Statistics

Confidence Interval Calculator

Estimate confidence intervals from mean, standard deviation, and sample size.

Last validated: 2026-02-14

Confidence Interval Calculator estimates a confidence interval around a sample mean using sample stats. It is useful for expressing uncertainty in reports and experiments. The tool turns point estimates into bounded ranges. Use it to communicate estimate precision rather than single values only.

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Input Pattern

Enter values in the left panel, keep units explicit, run the calculation, then copy or share the result. Invalid fields are highlighted immediately.

Confidence Interval Inputs

Interval

Margin: 5.3677

Lower: 94.6323

Upper: 105.3677

How to use this tool

Enter sample mean, standard deviation, sample size, and confidence level.
Run calculation to compute interval bounds.
Report interval alongside assumptions and sampling method.

Worked Example

Auto-generated from the tool's current default or entered inputs.

Example Inputs

Std dev: 15.0
Sample size: 30
Confidence: 95
Z score: 1.96
Margin of error: 5.367681063550628
Lower bound: 94.63231893644937
Upper bound: 105.36768106355063

Expected Outputs

Mean: 100
Std dev: 15
Sample size: 30
Z score: 1.96

Interpretation

Mean is 100.0. Use this as a decision input, not as a standalone conclusion.
Std dev is 15.0. Use this as a decision input, not as a standalone conclusion.
Sample size is 30. Use this as a decision input, not as a standalone conclusion.
Interpret this value alongside sample quality and assumptions to avoid overconfidence.

Scenario Compare (A vs B)

Use this to compare two input sets and quantify change in key outputs.

Scenario A

Std dev

Sample size

Confidence

Z score

Margin of error

Lower bound

Upper bound

Scenario B

Std dev

Sample size

Confidence

Z score

Margin of error

Lower bound

Upper bound

Confidence and limitations

Outputs are deterministic formula results and depend entirely on input quality and units.
Results are for planning and learning; verify with domain standards before safety-critical use.
Interpretation depends on assumptions (distribution, independence, sample quality).

Formula References

Frequentist estimation and hypothesis-test formulas used in standard textbooks.
Interpretation depends on sample quality and assumptions.

Assumptions

Outputs are deterministic formula results and depend entirely on input quality and units.
Results are for planning and learning; verify with domain standards before safety-critical use.
Interpretation depends on assumptions (distribution, independence, sample quality).

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