# Z-score Calculator

> Calculate a z-score, convert between z and normal probability, or find probability between two z-scores.

Page: https://askcalculators.com/calculator/z-score-calculator/
Definition: https://askcalculators.com/calculator/z-score-calculator/definition.json
JSON Schema: https://askcalculators.com/calculator/z-score-calculator/schema.json
Version: 2.0.0
Maintained by: AskCalculators (software project; not a credentialed reviewer)
Qualified review: pending. Automated checks do not establish professional approval.
Page status: Live
Review status: Pending

## Use
Open the calculator page and enter values. Query-string parameters can restore and bookmark a calculation.
Example: https://askcalculators.com/calculator/z-score-calculator/?mode=raw-score&rawScore=85&mean=75&standardDeviation=10

## Inputs
- mode: Calculation; type=select; required; default=raw-score; values=raw-score|z-to-probability|probability-to-z|between
- rawScore: Raw score (x); type=number; required; default=85; showWhen=mode:raw-score
- mean: Population mean (μ); type=number; required; default=75; showWhen=mode:raw-score
- standardDeviation: Standard deviation (σ); type=number; required; default=10; min=0.000001; showWhen=mode:raw-score
- zValue: Z-score; type=number; required; default=1; showWhen=mode:z-to-probability
- leftProbability: Left-tail probability P(X<z); type=number; required; default=0.841344746; min=1e-9; max=0.999999999; showWhen=mode:probability-to-z
- leftZ: Left z-score; type=number; required; default=-1; showWhen=mode:between
- rightZ: Right z-score; type=number; required; default=1; showWhen=mode:between

## Outputs
- zScore: Z-score; format=number; primary
- probabilityLess: P(X < z); format=percent
- probabilityGreater: P(X > z); format=percent
- probabilityMeanToZ: Area between mean and z; format=percent
- probabilityCentral: P(−|z| < X < |z|); format=percent
- probabilityTwoTail: Outside ±|z|; format=percent
- betweenProbability: Probability between bounds; format=percent

## Formula
z=(x−μ)/σ; probabilities use the standard-normal CDF Φ(z); inverse conversion uses z=Φ⁻¹(p).

## Rules
- Empty optional inputs are undefined, not zero.
- Hidden conditional inputs are ignored.
- Do not invent missing required inputs.