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Statistics

Confidence Interval Calculator

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

Last validated: 2026-02-14

Confidence Interval Calculator estimates a range around a sample mean that is likely to contain the corresponding population mean under repeated sampling. The sample mean is the observed average, standard deviation measures spread within the sample, and standard error estimates how much the sample mean would vary if the study were repeated. The confidence level, such as 95%, controls the critical value used to widen or narrow the interval. A 95% confidence interval does not mean there is a 95% probability that one fixed interval contains the true value; rather, the method would capture the true value in about 95% of comparable repeated samples. Use the result to express uncertainty, while remembering that bias, dependence, non-normal data, and poor sampling can invalidate the interpretation.

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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

  1. Enter Sample mean, Std dev, Sample size, Confidence for the confidence interval calculator, keeping units, dates, or text format consistent with the form labels.
  2. Confirm sample size, ordering, and distribution assumptions before relying on the calculated result.
  3. Click "Run the tool" and review Confidence Interval Inputs, Interval for the primary output.
  4. Check the statistical assumptions and sample context before using the result in a report or decision.

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

Confidence and limitations

Formula References

Assumptions

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