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Confidence Interval Calculator
Estimate a range that the true population mean likely falls in, from your sample statistics.
HOW TO USE
- 1Enter the sample mean, the sample size and the sample standard deviation, or the population standard deviation if it is known.
- 2Pick the confidence level: 90%, 95% or 99%. A higher level gives a wider interval.
- 3The margin of error is the t-critical value times the standard error (s ÷ √n).
- 4The confidence interval is the sample mean plus and minus the margin of error. For example a 95% interval of [95.87, 104.13] means you can be 95% confident the true mean lies between those bounds.
EXAMPLE
INPUT
Mean 100, sample size 25, standard deviation 10, 95% confidence
OUTPUT
Margin of error 4.13 · 95% CI [95.87, 104.13]
FAQ
Why does the calculator use the t-distribution?
When the population standard deviation is unknown and estimated from the sample, the t-distribution with n − 1 degrees of freedom is the correct model. For samples above about 120 values the t-distribution is indistinguishable from the normal distribution.
What does a confidence interval actually mean?
If you repeated the sampling many times and computed a 95% interval each time, roughly 95% of those intervals would contain the true population mean. It is a statement about the procedure, not about any single interval.
How can I make the interval narrower?
Collect a larger sample — the standard error shrinks with the square root of the sample size, so quadrupling the sample halves the margin of error. Lowering the confidence level also narrows the interval.
Why is the sample size limited to at least 2?
The t-distribution needs at least 1 degree of freedom (n − 1). With a single observation there is no way to estimate the spread of the population, so an interval cannot be computed.
Is my data sent anywhere?
No. All calculations run entirely in your browser, your numbers never leave your device.