Calculate confidence interval

Calculate a z-based confidence interval for a mean when population variation is known.

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ToolConfidence Interval Calculator
Input
Output
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How it works

The margin of error multiplies a selected two-sided z critical value by the standard error, which is the known population deviation divided by the square root of the sample size. Adding and subtracting that margin from the sample mean gives the interval bounds.

  • This z interval is for a known population deviation; a sample deviation requires a t interval.

Worked example

A sample of 25
Sample mean 50, standard deviation 10, at 95% confidence
Input
											Sample mean: 50
Standard deviation: 10
Sample size: 25
Confidence level: 95
Output
												Margin of error: 3.92
Lower bound: 46.08
Upper bound: 53.92
Z value: 1.96

When to use this

Manufacturing measurements, survey means, and laboratory controls report uncertainty intervals.

Edge cases

  • A sample standard deviation is not the known population deviation assumed here.
  • A sample size below two is rejected.
  • A zero deviation is rejected because the tool requires positive uncertainty.

References