Margin of Error Calculator

Multiply the critical value by the standard error. For a proportion, margin of error = z × √(p̂(1 − p̂)/n). For a mean, margin of error = z × (σ/√n). The critical value is 1.96 for a 95% confidence level.

It is z × √(p̂(1 − p̂)/n), where p̂ is the sample proportion and n is the sample size. With p̂ = 0.5 and n = 1000 at 95% confidence, the margin of error is about ±3.1%.

Most public polls aim for ±3% to ±5% at 95% confidence. Smaller margins require larger samples. The right target depends on how precise your decision needs to be and your budget for collecting data.

The margin of error shrinks with the square root of the sample size. To cut it in half you must roughly quadruple the sample. That is why very precise estimates are expensive to obtain.

Yes. A higher confidence level uses a larger critical value, which widens the interval. A 99% interval (z = 2.576) has a larger margin of error than a 95% interval (z = 1.96) for the same data.