Z-Score Calculator
Convert any raw score to a z-score and percentile: see how many standard deviations it is from the mean
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Common Z-Score Reference
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Assumes an approximately normal distribution
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Each row recalculates with your current inputs. Tap a row to apply it.
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Enter score, mean, and deviation
Fill in your raw score, the mean, and the standard deviation above
Authoritative sources and references
The official standards, guidelines, and research behind this calculator's methodology.
Z-Score Calculator FAQ
What is a z-score?
A z-score (standard score) tells you how many standard deviations a raw score is away from the population mean. z = (x − μ) ÷ σ. A z of +1.5 means the score is 1.5 standard deviations above the mean; a negative z means below the mean.
How do I turn a z-score into a percentile?
The percentile is the area under the standard normal curve to the left of z, written Φ(z). For example Φ(1.5) ≈ 0.9332, so z = 1.5 is roughly the 93rd percentile. This calculator computes Φ(z) automatically.
What do I use for μ and σ?
Use the mean and standard deviation of the reference group you are comparing against — for example the class average and its standard deviation on an exam. If only a sample is available, the sample mean and sample standard deviation are commonly used as estimates.
Can a z-score be greater than 3 or less than −3?
Yes. Z-scores have no fixed bounds; ±3 just covers about 99.7% of a normal distribution. Very large |z| means the value is extreme relative to the reference group, or that the distribution is not close to normal.
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