.4 within two and 99.7 within three. Beyond three sigma happens about once in 370 observations.

How does a z-score become a percentile?

The percentile is the area under the normal curve to the left of your z. z = 0 gives 50 percent, z = 1 about 84, z = 2 nearly 98.

Does this work on any data?

A z-score can always be computed, but converting it to a percentile only holds for roughly normal data. Income, for instance, is heavily skewed and the percentile would be wrong.

Worked example

An IQ of 130 against a mean of 100

Input: Value 130, mean 100, deviation 15

Output: z = 2, percentile 97.72

Note: Two deviations above the mean is the top 2.3 percent — the usual cut-off for gifted programmes.

Useful links

All tools in Math & Statistics

Z-score Calculator

Result

Related tools

Standard Deviation Calculator

Confidence Interval Calculator

P-value Calculator

Useful links