Margin of Error Calculator

Calculate Margin of Error

Enter the confidence level, sample size, sample proportion, and population size to find the margin of error.

Confidence Level:

Sample Size:

Please enter a valid sample size (must be positive).

Sample Proportion:

Please enter a valid sample proportion (between 0 and 1).

Population Size (optional):

Please enter a valid population size (must be positive or leave blank).

How to Calculate Margin of Error

The Margin of Error (MOE) is a statistical measure of the precision of an estimate from a sample. It represents the range within which the true population parameter is likely to fall, given a certain level of confidence.

Formula

The basic formula for the Margin of Error is:

\[ MOE = z \times \sqrt{\frac{p(1-p)}{n}} \]

Where:

\(z\) is the z-score corresponding to the chosen confidence level
\(p\) is the sample proportion
\(n\) is the sample size

Calculation Steps

Determine the z-score for the desired confidence level
Calculate the standard error using the sample proportion and sample size
Multiply the z-score by the standard error to get the margin of error
If the population size is known and finite, apply the Finite Population Correction (FPC)

Example

Let's calculate the Margin of Error for a sample with the following parameters:

Confidence Level: 95% (z-score = 1.96)
Sample Size: 1000
Sample Proportion: 0.5 (50%)

Z-score for 95% confidence level: 1.96
Calculate standard error: \(\sqrt{\frac{0.5(1-0.5)}{1000}} = 0.0158\)
Margin of Error: \(1.96 \times 0.0158 = 0.0310\) or 3.10%

Therefore, the Margin of Error is 3.10%.

Visual Representation

This diagram illustrates the Margin of Error for the example above. The red line represents the confidence interval, which extends 3.10% on either side of the sample proportion (0.5).