Toolstia / Confidence interval calculator
Confidence interval calculator
A confidence interval gives a range that is likely to contain the true mean of a population. Enter your sample mean, standard deviation and sample size, choose a confidence level, and get the lower and upper bounds with the margin of error.
Enter the mean, the standard deviation and a sample size of at least 2.
A 95% confidence interval means that if you repeated the study many times, about 95% of such intervals would contain the true mean. It does not mean a 95% chance for this one interval.
How it works
- Enter the sample mean, standard deviation and sample size.
- Choose the confidence level and the distribution.
- Read the interval, the margin of error and the critical value.
The formula
The interval is the mean ± margin of error. The margin of error is the critical value times the standard error, and the standard error is the standard deviation divided by the square root of n.
t or z
Use the t distribution when the standard deviation comes from your sample, which is the usual case. Use z only when the population standard deviation is known. For large samples the two give nearly the same answer.
Critical values
The t value is found for n − 1 degrees of freedom from the exact t distribution rather than from a rounded table, so any sample size and any confidence level works.
How to read it
A 95% interval means that if you repeated the sampling many times, about 95% of the intervals would contain the true mean. It is not the probability that this single interval does.
Questions
What makes the interval narrower?
A bigger sample, less variation in the data, or a lower confidence level.
Does it work for proportions?
No. This tool is for means. Use the sample size calculator for proportions.
Is anything uploaded?
No. Your numbers stays in your browser and is never sent anywhere.