Use this calculation to reproduce a defined quantitative method when the observations, units, sampling process, and assumptions match the method shown here.

Sample size

Required integer.

Sample mean

Required number.

Population standard deviation

Required number.

Confidence level

Required integer.

The cited overview of Statistics supplies background for the terminology and domain context used by this tool.^[1]

Calculate a two-sided confidence interval for a population mean when the population standard deviation is known. Inputs are interpreted exactly in the displayed units and the calculation returns the following fields without presentation rounding.

Lower bound

Returned number.

Upper bound

Returned number.

• A numerical result does not by itself establish data quality, causation, representativeness, independence, distributional fit, or practical significance.
• Sample size must be at least 1.
• Population standard deviation must be at least 0.
• Use finite inputs in the displayed units, preserve source measurements and assumptions, and independently verify consequential decisions.

Inspect the underlying data, visualize its distribution, report uncertainty and sample size, and compare the result with a robust or domain-specific method where appropriate.

• T-Interval Calculator

  Calculate a two-sided Student's t confidence interval for a population mean with unknown sigma.

• Coefficient of Variation Calculator

  Calculate population standard deviation as a percentage of the mean.

• Population Summary Calculator

  Calculate the count, mean, population variance, and population standard deviation of a finite dataset.