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Z-score calculator

Standardize a value and convert between Z-scores, normal probabilities and intervals.

Get started

  1. Use the example values or enter your own measurements.
  2. Calculate, then copy the result or download the available details.

Example

Input

Value 18, mean 23, deviation 4

Expected result

z = −1.25

Try it

Good to know

The calculation runs in your browser. Use consistent units in fields with no explicit unit.

Calculation method

The standard score is (x − μ)/σ. The left tail is the normal CDF at z. For symmetric regions the inverse returns the nonnegative boundary.

z=x−μσ,P(a<Z<b)=Φ(b)−Φ(a)z=\frac{x-\mu}{\sigma},\qquad P(a<Z<b)=\Phi(b)-\Phi(a)

Calculation mode

Standardize a value
  • Observed value
  • Mean
  • Standard deviation
Z-score to probabilities
  • Z-score
Probability to Z-score
  • Probability region · Left-tail probability / Right-tail probability / From the center to |z| / Between −|z| and |z| / Two-tail probability
  • Probability
Probability between Z-scores
  • Lower Z-score
  • Upper Z-score