Margin of Error Calculator

Find the margin of error of a survey or poll from its sample size, result and confidence level.

Sample size	1,000
Sample proportion (%)	50
Population size (optional)	0
Confidence level	95%

Sample size

Sample proportion (%)

Use 50% if unknown; it gives the largest margin.

Population size (optional)

Confidence level

Margin of error

± 3.099%

With 1,000 responses, a 50% result is accurate to within ±3.099 percentage points, 95% of the time.

z: 1.959964

Your result with its margin of error

Likely true value (95%)

About the Margin of Error Calculator

The margin of error is the “±” on poll results. It shrinks as the sample grows, but slowly: four times the sample halves the margin. For small populations, a finite population correction reduces it.

The formula

MOE = z × √(p(1 − p) ÷ n) × √((N − n) ÷ (N − 1))

Margin of error at 95% (p = 50%)

Sample size	± margin
100	9.8%
400	4.9%
1,000	3.1%
1,500	2.53%
2,500	1.96%
10,000	0.98%

Worked example

Example: Margin of error = ± 2.94%

Inputs: Sample size: 1,100; Sample proportion (%): 55; Confidence level: 95%.
Formula: MOE = z × √(p(1 − p) ÷ n) × √((N − n) ÷ (N − 1))
Result: Margin of error = ± 2.94%
z: 1.959964

Questions people ask

Why do polls use about 1,000 people?

It gives roughly ±3% at 95% confidence; going to ±2% needs about 2,400.

Does the margin cover bias?

No. It only covers random sampling error, not badly worded questions or unrepresentative samples.