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Margin of Error Calculator

Provide confidence level, sample size, and variability inputs to obtain margins of error for both means and proportions.

Use sample or population standard deviation as appropriate.

Enter the number of successes out of n observations.

Provide population size to apply finite population correction (must be at least the sample size).

Z critical value: 1.960

Finite population correction: 1.0000

Margin of error (mean): 2.3520

Sample proportion: 56.00%

Margin of error (proportion): 9.7290%

How to Use This Calculator

  1. Select the desired confidence level and enter the sample size.
  2. Provide the standard deviation for mean-based intervals and the number of successes for proportions.
  3. Optionally specify population size to apply finite population correction.
  4. Review both mean and proportion margins of error to understand sampling uncertainty.

Formulas

Margin of error (mean) = zα/2 × σ / √n

Margin of error (proportion) = zα/2 × √[p̂(1 − p̂) / n]

Finite population correction = √[(N − n) / (N − 1)] (optional)

Full Description

Margin of error quantifies sampling variability around a point estimate. Larger sample sizes, lower variability, and lower confidence levels reduce the margin. When sampling without replacement from a limited population, finite population correction further decreases the interval width.

For small samples with unknown population standard deviation, consider replacing the z critical value with an appropriate t critical value to better reflect uncertainty.

Frequently Asked Questions

Can I use t critical values instead of z?

Yes. For small samples with unknown population SD, use the t-distribution and substitute the appropriate t critical value.

What if I do not know the number of successes?

Use a conservative estimate—for example, assume p̂ = 0.5—to maximize the margin of error when planning surveys.

Does higher confidence increase margin of error?

Yes. Higher confidence requires a larger z critical value, widening the resulting confidence interval.

Why is finite population correction optional?

Apply it only when sampling without replacement from a population that is not much larger than the sample size.