About Confidence Interval for the Mean Calculator
This calculator builds a confidence interval for a population mean from a list of measurements, working out the mean, the standard deviation and the standard error for you. It is free, needs no sign-up and runs in your browser, so nothing you enter is uploaded.
The page opens on twelve measurements at the 99% level. Paste your own values separated by commas, spaces or new lines, and the interval updates as you type. The result shows the mean, the margin of error, the t critical value for n minus 1 degrees of freedom and the standard error.
The interval assumes a random sample from a roughly normal population, or a sample large enough for the mean to be roughly normal. For a skewed small sample, treat it with caution.
How to use Confidence Interval for the Mean Calculator
- Choose what you want an interval for: a mean (standard deviation unknown or known), a proportion or a difference of means.
- Enter raw data or summary statistics. For a proportion enter the number of successes and the sample size.
- For a known-sigma interval, type the population standard deviation.
- Pick the confidence level: 90%, 95% or 99%.
- Read the interval and the margin of error, then open the working to see each formula.
Features
- Mean with unknown sigma (t interval) or known sigma (z interval).
- Proportion with the Wald and Wilson score methods, compared side by side, with a small-sample warning.
- Difference of two means, with the Welch method by default.
- Raw data or summary statistics.
- Margin of error, critical value, standard error and degrees of freedom shown.
- A bell curve with the central confidence region shaded.
- Step-by-step KaTeX working and a plain-English reading of the interval.
Interval for a mean
The interval is the sample mean plus or minus the margin of error.
x̄ ± t(α/2, n−1) · s / √nWorked examples
102, 98, 110, 95, 104, 99, 107, 101, 96, 108, 103, 100 at 99% gives mean 101.92, interval 97.686 to 106.15, t = 3.106
NIST ZARR13: mean 9.261460, SD 0.022789, n 195 at 95% gives 9.258241 to 9.264679
NIST/SEMATECH e-Handbook, section 1.3.5.2.
Privacy: how it works
- The interval is calculated by code in your own browser tab. Your numbers are not sent to Ulkaa or any other server.
- There is no account and nothing is stored once you close the tab.
Tips
- Use the t interval unless you truly know the population standard deviation. Knowing it is rare outside textbooks.
- For a proportion, prefer Wilson. Use Wald only when you are matching a textbook answer.
- If a difference interval contains 0, the data are consistent with no difference at that confidence level.
- Quadrupling the sample size roughly halves the margin of error.
Frequently asked questions
Is it really free?
Yes. There is no price, no trial and no credit card. Ulkaa Tool does the work with your own device, so there is no server bill to pass on to you.
Do I need an account?
No. There is no sign-up and no login. Open the page and use it. An Ulkaa account is not needed for anything on this tool.
Does it run in my browser?
Yes. Your data are processed by code running in your browser tab, on your own device.
Is my data uploaded?
No. Your data are never sent to Ulkaa or to anyone else. You can check this yourself by watching the Network tab in your browser developer tools while you use the tool.
How many values do I need?
At least 2, since the standard deviation needs two values. The interval is very wide with so few, and it narrows as n grows.
Is the interval for the mean or for individual values?
For the population mean. Individual values spread much more widely than the mean, so a prediction interval would be needed for a single new value, and this calculator does not compute one.
More Confidence Interval Calculator pages
- Confidence Interval CalculatorGet a 90%, 95% or 99% confidence interval for a mean, a proportion or a difference of means, with every step shown.
- 95% Confidence Interval CalculatorType a mean, a standard deviation and a sample size and get the 95% interval and its margin of error.
- Confidence Interval for a Proportion CalculatorEnter the number of successes and the sample size to get a Wilson or Wald interval.
- Confidence Interval for a Difference of MeansEnter two groups and get the interval for the difference between their population means.
- Z Confidence Interval CalculatorUse the normal distribution for a mean when you know the population standard deviation.