Confidence Interval Calculator
Find the confidence interval for a mean from the sample mean, standard deviation, sample size, and confidence level. Calculates in your browser.
Confidence interval
-
Show the math
The interval is the mean plus or minus a margin from the standard error:
CI = mean ± z × (σ ÷ √n)
The z value comes from the confidence level (1.96 for 95%). This normal approximation is best for larger samples (n ≥ 30). All math runs locally in your browser.
What this does
The confidence interval calculator finds the range that likely contains the true population mean, using the sample mean, standard deviation, sample size, and a confidence level. It also reports the margin of error.
How to use it
- Enter the sample mean and standard deviation.
- Enter the sample size.
- Choose a confidence level (e.g. 95%).
- Read the interval and margin of error.
How it works
The margin of error is the critical z-value for your confidence level times the standard error (sd divided by the square root of n). The interval is the mean plus and minus that margin. This normal approximation is best for large samples (n ≥ 30).
CI = mean ± z × (sd ÷ √n)
Understanding your result
A 95% confidence interval means that if you repeated the sampling many times, about 95% of the intervals built this way would contain the true mean — not that any single interval has a 95% chance of doing so. A larger sample or a lower confidence level narrows the interval; a higher confidence level widens it.
Example
A mean of 100, sd 15, n 36 gives a 95% interval of about 100 ± 4.9, or 95.1 to 104.9.
Sources & methodology
Last updated .
Frequently asked questions
What does a 95% confidence interval mean?
If you repeated the study many times, about 95% of the intervals computed this way would contain the true population mean. It is a statement about the method, not a single interval.
How do I make the interval narrower?
Increase the sample size or accept a lower confidence level. Both shrink the margin of error; a higher confidence level widens it.
Does this use the z or t distribution?
It uses the normal (z) approximation, which is reliable for large samples (n ≥ 30). Very small samples are better served by a t-interval.
Is my data stored?
No. Everything is calculated locally in your browser.
Related tools
Permutation & Combination Calculator
Calculate permutations (nPr) and combinations (nCr) for choosing r items from n, with the factorial behind each. Calculates in your browser.
Z-Score Calculator
Find the z-score (standard score) of a value — how many standard deviations it sits above or below the mean. Calculates in your browser.
Sample Size Calculator
Find the sample size needed to estimate a proportion to within a margin of error at a chosen confidence level, with a population correction. Calculates in your browser.
Statistics Calculator
Paste a list of numbers and get count, sum, mean, median, mode, range, quartiles, IQR, variance, and standard deviation. Calculates in your browser.