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Z-score Calculator

Z-scores, percentiles and probabilities either way.

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The empirical rule

WithinValue rangeContains

Common z-scores

ZPercentileRight tailTwo-tailed

Z-score

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Probabilities

Percentile—
Area to the left—
Area to the right—
Two-tailed—

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How unusual this value is

A z-score says how many standard deviations a value sits from the mean, which makes otherwise incomparable measurements comparable. In hypothesis testing, |z| above 1.96 is significant at the 5 percent level. The empirical rule gives the 68-95-99.7 landmarks.

Quick Tool Overview

The Z-score Calculator converts a raw value to a standard score and back, and reports the percentile, tail probabilities and the area between any two z-scores — which is what most textbook questions actually ask for.

What it does
Converts between raw values, z-scores and probabilities
You give it
A mean, a standard deviation and a value or z-score
You get back
Z-score, percentile and tail probabilities
Best for
Statistics coursework and standardising measurements
Calculators Free, unlimited use No sign-up Runs in your browser

About the Z-score Calculator

Convert a raw value into a z-score, or a z-score back into a raw value, and read off the percentile and tail probabilities that go with it. The area between any two z-scores is calculated too, which is what most textbook questions actually ask for.

A z-score says how many standard deviations a value sits from the mean, which makes otherwise incomparable measurements comparable: a z-score of 1.5 means the same thing whether the underlying scale was exam marks, blood pressure or rainfall. That standardisation is what replaces a shelf of distribution tables with a single one, and it is the step behind almost every significance test.

Key features of the Z-score Calculator

Both directions

Raw value to z-score, or z-score back to the raw value on your own scale.

Area between two z-scores

The calculation most z-table questions want, done without reading off a table.

Percentile included

The cumulative area to the left, expressed as the percentile the value sits at.

Empirical rule shown

The 68-95-99.7 landmarks are displayed for context around your result.

Replaces the z-table

Accurate to many decimal places, rather than the two a printed table offers.

How to use the Z-score Calculator

  1. 1

    Choose a direction

    Raw value to z-score, z-score to raw value, or the area between two z-scores.

  2. 2

    Enter the distribution

    The population mean and standard deviation.

  3. 3

    Enter your value

    The raw score or the z-score, depending on which direction you chose.

  4. 4

    Read the probabilities

    Percentile, left and right tail areas, and the two-tailed probability.

Frequently asked questions

The number of standard deviations a value lies from the mean, calculated as (value − mean) ÷ standard deviation. A z-score of 2 means the value is two standard deviations above the mean.

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