Z-Score Calculator
Calculate the z-score (standard score) of a data point given the mean and standard deviation.
How to use this tool
- Enter data point (x), mean (μ) and standard deviation (σ) in the fields above.
- Results update instantly as you type — or click Calculate.
- Read your z-score and the full breakdown beneath it.
Calculate the z-score: z = (x − μ) / σ. A z-score tells you how many standard deviations a value is from the mean.
Formula
Z-score: z = (x − μ) / σ
How it works
The z-score expresses how many standard deviations a data point x lies above or below the population mean μ. A positive z indicates the value is above the mean; a negative z indicates it is below. Z-scores allow values from different normal distributions to be compared on a common scale and are used to look up probabilities in the standard normal table. The formula assumes the provided mean and standard deviation are correct descriptors of the reference distribution.
Worked example
Worked example
- Inputs: x = 75, mean μ = 70, standard deviation σ = 5.
- z = (75 − 70) / 5 = 5 / 5 = 1.0.
Z-score = 1.0 (the value 75 is exactly 1 standard deviation above the mean).
Key terms
- Z-score (standard score)
- The number of standard deviations a data point is from the mean of its distribution.
- Standard normal distribution
- A normal distribution with mean 0 and standard deviation 1; any normal distribution can be transformed to it using z-scores.
- Mean (μ)
- The arithmetic average of the reference distribution used as the baseline for comparison.
- Standard deviation (σ)
- A measure of spread in the reference distribution; one unit on the z-score scale equals one standard deviation.
- Standardisation
- The process of converting raw scores to z-scores so that values from different distributions can be compared directly.
Frequently asked questions
- What does a z-score mean?
- A z-score of +1 means the value is 1 standard deviation above the mean; −2 means 2 standard deviations below. Z-scores allow comparison across different scales and distributions.