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Z-Score Calculator

Convert a raw score into a standard score using the mean and standard deviation.

 

 

 

z

About this calculator

Use this calculator to standardise a measurement so you can compare it with a reference mean and spread. A z-score says how many standard deviations a value sits above or below the mean. IQ scores, exam marks, and process measurements are common examples.

The formula is: z = (x − μ) / σ. Enter x, μ, and σ in the same units. An IQ of 115 with mean 100 and σ = 15 gives z = 1, one standard deviation above the mean. Negative z means below the mean.

This is a location on the standard scale, not a p-value. σ must be positive. The calculator does not assume a normal shape; normality matters only if you later read z against a normal table.

Value (x): Raw score to standardise.

Mean (μ): Reference mean of the group or process.

Standard deviation (σ): Reference spread; must be positive.

z: Standard score, (x − μ) / σ.