📐 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.