Margin of Error Calculator
Find the margin of error for a survey or poll from the sample size, the observed proportion and the confidence level, with an optional finite population correction.
Margin of error formula
MOE = z × √(p × (1 − p) ÷ n)
p is the sample proportion, n is the sample size and z is the critical value for your confidence level: 1.645 for 90%, 1.96 for 95% and 2.576 for 99%.
Worked example
A poll of 1,000 people finds 50% support. At 95% confidence: 1.96 × √(0.5 × 0.5 ÷ 1,000) = ±3.10%, so the true value is likely between 46.9% and 53.1%.
Sample size and margin of error
| Sample size | MOE at 95% (p = 50%) |
|---|---|
| 100 | ±9.8% |
| 400 | ±4.9% |
| 1,000 | ±3.1% |
| 2,500 | ±2.0% |
Quadrupling the sample size only halves the margin of error. When the sample is a large share of a small population, the finite population correction makes the margin smaller.
Frequently asked questions
What is a good margin of error?
Many polls aim for ±3% to ±5% at 95% confidence.
Why use 50% when the proportion is unknown?
p × (1 − p) is largest at 50%, so it gives the most cautious margin of error.
Does margin of error cover all survey errors?
No. It only covers random sampling error, not bias from wording, non-response or unrepresentative samples.
What sample size do I need for ±5%?
About 385 responses at 95% confidence for a large population.
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