Confidence Interval Width Planner Calculator

Plan sample size required for a target confidence-interval width using confidence level and estimated standard deviation.

Quick Facts

Core Formula
n = (z * sigma / ME)^2 where width = 2 * ME
Use this as a planning and validation aid, then confirm assumptions with your context.

Your Results

Calculated
Required Sample Size
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Primary output
Margin of Error
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Secondary output
z-score Used
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Verification metric
Planning Note
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Interpretation

Ready

Enter values and calculate to get scenario outputs.

Using the Confidence Interval Width Planner Calculator - Sample Size Planning

Statistical calculators apply quantitative methods to summarize data, test hypotheses, and quantify uncertainty. Understanding the output in context — not just the number — is what makes statistics useful.

Key questions before interpreting results

  • Is the sample size large enough for the result to be reliable? Small samples produce unreliable estimates even with correct formulas.
  • Is the underlying distribution appropriate for the method being used? Many statistics assume normality or independence.
  • What is the practical significance alongside statistical significance? A statistically significant difference can be too small to matter in practice.

Communicating results

Always report results with their context: the sample size, the confidence level, and the measure used. A result of "p = 0.04" means nothing without knowing the test performed, the sample, and whether the test was pre-registered or exploratory.

Frequently Asked Questions

How accurate are the results?
The Confidence Interval Width Planner applies a standard formula to your inputs — accuracy depends on how precisely you measure those inputs. For planning and estimation, results are reliable. For high-stakes or professional decisions, cross-check the output with a domain expert or primary source.
What sample size do I need for reliable results?
It depends on the desired confidence level, margin of error, and population variance. For a typical survey (95% confidence, ±5% margin), n ≈ 385 for a large population. Smaller samples are fine for exploratory analysis, but don't over-interpret the results — widen your confidence intervals to reflect the uncertainty.