Known-Sigma or Student-t Mean Interval Calculator
Calculate a two-sided normal mean interval when the population standard deviation is known.
Your result
MATHEnter your values and select calculate.
On this page How it works & practical examples
How to use the Known-Sigma or Student-t Mean Interval Calculator
Choose known-sigma mode with the appropriate normal multiplier, or sample-SD mode with a confidence level. Student-t mode uses n−1 degrees of freedom and requires at least two independent observations.
The calculation
Worked example
Mean 100, known σ = 15, n = 36 and z = 1.96 give margin 4.9 and interval [95.1, 104.9].
Assumptions and limits
No protection against sampling bias, clustering or invalid normal approximation. Sample SD must be supplied, not a standard error. The tool does not establish confidence assumptions.
Common questions
Which inputs should I use?
Enter a known population standard deviation, an independent random sample size, and the normal critical multiplier for your intended two-sided confidence level. For the usual normal model, 1.96 is approximately the 95% multiplier.
What does the result exclude?
If sigma is estimated from a small sample, this z interval is not the appropriate Student-t interval. Sampling bias, clustering and repeated testing are not corrected.