Skip to content
ENExplore Calculators

Confidence Level For Survey Calculator

Work out confidence level for survey instantly with clear inputs, formula shown and shareable results.

About Confidence Level For Survey Calculator

The margin of error for a proportion is z times sqrt(p(1-p)/n), maximised when p is 50%. At n = 400 and 95% confidence that gives 4.9 percentage points, so a 50% result means 45.1% to 54.9%. The finite population correction only matters when the sample exceeds about 5% of the population.

Formulas

Margin of error

MOE = z x sqrt(p(1-p) / n)

Finite population correction

multiply by sqrt((N - n) / (N - 1))

Worked example

With the default values below, Confidence Level For Survey Calculator returns Margin Of Error of 4.90%. Change any input above and every figure here is recalculated in your browser.

Inputs used

Sample sizeminimum 1
400
Observed proportionaccepts 0–100 %
50 %
Confidence levelaccepts 50–99.9 %
95 %
Population sizeminimum 1
500,000

Results

Margin Of Error
4.90%
Critical z Value
1.9600
Standard Error
2.500%
Full Confidence Interval Width
9.80%

Step by step

  1. 1Values used
  2. 2Margin of error
  3. 3Finite population correction
  4. 4Margin Of Error= 4.90
  5. 5Critical z Value= 1.9600
  6. 6Standard Error= 2.500
  7. 7Full Confidence Interval Width= 9.80

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 4 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

Why is 50% the worst case?

Because p(1-p) peaks there at 0.25. A proportion near 5% or 95% has a much smaller standard error for the same sample size.

How do I halve the margin of error?

Quadruple the sample. Precision improves with the square root of n, which is why national polls stop around 1000-2000 respondents.

Related Calculators

Confidence Level For Survey Calculator | Calcrivo