About 95% Confidence Interval Calculator
This 95% confidence interval calculator takes a sample mean, standard deviation and size and returns the interval, using the t distribution with n minus 1 degrees of freedom. It is free, needs no sign-up and runs in your browser, so nothing you enter is uploaded.
The 95% level is the default in most research, and you can switch to 90% or 99% in one tap to see how the interval changes. The calculator opens on a mean of 50, a standard deviation of 10 and 25 observations, so you can see the interval and the working at once.
You can also paste raw data. For a proportion, a difference of two means or a known population standard deviation, use the switch at the top of the tool.
How to use 95% Confidence Interval 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.
Worked examples
mean 50, SD 10, n 25, 90% gives 46.58 to 53.42, t = 1.711
mean 50, SD 10, n 25, 95% gives 45.87 to 54.13, t = 2.064
mean 50, SD 10, n 25, 99% gives 44.41 to 55.59, t = 2.797
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.
What is a 95% confidence interval?
A range calculated so that, over many repeated samples, about 95% of the ranges built this way contain the true population value. It reflects the uncertainty from sampling.
Can I use the number 1.96?
Only for a known standard deviation or a large sample. With 25 observations and an estimated standard deviation the correct multiplier is the t value, 2.064, which is wider.
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.
- Confidence Interval for the Mean CalculatorPaste a list of values and get the confidence interval for the population mean.
- 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.