ZLab

Z-Score Calculator

z = (x − μ) / σ, plus the percentile it maps to.

How many standard deviations away?

A z-score converts a raw value into 'number of standard deviations from the mean' — a z of +2 means the value sits two standard deviations above average, regardless of the original units.

Why standardising helps

Z-scores let you compare values from entirely different scales — a test score and a height measurement — on the same standardized footing, and directly translate to a percentile ranking.

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ZLab

Z-Score Calculator

z = (x − μ) / σ, plus the percentile it maps to.

Score x

Mean μ

Std dev σ

Z-score: 1.5
Percentile: 93.32%

z = (x − μ) / σ

What you entered

Score x: 85Mean μ: 70Std dev σ: 10

1
Subtract the mean
85 − 70= 15
2
Divide by the standard deviation
15 ÷ 10= 1.5
3
Convert to a percentile (standard normal CDF)
Φ(1.5)= 93.3193%

Result

Z-score: 1.5

A score of 85 is 1.5 standard deviations above the mean, placing it around the 93.3th percentile.

How many standard deviations away?

A z-score converts a raw value into 'number of standard deviations from the mean' — a z of +2 means the value sits two standard deviations above average, regardless of the original units.

Why standardising helps

Z-scores let you compare values from entirely different scales — a test score and a height measurement — on the same standardized footing, and directly translate to a percentile ranking.