Calculate plug-in standard error, approximate normal confidence intervals, margin of error, and sample size. Finite population correction is available for a single proportion sampled without replacement; two-proportion calculations assume independent samples.

Uses a simple random sample and a normal approximation. Population correction assumes sampling without replacement.

Optional settings

Blank uses the uncorrected model; otherwise sample without replacement.

Related Calculators

Standard Error Of Proportion Formula

The following plug-in formula estimates standard error for a simple random sample. With a finite population N sampled without replacement, multiply it by √((N − n)/(N − 1)). Normal confidence intervals can be unreliable with small success or failure counts; a zero plug-in SE at p = 0 or 1 does not establish zero population uncertainty.

SEₚ = √(p × (1 - p) / n)

Variables:

  • SE_p is the standard error of the proportion
  • p is the sample proportion
  • n is the sample size

To calculate the standard error of the proportion, take the square root of the product of the sample proportion times one minus the sample proportion divided by the sample size.

What is the Standard Error Of Proportion?

The standard error estimates the sampling variability of a sample proportion. This calculator uses a simple random-sample plug-in model and approximate normal intervals, which require adequate success and failure counts. Pooled two-proportion SE applies to the equal-proportions null hypothesis; its confidence interval uses unpooled SE.

How to Calculate Standard Error Of Proportion?

The following steps outline how to calculate the Standard Error Of Proportion.

  1. First, determine the sample proportion (p).
  2. Next, determine the sample size (n).
  3. Use the formula SE_p = √(p * (1 - p) / n).
  4. Finally, calculate the Standard Error Of Proportion (SE_p).
  5. After inserting the variables and calculating the result, check your answer with the calculator above.

Example Problem:

Use the following variables as an example problem to test your knowledge.

Sample Proportion (p) = 0.5

Sample Size (n) = 100. The uncorrected standard error is √(0.5 × 0.5 / 100) = 0.05, or 5 percentage points.