Margin of error calculator

Calculate margin of error with your own figures.

Your numbers

Use the units shown. Results update as you change valid inputs.

Use margin of error to compare changes to your inputs. The method and limits below explain the scope.

Examples

Examples

Try the starting example

Sample size
100
Critical z
1.96
Expected proportion
0.5
Margin of error (percentage points)
9.8

Try another scenario

Sample size
101
Critical z
1.96
Expected proportion
0.5
Margin of error (percentage points)
9.751364
Calculation method

Calculation method

Margin of error (percentage points)

b × sqrt(c × (1-c) ÷ a) × 100

Symbols and units
a
Sample size
b
Critical z
c
Expected proportion

Use the units shown. A list keeps the order in which you enter its values. The symbol ^ means “raised to the power of”.

Calculation steps and notation

sqrt(x) is the non-negative square root of x.

Assumptions & limits

Assumptions & limits

  • Normal approximation for a simple random sample, ignoring population correction and sampling design.
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Further reading

Method reference ↗

Background reading; this does not imply endorsement or independent review of SumFizz.

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