Confidence Interval Calculator – Calculate Statistical Ranges
Build a confidence interval for a mean from your sample.
About the Confidence Interval Calculator
What is the Confidence Interval Calculator?
A confidence interval calculator reports the range likely to contain the true population mean, from your sample statistics.
Why use this calculator?
Surveys and studies rarely show raw numbers alone — a 95% confidence interval is the standard way to say how precise an estimate is.
How to use it
- Enter the sample mean, standard deviation and size.
- Choose a confidence level (90%, 95%, 99%).
- Read the interval and margin of error.
Formula
CI = mean ± z · (σ/√n).
Wider confidence (99%) makes the interval wider; more data shrinks it.
Frequently Asked Questions
What does "95% confident" actually mean?
Over many repeated samples, about 95% of intervals built this way would capture the true mean.
How do I make an interval narrower?
Increase the sample size, or accept a lower confidence level.
What order of operations does this use?
It follows standard PEMDAS/BODMAS rules: parentheses, exponents, multiplication and division, then addition and subtraction.
How precise are the answers?
The calculator uses double-precision floating-point math (about 15 significant digits) and rounds the display. For exact symbolic results use dedicated algebra software.
Can I enter negative numbers or decimals?
Yes. Negative values, decimals and very large or small numbers are all supported unless a field says otherwise.
What does it mean if I get an error?
Errors usually mean an invalid input, such as division by zero or a negative value where only positives make sense. Check your entries and try again.
What is the difference between population and sample?
A population includes every member of a group; a sample is a subset. Sample statistics use n−1 in the denominator to correct for bias.
When should I use median instead of mean?
Use the median when data contains outliers or is skewed, because it is less affected by extreme values than the mean.
What does standard deviation tell me?
It measures how spread out the values are around the mean. A small standard deviation means the data clusters tightly; a large one means it is more scattered.
Is this calculator free to use?
Yes. Every calculator on this site is completely free, with no hidden fees, no subscriptions and no limits on how many times you can use it.