About Confidence Interval Calculator
This confidence interval calculator estimates a range for the true mean from a list of sample values, at 90%, 95% or 99% confidence, using the Student t distribution. It is free, needs no sign-up and runs in your browser, so nothing you enter is uploaded.
Paste your sample, choose the level, and the page shows the mean, the critical t value for n - 1 degrees of freedom, the standard error, and the lower and upper limits. It needs at least two values. The interval always uses the sample standard deviation, whichever switch is selected, because it is built from a sample.
The interval answers one question: how precisely does this sample pin down the mean? It does not cover proportions or differences between groups, and it does not check that your data is roughly normal. With a small sample, look at the histogram first. Few values mean a large t value and a wide interval.
How to use Confidence Interval Calculator
- Paste or type your numbers in the data box. Commas, semicolons, spaces and line breaks all work as separators, and the line under the box tells you how many values were read.
- Choose Sample (n - 1) if your numbers are a sample of a larger group, or Population (n) if they are every value you care about.
- Pick the quartile method if you need to match a textbook, Excel or R. The quartiles, the IQR, the fences, the box plot and the percentile box all follow the same choice.
- For grouped data, switch Input type to Grouped data and enter one class per line, such as 10-20 5, meaning the class 10 to 20 with a frequency of 5.
- Read the result cards. The card for the page you opened is outlined, for example the standard deviation on the standard deviation page.
- For a z-score or percentile, type a value or a percentage in the matching box and read the line below it.
- For a confidence interval, pick 90%, 95% or 99%. For correlation and regression, paste a second list of the same length in the Y box.
- Open Steps and formulas at the bottom to see the calculation written out with your numbers.
Features
- Count, sum, mean, median, mode (all tied values), minimum, maximum and range.
- Sample or population variance and standard deviation with one switch, plus the standard error of the mean.
- Quartiles by a method you choose (inclusive, exclusive or linear), the same method for the percentile box, the interquartile range, outlier fences and a list of flagged outliers.
- Grouped data: class intervals with frequencies give the mean, variance, SD and the median by interpolation inside the median class.
- A box plot with whiskers and outlier dots, and a frequency table with relative and cumulative columns.
- A warning that lists every item that was left out because it is not a number.
- Skewness and excess kurtosis, using the adjusted forms for a sample and the plain moment forms for a population.
- z-score of any value against your data and any percentile by linear interpolation.
- Confidence interval for the mean at 90%, 95% or 99%, using the t distribution with n - 1 degrees of freedom.
- Pearson r, R squared, slope and intercept for paired X and Y lists.
- A histogram with axis titles and a values table for screen readers, and a written-out working for the mean, variance, standard deviation, range and IQR.
- Fifteen focused pages (standard deviation, variance, quartiles, five-number summary, grouped data, z-score and more) that open the same tool with the matching result outlined.
Confidence interval formula
The margin of error is the critical t value times the standard error. The interval is the mean plus and minus that margin. The critical t depends on the confidence level and on n - 1.
CI = x̄ ± t × (s / √n), df = n − 1Worked examples
72, 75, 78, 80, 85, 88, 90, 94 (95%) gives n 8, mean 82.75, s 7.7229, SE 2.7304, t 2.3646, margin 6.4565, interval 76.2935 to 89.2065.
4, 8, 15, 16, 23, 42 gives 90%: 6.9020 to 29.0980 (t 2.0150). 95%: 3.8423 to 32.1577 (t 2.5706). 99%: -4.2073 to 40.2073 (t 4.0321).
A higher confidence level gives a wider interval. With only six values the intervals are very wide.
Good to know
Entering your data
Separate values with commas, semicolons, spaces or line breaks and use a dot as the decimal mark. Text that is not a number is skipped, so check the "values parsed" count under the box matches what you pasted.
Privacy: how it works
- Everything is calculated by JavaScript running in your own browser tab. Your numbers are not sent to Ulkaa or to any other server, and the page makes no network requests while you type.
- There is no account and nothing is stored. Closing or reloading the tab clears what you entered.
Tips
- If two sources give different standard deviations for the same data, check whether one divides by n and the other by n - 1 before assuming a mistake.
- Compare the mean with the median. A mean far above the median usually means a few large values are pulling it up, and the outlier fences will often show them.
- The confidence interval gets narrower with more data and wider with a higher confidence level. Try 90%, 95% and 99% on the same list to see how much.
- Correlation only measures a straight-line relationship. Two lists can have an r near 0 and still be tightly related by a curve, so look at the histogram and your data before you rely on r.
- Pair the X and Y lists by position. If they differ in length, only the first n pairs, where n is the shorter list, are used.
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 numbers are processed by code running in your browser tab, on your own device.
Is my data uploaded?
No. Your numbers 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 does a 95% confidence interval mean?
If you drew many samples and built an interval from each one the same way, about 95 percent of those intervals would contain the true mean. It is not a 95 percent probability that this particular interval contains it.
Why does the calculator use the t distribution?
You are estimating the standard deviation from the same small sample, which adds uncertainty. The t distribution has heavier tails than the normal to account for that, and it approaches the normal as n grows.
Can I get a confidence interval for a proportion?
No. This page gives the interval for a mean only.
More Statistics Calculator pages
- Statistics CalculatorPaste a list of numbers and get the mean, median, mode, spread, quartiles, a z-score, a confidence interval and a regression line.
- Standard Deviation CalculatorPaste your numbers and get the sample and population standard deviation with every step.
- Mean, Median and Mode CalculatorMean, median, mode and range of any list, in one view.
- Mean CalculatorThe average of a list of numbers, with the sum and count.
- Median CalculatorThe middle value of a list, with the quartiles alongside.
- Mode CalculatorThe most frequent value in a list, with ties handled.
- Variance CalculatorSample or population variance, with the sum of squares.
- Range CalculatorMinimum, maximum and range of a list of numbers.
- Z-Score CalculatorHow many standard deviations a value is from the mean of your data.
- Correlation CalculatorPearson r and R squared for two paired lists.
- Linear Regression CalculatorThe least-squares line y = mx + b for paired data.
- Quartile and IQR CalculatorQ1, median, Q3, IQR and outlier fences for a list of numbers.
- Interquartile Range (IQR) CalculatorThe IQR of your data, with Q1, Q3 and the outlier fences.