Sample Size and Power Calculators
Sample Size Statistical Calculator
Statistical Sample Size Calculator calculate statistical sample size for a mean, proportion, two means, or two proportions with power, finite-population, design-effect, and attrition adjustments. Use the tabbed test workspace below for data, variables, analysis, visualizations, results, interpretation and reporting.
Quick method summary
The Sample Size Statistical Calculator calculates the named method using calculator-specific formulas and reports auditable results, warnings, and interpretation. It uses the calculator-specific formula and reports the intermediate values, final result, warnings, and interpretation.
Sample Size and Power Calculators
Statistical Sample Size Calculator
Calculate statistical sample size for a mean, proportion, two means, or two proportions with power, finite-population, design-effect, and attrition adjustments.
Calculated result
Calculation method
Calculate statistical sample size for a mean, proportion, two means, or two proportions with power, finite-population, design-effect, and attrition adjustments.
Formula
The calculator uses the selected design formula, rounds required sample sizes upward, then applies finite-population, design-effect, allocation, and attrition adjustments.
Assumptions and limits
The selected design, data type, independence or pairing, missing-data handling, sample-size conditions, and model assumptions must match the research question.
Formula review
Formula, input validation, output contract, and independent control cases reviewed 2026-08-02; study-design assumptions remain visible to the user.
Statistical Sample Size Calculator method, assumptions and reporting guideComplete selected-test explanation, assumptions, formula and reporting details
Data Import and Variable Requirements
For the Sample Size Statistical Calculator, enter the method-specific values requested by the calculator: Study design, Confidence level, Margin of error, Estimated population standard deviation, Estimated baseline proportion, Target standardized effect / proportion difference. Review the selected mode, units, tails, and limits before calculating. For Statistical Sample Size Calculator, map Study design, Confidence level, Margin of error, Estimated population standard deviation, Estimated baseline proportion, Target standardized effect / proportion difference from the cleaned browser-local table; every mapped variable remains editable before calculation, and the active dataset remains available while you work with this selected test and when you return to the Test Finder.
Uploaded files are processed locally in the browser. The cleaning report appears before variable selection, and the selected cleaned columns are mapped to this exact calculator rather than a generic fallback.
Statistical Sample Size Calculator Workspace Features
- Dedicated Statistical Sample Size Calculator variable mapping, calculation contract, result explanation, and diagnostics
- Calculator-specific inputs and validation instead of a generic fallback form
- Visible formula, substituted values, intermediate quantities, and final result
- Method-specific assumptions, warnings, decision guidance, and interpretation
- Responsive chart or visual that changes with entered values where the method benefits
- Copy, result CSV, chart PNG, and result-only print controls
- Protected canonical URL, focused FAQs, and a dedicated selected-test workspace
About the Statistical Sample Size Calculator
Calculate statistical sample size for a mean, proportion, two means, or two proportions with power, finite-population, design-effect, and attrition adjustments. Planning calculators connect effect size, precision, alpha, power, group count, and sample size for the specific design shown.
When to Use the Statistical Sample Size Calculator
Use the Sample Size Statistical Calculator when your research question, variable types, and sampling or experimental design require statistical sample size. Do not select it only because the data produce a convenient p-value or familiar output.
How the Statistical Sample Size Calculator Works
The calculator uses the selected design formula, rounds required sample sizes upward, then applies finite-population, design-effect, allocation, and attrition adjustments.
The calculation runs in the browser. Submitted values are validated for required numeric ranges, data shape, units and method-specific restrictions before results are shown.
Assumptions and Checks
- The selected design, tail, alpha level, allocation ratio, effect-size definition, and variance assumptions must match the planned study.
- The effect size should be scientifically meaningful and supported by defensible pilot data or prior evidence.
- Inflate the calculated requirement for attrition, nonresponse, clustering, multiple testing, or design effects when applicable.
Required Inputs
- Study design (required) Options: Estimate one mean, Estimate one proportion, Compare two means, Compare two proportions
- Confidence level (required)
- Margin of error (required)
- Estimated population standard deviation (required)
- Estimated baseline proportion (required)
- Target standardized effect / proportion difference (required)
- Target power (required)
- Group 2 / Group 1 allocation ratio (required)
- Finite population size (optional) (optional)
- Design effect (required)
- Expected attrition / nonresponse rate (required)
Results Reported
The result workspace shows the final answer and intermediate quantities needed to audit the calculation. Depending on the method, reported values include:
- Mode
mode - Z Critical
z_critical - Unadjusted Sample Size
unadjusted_sample_size - Finite Population Sample Size
finite_population_sample_size - Design Adjusted Sample Size
design_adjusted_sample_size - Final Sample Size
final_sample_size - Group 1 Sample Size
group_1_sample_size - Group 2 Sample Size
group_2_sample_size
Statistical Sample Size Calculator Worked Example
Use the example data button, calculate, then review the result table, formula, and worked solution before using the answer.
