Math & Statistics Calculator
Confidence Interval Calculator
Build confidence intervals for means and proportions with margin of error, standard error, critical values and clear interpretation notes.
Choose interval type
Mean inputs
Your confidence interval
The dot marks the sample estimate; the coloured line runs from the lower to the upper bound.
Compare 90%, 95% and 99%
Higher confidence produces a wider interval from the same sample.
Calculation steps
- Estimate and sample size
- Standard error
- Critical value
- Interval bounds
How to interpret this interval
Plan a sample size
Planning estimate only. It assumes independent random observations and uses the current standard deviation or proportion. It does not account for bias, clustering or a finite population.
Mean confidence interval
For a mean, the calculator uses mean +/- critical value x standard error, where standard error = SD / sqrt(n).
The t critical value is recommended when the standard deviation comes from the same sample.
Proportion confidence interval
For a proportion, the calculator uses the Wilson score interval. This is often better behaved than the basic normal approximation when samples are small.
Enter successes and total sample size, for example 56 successes out of 100 observations.
Confidence Interval Calculator FAQ
What is a confidence interval?
A confidence interval gives a plausible range for a population value based on a sample estimate and a chosen confidence level.
What is margin of error?
Margin of error is the amount added to and subtracted from the estimate to create the interval.
Should I use t or z for a mean interval?
Use t when the population standard deviation is unknown and you are using a sample standard deviation. Use z when the population standard deviation is known or for large-sample approximations.
Why does the proportion calculator use Wilson interval?
The Wilson score interval is usually more stable than the simple Wald interval, especially with small samples or proportions near 0 or 1.
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