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math.z-score Calculator
Converts a raw observation to a z-score relative to a population mean and standard deviation. A z-score of 0 means exactly average; ±1 means one standard deviation from the mean — the standard way to compare across distributions.
Inputs
X
Reference formula or conversion factor shown for context.
Mu
Arithmetic average. Sensitive to outliers — if your data has extreme values, the median may be more representative.
Sigma
Reference formula or conversion factor shown for context.
N
Number of data points collected. Larger samples give narrower confidence intervals. Rule of thumb: 30+ for most statistical tests.
Results
z-score
Number of standard deviations a value is from the mean. |z| below 2: within normal range. |z| above 2: in the outer 5% of the distribution. |z| above 3: in the outer 0.3%.
P(X ≤ x)
Reference formula or conversion factor shown for context.
P(X > x)
Reference formula or conversion factor shown for context.
standard error (SE)
The difference between the computed result and the exact or true value — a measure of approximation accuracy.
t-statistic (for n=
The test statistic for a t-test. Compare to critical t for your chosen significance level (typically 1.96 for p < 0.05 with large samples).
outlier?
Reference formula or conversion factor shown for context.