Z-score Calculator

X (observed value)

Mean (μ)

Standard Deviation (σ or s)

Use the population σ if known, otherwise sample s.

Batch values (optional)

Batch uses the same Mean and SD. A results table will appear below.

Drag & drop a .txt/.csv of X values here (client-side parse only)

Or click to choose a file. Values will populate the “Batch values” box.

Format tips: 12, 13, 14 or one value per line.

Z-score – Quick Cheat Sheet

Definition: Z-score standardizes a value relative to the mean and SD: z = (x − μ) / σ.
Interpretation: Z=0 at the mean; Z=+1 is 1 SD above; Z=−2 is 2 SD below, etc.
Percentile: One-tailed percentile = Φ(z)×100%, where Φ is the standard normal CDF.
Two-tailed p: p = 2 × (1 − Φ(|z|)).
Population vs Sample: If σ (population SD) is unknown, use sample SD (s) as an estimate.
Batch mode: Provide multiple X values; the same μ and SD are applied to all.
Edge cases: SD must be non-zero; all inputs must be numeric and finite.

Notes on calculations

Percentiles and p-values are approximated using a standard erf-based CDF; accurate for practical use.
Batch parsing accepts commas, spaces, tabs, and newlines.
Client-side drag & drop/file select only fills the textarea; no files are uploaded.