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Margin of Error Calculator — result sheet
Calculate a normal-approximation margin of error from a critical value, standard deviation, and sample size.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: Standard error=standard deviation/√sample size; margin of error=critical value×standard error.
This calculator separates the uncertainty scale from the chosen critical value so the confidence convention remains visible.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Critical value — minimum 0; maximum 100
- Standard deviation — minimum 0; maximum 1000000000000
- Sample size — minimum 1; maximum 1000000000
Worked example
| Input | Value |
|---|---|
| Critical value | 1.96 |
| Standard deviation | 15 |
| Sample size | 100 |
Standard error = 1.5; margin of error = 2.94.
Assumptions and limits
- The critical value is appropriate for the intended interval and statistic.
- The standard deviation is either known or intentionally used as an estimate.
- Sampling design, finite-population corrections, nonresponse, and coverage quality are not inferred.
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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