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Mean Confidence Interval Calculator — result sheet
Build a two-sided mean confidence interval from a sample mean, standard deviation, sample size, and supplied critical value.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: SE = s/√n; margin = critical value × SE; interval = x̄ ± margin.
The calculator separates the standard error from the supplied critical value. Use a z critical value when the normal approximation is justified, or a t critical value chosen for the relevant degrees of freedom.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Sample mean — minimum -1000000000; maximum 1000000000
- Sample standard deviation — minimum 1.0E-6; maximum 1000000000
- Sample size n — minimum 2; maximum 1000000000
- Two-sided critical value — minimum 1.0E-6; maximum 1000
Worked example
| Input | Value |
|---|---|
| Sample mean | 100 |
| Sample standard deviation | 15 |
| Sample size n | 64 |
| Two-sided critical value | 1.96 |
Standard error: 1.875; margin: 3.675; interval: 96.325 to 103.675.
Assumptions and limits
- The entered critical value already matches the intended confidence level and distribution; it is not inferred from a percentage.
- The sample standard deviation is positive and the sample size is a whole number of at least two.
- The interval describes a method under its sampling assumptions, not a guarantee that one realized interval contains the parameter.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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