Confidence Interval Calculator
Calculate a symmetric confidence interval around a sample mean at common confidence levels.
Confidence interval47.648 to 52.352
Margin of error2.352
Standard error1.2
Critical z1.96
This uses a z-based interval for a mean. For small samples with an unknown population standard deviation, a t-interval is generally more appropriate.
How this tool works
Standard error = s/√n and margin = z* × standard error. The interval is mean ± margin.
Example
With mean 50, standard deviation 12 and n=100, a 95% z interval uses approximately 1.96 standard errors on each side.
Common questions
When should I use a t interval instead?
For small samples when the population standard deviation is unknown, a t-based interval is usually more appropriate.
Does 95% confidence mean a 95% chance this fixed interval contains the parameter?
In frequentist interpretation, 95% refers to the long-run coverage of the interval procedure across repeated samples.