Statistics
Confidence Interval Calculator
Use this confidence interval calculator to estimate a plausible range for a population mean or proportion.
Try an example
Result
Confidence interval
—
- Margin of error
- —
- Lower bound
- —
- Upper bound
- —
Student quick launch
Grade planning, algebra checks, and formulas students reach for most.
Study path
Use this calculator with
Follow these when you want the formula behind the answer, a short lesson, or nearby tools in the same topic.
What the confidence interval calculator solves
Use this A range of values that probably contains the true answer, given your data. calculator to estimate a plausible range for a Every member of the group you actually care about, not just the ones measured. mean or proportion.
Formula
How to use it
- Choose mean or proportion.
- Enter confidence level and A smaller group taken from a population, used to estimate facts about the whole group. information.
- Read lower bound, upper bound, and margin.
How to read the answer
A confidence interval estimates a range of plausible population values under the model assumptions.
Common mistakes and edge cases
- Confidence is about the method, not the probability a fixed interval contains the parameter.
- Small samples may need t intervals or exact methods.
- Biased samples break interval meaning.
Worked examples
Mean interval
Confidence interval
71.3599 to 72.6401
Proportion interval
Confidence interval
66.33% to 73.67%
Frequently asked questions
What does 95% confidence mean?+
In repeated sampling, the method would capture the true value about 95% of the time.
Why use z instead of t?+
This calculator uses common z intervals. Small samples with unknown population standard deviation often use t intervals.
About this calculator
- Written by
- mathcheck editorial team
- Last reviewed
- May 8, 2026
Method
- Uses the values entered by the user and stable formulas documented on the page.
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Last updated: May 8, 2026