Confidence interval calculator

Calculate a two-sided normal confidence interval for a mean when the population standard deviation is known.

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Sample mean

Known population standard deviation

More inputs and assumptions

Sample size

Confidence percent

Answer

…

Calculate a two-sided normal confidence interval for a mean when the population standard deviation is known.

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Formula and assumptions

Requires independent sampling and a normal population or a suitable large-sample approximation. If you estimated standard deviation from this sample, use an appropriate t interval instead. Confidence describes long-run coverage of the method, not the probability of this fixed interval containing the mean.

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Updated 2026-09-26

Using Confidence interval calculator

Calculate a two-sided normal confidence interval for a mean when the population standard deviation is known.

Next: Basic calculator

A worked example

With sample mean = 100, known population standard deviation = 15, sample size = 100, confidence percent = 95, the lower confidence limit is 97.06005402318992.

Before you use the result

Example results for sample mean

These examples use Known population standard deviation: 15; Sample size: 100; Confidence percent: 95. They are reference calculations, not recommended settings.

Sample mean	Lower confidence limit
50	47.0600540232
100	97.0600540232
200	197.060054023

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