Calculators
Z-Score Calculator
Calculate the z-score (standard score) from a value, mean, and standard deviation locally in your browser.
Enter a value, the population mean, and the population standard deviation to calculate the z-score (standard score). A positive z-score means the value is above the mean; a negative z-score means it is below. Calculations run locally in your browser; your values are not uploaded or stored.
Find how many standard deviations a value is from the mean.
Enter a value, the population mean, and the population standard deviation to calculate the z-score: z = (x − μ) ÷ σ. A positive z-score means the value is above the mean; a negative z-score means it is below. The approximate percentile from the standard normal distribution is also shown. Everything runs locally in your browser, so your values are not uploaded or stored.
Frequently Asked Questions
Everything you need to know about this tool, how it works, and privacy.
What does the z-score calculator show?
Enter a value, the population mean, and the population standard deviation. The calculator returns the z-score using z = (x − μ) ÷ σ and the approximate percentile from the standard normal distribution. For example, a value of 85 with mean 70 and standard deviation 10 gives z = 1.50 and about the 93.32nd percentile.
Which formula does the z-score calculator use?
It uses z = (x − μ) ÷ σ, where x is the value, μ is the population mean, and σ is the population standard deviation. The percentile uses the error function: percentile = 0.5 × (1 + erf(z / √2)) × 100. A positive z-score means the value is above the mean; a negative z-score means it is below the mean.
Which inputs are accepted?
Enter a value, a mean, and a standard deviation greater than zero. Decimal values are accepted. Non-numeric text, empty fields, and a standard deviation of zero or negative show a clear error instead of a result.
Do my values stay private?
Yes. The calculation and copy action run locally in your browser. CodeASystem does not upload or store the values you enter.