📐 Z-Score Calculator
Enter a value, the mean and the standard deviation to get its z-score and the percentile it falls at.
Z-score
1.5
Percentile (below)
93.32%
Above
6.68%
A z-score (standard score) is how many standard deviations a value sits from the mean: z = (x − μ) ÷ σ. A positive z is above the mean, negative below. Assuming a normal distribution, the percentile is the area to the left under the bell curve, so z = 0 is the 50th percentile and z = 1.96 is about the 97.5th. 🔒 In your browser.
How the z-score calculator works
A z-score expresses how far a value is from the mean in units of standard deviation: z = (x − μ) ÷ σ. A z of +1 means one standard deviation above the mean, −2 means two below. Assuming the data is normally distributed, the tool also gives the percentile, the proportion of the distribution below your value, by integrating the standard normal curve, so you can see how a score ranks (z = 0 is the 50th percentile, z ≈ 1.96 the 97.5th).
The percentile assumes an approximately normal (bell-shaped) distribution; for strongly skewed data the z-score is still valid as a standardised distance but the percentile will be off. Z-scores are how you compare values measured on different scales, a test score and a height, say, on a common footing.
Frequently asked questions
What is a z-score?
A standard score: the number of standard deviations a value lies from the mean, z = (x − μ) ÷ σ. It puts values from different distributions on the same scale so they can be compared directly.
How do I calculate a z-score?
Subtract the mean from your value and divide by the standard deviation. For x = 85, μ = 70, σ = 10: z = (85 − 70) ÷ 10 = 1.5, meaning the value is 1.5 standard deviations above the mean.
What does a negative z-score mean?
That the value is below the mean. A z of −1.5 is 1.5 standard deviations below average; positive z-scores are above the mean, and z = 0 is exactly at the mean.
How does a z-score relate to percentile?
For a normal distribution, the percentile is the area under the curve to the left of the z-score. z = 0 is the 50th percentile, z = 1 about the 84th, and z = 1.96 about the 97.5th. This tool computes it for you.
What is considered an unusual z-score?
By a common rule of thumb, z-scores beyond ±2 are somewhat unusual (outside ~95% of the data) and beyond ±3 are rare (outside ~99.7%). The exact cut-off depends on your context and significance level.