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90% Mean Confidence Interval Calculator — result sheet
Calculate a normal-approximation 90% confidence interval for a sample mean from standard deviation and sample size.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: 90% interval = mean ± 1.645×standard deviation/√n.
The margin of error is reported separately so the confidence level and sampling scale remain visible.
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 0; maximum 1000000000
- Sample size — minimum 1; maximum 1000000
Worked example
| Input | Value |
|---|---|
| Sample mean | 100 |
| Sample standard deviation | 15 |
| Sample size | 36 |
90% interval ≈95.89 to104.11.
Assumptions and limits
- The standard deviation is nonnegative and sample size is a positive whole number.
- The normal critical value 1.645 is used as a large-sample or known-standard-deviation approximation.
- Finite-population correction, nonresponse, bias, design effects, and t critical values are not modeled.
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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