Z-Score Calculator
Calculate z-score, percentile, and cumulative probability with step-by-step and z-score lookup table.
Distribution & score
Updates as you typeMode
What do you want to solve for? ?
Preset
Load a common distribution ?
Distribution
Population mean (μ) ?
—
Standard deviation (σ) ?
—
Your value
Raw score (x) ?
—
Z-score (z) ?
—
Percentile ?
—
%
Lower bound (a)
—
Upper bound (b)
—
Normal distribution
Your value on the bell curve
Shaded region
Mean (μ)
Your value
Z-score lookup table
Cumulative probability: the percentage of values at or below each z-score in the standard normal distribution (±3σ in 0.1 steps).
Show table (61 rows)
| Z-score | Percentile | % above | Two-tailed p |
|---|
Formula
z
=
x − μ
σ
- z
- Standard score — number of standard deviations the value sits above (positive) or below (negative) the mean.
- x
- The observed value (raw score).
- μ
- Population mean.
- σ
- Population standard deviation (must be positive).
- Φ(z)
- Cumulative probability — the percentage of values at or below z in a standard normal distribution.
Worked example — your numbers
- x = —, μ = —, σ = —
- x − μ = —
- z = (x − μ) / σ = —
- Φ(z) = — (percentile)
- Two-tailed P(|Z| > |z|) = —
The z-score tells you where a value sits on a standard normal curve. Roughly 68% of values fall between z = −1 and z = 1, 95% between −2 and 2, and 99.7% between −3 and 3 (the empirical rule).