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Chebyshev's Probability Bound Calculator

P(|X−μ| ≥ kσ) ≤ 1/k² — guaranteed probability bound.

Applies Chebyshev's inequality to give a distribution-free bound on the probability of a value lying more than k standard deviations from the mean.

Dr. Helena Ortiz By Dr. Helena Ortiz
Published Last reviewed 1 min read

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How to use this calculator

  1. Fill in the inputs above using the units you already have.
  2. Values update automatically as you type — no submit button needed.
  3. Hover any result row for the underlying formula and intermediate values.

Formula

P(|X−μ| ≥ kσ) ≤ 1/k²; P(within kσ) ≥ 1 − 1/k²

In depth

Applies Chebyshev's inequality to give a distribution-free bound on the probability of a value lying more than k standard deviations from the mean.