Confidence Interval Calculator
Calculate a two-sided normal confidence interval for a population mean when its standard deviation is known.
Make this result useful
Use it now, or keep a copy for later. We never save your tool input automatically.
How to use this tool
Enter the sample mean, known population standard deviation, sample size and 90%, 95% or 99% confidence level.
Important to know
Calculate a two-sided normal confidence interval for a population mean when its standard deviation is known.
This z interval assumes an independent random sample and a normal population or an appropriate large-sample approximation. It is not the t interval used when population standard deviation is unknown. A confidence level describes the procedure over repeated samples, not the probability that this fixed interval contains the parameter.
Formula and methodology
Interval = sample mean ± z × known population SD ÷ √n. The z critical values are approximately 1.644854, 1.959964 and 2.575829 for 90%, 95% and 99%. Method: NIST/SEMATECH e-Handbook of Statistical Methods, section 7.1.4.
Example
For mean 100, known SD 15 and n = 100, the 95% margin is about 2.94, giving roughly 97.06 to 102.94.
Frequently asked questions
Can I enter the standard deviation estimated from my sample?
No. This tool assumes the population standard deviation is known; a sample-estimated SD generally calls for a t interval.