| Input | Example value |
|---|---|
| Study design | proportion |
| Confidence level | 0.95 |
| Margin of error | 0.03 |
| Estimated population standard deviation | 12 |
| Estimated baseline proportion | 0.50 |
| Target standardized effect / proportion difference | 0.30 |
| Target power | 0.80 |
| Group 2 / Group 1 allocation ratio | 1 |
| Finite population size (optional) | |
| Design effect | 1 |
| Expected attrition / nonresponse rate | 0.10 |
Verified Worked Result
The packaged automated fixture produces the following checked values from the example inputs. Display rounding can differ from the full-precision browser result.
| Result | Verified value |
|---|---|
| Z Critical | 1.9599639861202 |
| Unadjusted Sample Size | 1067.0718963578 |
| Final Sample Size | 1186 |
How to Use This Workspace
- Confirm that the method matches the quantity, hypothesis, model or planning question you need to solve.
- Enter values with compatible units and the requested sample, group, matrix, count, date or option format.
- Use Example Data to inspect a valid input layout, or enter your own values and run the calculation.
- Review the result table, formula, substitutions, warnings and interpretation rather than relying only on the headline number.
- Copy, download or print the result when you need a reusable analysis record.
Understanding and Reporting the Result
Review Mode, Z Critical, Unadjusted Sample Size, Finite Population Sample Size, Design Adjusted Sample Size, Final Sample Size, Group 1 Sample Size, and Group 2 Sample Size. Use the displayed assumptions, warnings, and interpretation before reporting the result. In the Statistical Sample Size Calculator result workspace, interpret mode, z_critical, unadjusted_sample_size, finite_population_sample_size, design_adjusted_sample_size, final_sample_size together with the method assumptions, warning messages, confidence information, effect magnitude, and diagnostic plots shown for the selected variables.
Planning assumptions should be justified before data collection; attrition, clustering, unequal allocation, and multiplicity may require a larger design.
Keep the entered values, units, selected options and any warning shown beside the result. For a hypothesis test, report the statistic, degrees of freedom where applicable, p-value, alpha level, effect size and decision. For an estimate or conversion, report the formula convention and final unit.
How to Report the Result
When reporting results from the Sample Size Statistical Calculator, identify the design and software, state the valid sample size and exclusions, then report Mode, Z Critical, Unadjusted Sample Size, Finite Population Sample Size, Design Adjusted Sample Size, Final Sample Size, Group 1 Sample Size, Group 2 Sample Size. Include the selected alpha level, tail, coding, and assumption decisions when they apply. A reproducible Statistical Sample Size Calculator report should identify the mapped variables, valid observations, exclusions or missing-data handling, selected options, principal outputs, uncertainty, diagnostics, and the practical conclusion supported by the analysis.
Accuracy and Limitations
The calculator keeps full browser precision during calculation and rounds only for display. Accuracy still depends on correct inputs and on whether the displayed model represents the real problem. Educational calculators cannot replace required professional review, current official rules, field measurements, laboratory methods or specialist statistical software where those are necessary.
Frequently Asked Questions
What does the Statistical Sample Size Calculator calculate?
Calculate statistical sample size for a mean, proportion, two means, or two proportions with power, finite-population, design-effect, and attrition adjustments.
Which formula does the Statistical Sample Size Calculator use?
The calculator uses the selected design formula, rounds required sample sizes upward, then applies finite-population, design-effect, allocation, and attrition adjustments.
When should I use the Sample Size Statistical Calculator?
Use the Sample Size Statistical Calculator when your research question, variable types, and sampling or experimental design require statistical sample size. Do not select it only because the data produce a convenient p-value or familiar output.
What inputs does the Sample Size Statistical Calculator require?
Enter the method-specific values requested by the calculator: Study design, Confidence level, Margin of error, Estimated population standard deviation, Estimated baseline proportion, Target standardized effect / proportion difference. Review the selected mode, units, tails, and limits before calculating.
What does the Sample Size Statistical Calculator report?
Review Mode, Z Critical, Unadjusted Sample Size, Finite Population Sample Size, Design Adjusted Sample Size, Final Sample Size, Group 1 Sample Size, and Group 2 Sample Size. Use the displayed assumptions, warnings, and interpretation before reporting the result.
Can the Sample Size Statistical Calculator analyze Excel or CSV data?
This page uses direct method-specific inputs because a spreadsheet is not required for the calculation. Results still include the formula, steps, visual, warnings, and export controls.