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Calculation Machine

Z-Score Calculator

Standard score, percentile and tail probabilities.

Reviewed by the Calculation Machine team · How we check our maths

Your values

ⓘ Live results

Results
Z-score
2.1333
Percentile
98.36%
Probability above this value
1.645%
Two-tailed p-value
3.2897%

Working

  1. 1z = (132 − 100) ÷ 15 = 2.1333

Quick answer

A z-score is how many standard deviations a value sits from the mean: z = (x − μ) ÷ σ.

The formula

z = (x − μ) ÷ σ

Worked example

Worked example

Using the values the calculator loads with.

Inputs

  • Value (x)132
  • Mean (μ)100
  • Standard deviation (σ)15

Result

  • Z-score2.1333
  • Percentile98.36%
  • Probability above this value1.645%
  • Two-tailed p-value3.2897%

How to use the Z-Score Calculator

  1. 1Enter the raw value.
  2. 2Add the population mean and standard deviation.
  3. 3Read the z-score and percentile.

Frequently asked questions

What z-score is significant?

At the conventional 5% two-tailed level, |z| above 1.96 is significant; 2.58 corresponds to the 1% level.

Can a z-score be negative?

Yes — it simply means the value sits below the mean.

About this calculator