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Survey Margin Calculator

Calculate the margin of error for a survey result at a chosen confidence level.

About Survey Margin Calculator

The margin of error depends far more on sample size than on population size. A 1,000-person sample gives roughly the same precision whether the population is fifty thousand or fifty million. That population independence surprises people, but it is why national polls need only about a thousand respondents.

Formula

Survey Margin

Margin = z √(p(1−p) ÷ n) × finite population correction

finite population correction
Reduces the margin when the sample is a large share of the population

Worked example

With the default values below, Survey Margin Calculator returns Margin of Error of 3.4377%. Change any input above and every figure here is recalculated in your browser.

Inputs used

Completed responsesminimum 1
800
Population sizeminimum 1
50,000
Observed proportionaccepts 0–100 %
50 %
Confidence levelaccepts 50–99.9 %
95 %

Results

Margin of Error
3.4377%
Lower Bound
46.562%
Upper Bound
53.438%
Sample Needed for a Three-Point Margin
1,068
Finite Population Correction
0.99198

Step by step

  1. 1Values used
  2. 2Survey Margin
  3. 3Margin of Error= 3.4377
  4. 4Lower Bound= 46.562
  5. 5Upper Bound= 53.438
  6. 6Sample Needed for a Three-Point Margin= 1,068
  7. 7Finite Population Correction= 0.99198

Assumptions and limits

  • The result is derived only from the 4 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 5 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

How is Survey Margin calculated?

Margin = z √(p(1−p) ÷ n) × finite population correction The margin of error depends far more on sample size than on population size. A 1,000-person sample gives roughly the same precision whether the population is fifty thousand or fifty million.

Why does Survey Margin matter?

That population independence surprises people, but it is why national polls need only about a thousand respondents.

What values do I need to enter?

This calculator takes 4 inputs: Completed responses, Population size, Observed proportion, Confidence level. The pre-filled defaults are a realistic starting point — replace them with figures from your own environment for a result you can act on.

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