Statistics & Probability

Z-Score Calculator

See how many standard deviations a value is from the mean.

By TheCalcTools Updated Formula checked and tested

Your numbers

Your results

z-score
z-score
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Percentile
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Distance from the mean
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Z-Score Calculator by TheCalcTools

How the Z-Score Calculator works

Enter a score, the mean of the group and its standard deviation.

The z-score is the distance from the mean divided by the standard deviation.

The percentile is the share of the distribution below that z-score.

The formula

z = (x − μ) ÷ σ

Worked example

Using the default values shown in the calculator:

Raw score (x)85
Mean (μ)70
Standard deviation (σ)10
  1. z = (85 − 70) ÷ 10 = 1.50.
  2. That is the 93.3% percentile.

Result:

z-score1.5000
Percentile93.3%
Distance from the mean15.00

Frequently asked questions

What does a negative z-score mean?

The value is below the mean.

Is a z-score of 2 unusual?

In a normal distribution only about 2.3% of values lie above z = 2, so it is fairly unusual.

Sources and further reading

Normal Distribution CalculatorEnter the mean, standard deviation and a value x to find its z-score and probabilities Confidence Interval Calculator (Mean)Estimate a range likely to contain the true mean, using the normal (z) approximation Binomial Distribution CalculatorCalculate binomial probabilities for n trials with success probability p Poisson Distribution CalculatorFind the probability of k events in an interval when events happen at an average rate λ Hypergeometric Probability CalculatorDraw n items without replacement from a population containing K successes Geometric Distribution CalculatorHow many attempts until the first success?

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This calculator gives estimates for information only. Check important results independently before you rely on them. See our disclaimer.