Mean Confidence Interval Calculator
Estimate a two-sided confidence interval around a sample mean.
Estimate uncertainty around a sample mean
A confidence interval pairs a sample estimate with a margin that reflects sampling variation under a stated model. This calculator uses a normal critical value, multiplying that value by the standard deviation divided by the square root of the sample size. It reports the lower and upper limits, margin of error, and standard error, which makes it useful for checking coursework, planning summaries, or reproducing a published z-based calculation.
Using the defaults, a mean of 50, standard deviation of 10, sample size of 100, and z value of 1.96 produce a standard error of 1 and a margin of error of 1.96. The resulting interval runs from 48.04 to 51.96. Increasing sample size narrows the interval when all other inputs remain unchanged because the standard error decreases with the square root of n.
Interpret the interval with its assumptions
Inputs are evaluated only in your browser. The numerical interval is not automatically appropriate for every dataset: observations should match the sampling assumptions, the chosen critical value should match the intended confidence level, and small samples with an estimated population deviation may call for a t distribution. Statistical significance also does not establish practical importance or remove bias from data collection.
Frequently Asked Questions
Which formula does this calculator use?
It uses the sample mean plus or minus a chosen z critical value times the standard deviation divided by the square root of n.
What z value gives a 95 percent interval?
A two-sided normal interval commonly uses 1.96 for 95 percent confidence.
When should I use a t interval instead?
A t interval is generally preferred when population variation is unknown and the sample is small.
Browse the full set of free, private, in-browser tools.