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Sample Size For Proportion Calculator

Work out sample size for proportion instantly with clear inputs, formula shown and shareable results.

About Sample Size For Proportion Calculator

Rearranging the margin of error formula gives n = z²p(1 − p)/E². Since p(1 − p) peaks at 0.25 when p = 0.5, using that value gives the largest sample any proportion could need.

Formula

Sample size

n = z²·p(1 − p) / E², rounded up

Worked example

With the default values below, Sample Size For Proportion Calculator returns Required sample size of 1,068. Change any input above and every figure here is recalculated in your browser.

Inputs used

Desired margin of errorminimum 0.01 %
3 %
Confidence levelaccepts 50–99.99 %
95 %
Expected proportionaccepts 0.01–99.99 %
50 %

Results

Required sample size
1,068
Worst-case size assuming p = 0.5
1,068
Critical z value
1.959964
p(1 − p)
0.25000000

Step by step

  1. 1Values used
  2. 2Sample size
  3. 3Required sample size= 1,068
  4. 4Worst-case size assuming p = 0.5= 1,068
  5. 5Critical z value= 1.959964
  6. 6p(1 − p)= 0.25000000

Assumptions and limits

  • The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 8 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

For a 3% margin at 95% confidence?

z = 1.96 and p(1−p) = 0.25 give n = 1068 — which is why national polls typically survey about a thousand people.

Why does halving the margin quadruple the sample?

Because n depends on 1/E², so precision improves only as the square root of effort.

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