Z-Score Calculator
Calculate the z-score (standard score) of a value, showing how many standard deviations above or below the mean it falls.
Inputs
Z-score
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Percentile (under normal curve)
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P(X ≤ x)
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P(X > x)
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Two-tailed p-value
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About Z-Score Calculator
What z-score means
A z-score standardizes any value to "how many standard deviations from the mean". z = +2 means 2 SD above; z = -1 means 1 SD below. Allows comparison across different distributions.
Common reference points
z = ±1.96 → 95% confidence interval bounds. z = ±2.58 → 99% bounds. z = +1.65 → 95th percentile (one-sided). These come up constantly in statistics.
Normality assumption
The percentile interpretation only holds if the underlying distribution is normal (bell-shaped). For skewed distributions, z-score is still useful but percentile is not 50% at z = 0.