Standard Error of Proportion Calculator

Calculate the standard error and margin of error for a sample proportion.

About Standard Error of Proportion Calculator

The standard error of a proportion is largest at 50 per cent and shrinks toward the extremes. That is why published poll margins usually quote the worst case, which applies regardless of the actual result. A 1,000-person poll has a worst-case margin of about ±3.1 points, which is why small changes between polls are usually noise.

Formula

Standard Error of Proportion

SE = √(p(1−p) ÷ n); margin of error = z × SE

p(1−p): Maximised at p = 0.5, which gives the worst-case margin of error

Worked example

With the default values below, Standard Error of Proportion Calculator returns Standard Error of 1.57321%. Change any input above and every figure here is recalculated in your browser.

Inputs used

Sample proportionaccepts 0–100 %: 45 %
Sample sizeminimum 1: 1,000
Confidence levelaccepts 50–99.9 %: 95 %

Results

Standard Error: 1.57321%
Margin of Error: 3.0841%
Lower Confidence Bound: 41.9159%
Upper Confidence Bound: 48.0841%
Margin of Error at a 50 Per Cent Proportion: 3.0997%

Step by step

1Values used
2Standard Error of Proportion
3Standard Error= 1.57321
4Margin of Error= 3.0841
5Lower Confidence Bound= 41.9159
6Upper Confidence Bound= 48.0841
7Margin of Error at a 50 Per Cent Proportion= 3.0997

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 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 Standard Error of Proportion calculated?

SE = √(p(1−p) ÷ n); margin of error = z × SE The standard error of a proportion is largest at 50 per cent and shrinks toward the extremes. That is why published poll margins usually quote the worst case, which applies regardless of the actual result.

Why does Standard Error of Proportion matter?

A 1,000-person poll has a worst-case margin of about ±3.1 points, which is why small changes between polls are usually noise.

What values do I need to enter?

This calculator takes 3 inputs: Sample proportion, Sample size, 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.