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Sample Size Calculator

Estimate completed responses for one population proportion, including an optional finite-population correction.

Your numbers

Make it your own
Updates as you type
Required completed responses
385

Calculated from your inputs · rounded for display

Unrounded sample384.1459
Without finite-population correction384.1459
Critical z1.96

Estimates one population proportion under simple random sampling. Does not include nonresponse, clustering or selection bias.

Your calculation, step by step

No black boxes
  1. n₀ = z²p(1−p) / E²; E is a proportion, not a percent.
  2. For population N > 0: n = n₀ / (1 + (n₀−1)/N). Round up only after correction.

How to use this calculator

  1. Enter your own values in the labeled fields. Check the units and assumptions before comparing results. Only the fields needed for your selected calculation mode are shown.
  2. Your answer updates automatically. Review the calculation steps to see exactly how it was calculated.
  3. Copy, share, save, or download your result. Saved inputs stay on this device.

How the calculation works

n₀=z²p(1−p)/E²; n=n₀/[1+(n₀−1)/N]

This is a simple-random-sample estimate for a population proportion. Margin of error is entered in percentage points. Population correction happens before rounding up; nonresponse, clustering and biased recruitment require separate adjustments. Review the units, period and assumptions before comparing scenarios. Displayed values are rounded, while the underlying calculation retains its available precision.

A worked example

95% confidence, a 5-point margin and p=50% require 385 completed responses for an unbounded population, or 278 for N=1,000.

Reading your result

Use the main result together with its units and supporting figures. Display values are rounded; calculations keep their underlying precision. A change in inputs or assumptions can change the answer. Compare the step-by-step working with your intended use before relying on an estimate.

Frequently asked questions

What assumptions does this calculation use?

This is a simple-random-sample estimate for a population proportion. Margin of error is entered in percentage points. Population correction happens before rounding up; nonresponse, clustering and biased recruitment require separate adjustments.

Can I save or check a scenario?

The result includes the working and supporting values. Save and Restore keep inputs on this device; Copy, Download and Print export the result. Sharing a scenario explicitly includes the inputs in its link.

Sources & methodology

This calculator uses the mathematical identity and assumptions stated above. No current rates, prices, or external data are loaded. Conversion tools use international unit definitions.

Formula review: October 24, 2026. Read our methodology.