Math & Statistics
Confidence Interval Calculator for a Mean
Estimate a normal-approximation confidence interval for a mean from sample mean, sample standard deviation, size, and confidence level. The calculator uses interval = sample mean ± z* × sample SD ÷ √n. It returns more than one result so you can check the main answer against a useful secondary measure. A larger sample narrows the standard error when variability stays constant. Small samples, skewed data, dependence, or unknown population behavior may require a t interval or another method.
Check the displayed units, assumptions, and rounding before relying on the result.
Calculate and compare
Use the number box for precision or the slider for fast scenario testing.
Scenario results
Confidence interval
50.2887 to 54.5113
Normal-approximation interval.
Margin of error
±2.1113
Critical value times standard error.
Standard error
1.0772
Sample SD divided by square root of n.
How the calculation works
Use consistent units and retain full precision until the final display step.
Worked example
Reproduce the displayed scenario, then change one assumption at a time.
Assumptions behind the result
- • Inputs use the units shown beside each control.
- • The displayed formula is applied without hidden market or demographic data.
- • Rounding occurs only for display; calculations keep full numeric precision.
- • A larger sample narrows the standard error when variability stays constant.
- • Small samples, skewed data, dependence, or unknown population behavior may require a t interval or another method.
Mistakes that change the answer
- • Mixing percentages with decimals or mixing incompatible units.
- • Relying on a rounded intermediate value instead of the full result.
- • Changing several assumptions at once instead of testing sample mean separately.