Sample Size Planning Calculator
Estimate the sample count needed for a target margin of error for a mean or a proportion. Optionally apply a finite-population correction and round upward.
YOUR CALCULATION
Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Use the normal planning formula with an assumed standard deviation or proportion. For a known finite population sampled without replacement, adjust the variance for sampling fraction. Round the required count upward and report the resulting model margin.
Mean n0=(zσ/E)²; proportion n0=z²p(1−p)/E²; finite n=Nn0/(N+n0−1)
Worked example
For95% confidence, a5-percentage-point margin and planning proportion50%, the large-population calculation needs385 observations. For a finite population of1000, the corrected count is278.
Assumptions and input details
This is normal-approximation planning for a simple random sample, not a guarantee of coverage or a power-analysis calculation. For proportions, margin is in percentage points, not a relative percent; p must be strictly between0 and100%. Use50% when no planning proportion is available. Mean planning requires positive SD and absolute margin. Finite population is an integer1–1e9; supported required counts are at most1e9. Clustering, nonresponse, weighting and design effects are not automatically added.
References: NIST sample-size planning for means
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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Find exact-count and tail probabilities when drawing from a finite population without replacement. Inspect feasible success counts and exact combinatorial fractions.
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