Standard Error of Proportion Calculator
Calculate the standard error of a sample proportion.
Standard Error Formula
SE = √[p(1−p)/n]. It estimates the sampling variability of a sample proportion.
Standard Error of a Proportion
The standard error of a sample proportion estimates how much the observed proportion would vary across repeated random samples of the same size.
Proportion SE Example
If 60% of a sample of 400 respondents choose an option, the standard error is based on p(1-p)/n and is about 0.0245.
Why Sample Size Matters
Larger samples reduce standard error, producing more precise estimates when other conditions are unchanged.
Frequently Asked Questions
Can standard error be negative?
No.
Does a larger sample reduce SE?
Yes, generally at the rate of the square root of sample size.
Is SE the same as margin of error?
No. Margin of error multiplies SE by a critical value.
Standard Error of a Proportion Explained
The standard error of a proportion estimates how much a sample proportion would vary across repeated samples. For a sample proportion p and sample size n, the common formula is √[p(1−p)/n]. As sample size increases, the standard error usually becomes smaller.
Use this value when evaluating the precision of percentages or proportions from surveys, experiments and other sample data. Enter the proportion on the scale requested by the calculator and use the actual sample size. A smaller standard error indicates a more precise sample estimate, although it does not eliminate sampling bias.
The usual formula assumes observations are sufficiently independent and is most informative when the sample design is appropriate. Very small samples or proportions extremely close to zero or one may require alternative statistical methods, especially when constructing confidence intervals.
Methodology and Practical Limits
For a sample proportion, SE is commonly √[p(1−p)/n]. When p is estimated from the same sample, use the sample proportion for descriptive uncertainty; hypothesis tests may instead use a null value, and complex survey designs require adjusted standard errors.