basic

Confidence Interval for Mean (σ Known) Calculator

CI = x̄ ± z* · σ / √n for a known population σ.

Compute a z-based confidence interval for a population mean when the population standard deviation σ is known: CI = x̄ ± z* · σ / √n. Supports 90 %, 95 %, 98 %, and 99 % confidence levels.

Daniel Oh By Daniel Oh
Published Last reviewed 1 min read

Inputs

Results

Enter values and click Calculate to see results.
Was this helpful?

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

Compute a z-based confidence interval for a population mean when the population standard deviation σ is known: CI = x̄ ± z* · σ / √n. Supports 90 %, 95 %, 98 %, and 99 % confidence levels.