Statistics
Confidence Interval Calculator
Use this confidence interval calculator to estimate a plausible range for a population mean or proportion.
Confidence interval
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- Margin of error
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- Lower bound
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- Upper bound
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Study path
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What the confidence interval calculator solves
Use this confidence interval calculator to estimate a plausible range for a population mean or proportion.
Formula
How to use it
- Choose mean or proportion.
- Enter confidence level and sample 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.
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Last updated: May 8, 2026