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Confidence Interval for Mean (Known σ) Calculator

Z-based CI for a population mean when σ is known.

Constructs a confidence interval for a population mean using the z-distribution: CI = x̄ ± z* · (σ/√n). Common z* values: 90% → 1.645, 95% → 1.960, 99% → 2.576.

Priya Venkatesan By Priya Venkatesan
Published Last reviewed 1 min read

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Results

Enter values and click Calculate to see results.
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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

CI = x̄ ± z* · σ/√n

In depth

Constructs a confidence interval for a population mean using the z-distribution: CI = x̄ ± z* · (σ/√n). Common z* values: 90% → 1.645, 95% → 1.960, 99% → 2.576.