Confidence Interval Calculator
Calculate a two-sided confidence interval for a population mean from your sample mean, standard deviation and sample size. Choose Student’s t when the SD is estimated from the sample; use z only when the population SD is known. This form does not calculate a proportion or prediction interval.
Enter your values or load an example. Calculations stay in this browser.
Choose the source of your standard deviation
Most samples estimate variability from their own observations. Choose Student’s t in that case. Knowing the sample SD very precisely does not turn it into a known population SD.
See the interval calculation
The standard error is SD divided by the square root of n. Multiply by the appropriate critical value and add or subtract that margin from the sample mean.
Check the sampling assumptions
The observations should be independent and appropriately sampled. Small samples from skewed distributions or samples with strong outliers may need another method.
Read confidence correctly
A confidence level describes how the method performs over repeated samples. The interval estimates the population mean, not the range containing a chosen percentage of individual measurements.
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Sources and methods
Frequently Asked Questions
Why use t instead of 1.96?
Student’s t accounts for estimating SD from the sample. Its critical value depends on n−1 degrees of freedom and is especially larger for small samples.
Can this calculate an interval for a proportion?
No. This page estimates a population mean. Proportions require a suitable binomial interval method.
Does 95% mean a 95% probability for this mean?
The population mean is treated as fixed. The 95% refers to the long-run coverage of intervals produced by the method.
What sample sizes are supported?
Enter a whole-number sample size from 2 to 100,001. This numeric limit does not guarantee the sampling assumptions are satisfied.
Continue in the app
Use Statistics AI: Statikia for the full guided result after this quick check.
