Margin of Error Calculator

This simple margin of error (MOE) calculator can be employed to compute the MOE of a survey in accordance with the sample proportion and size, and the desired confidence level.

You can use the calculator to compute the MOE in four simple steps:

1. Use the drop-down menu to select the confidence level
2. Input the sample size and then the proportion percentage
3. If required, provide details of the population size
4. Click on the "Calculate" button to generate the outputs.

The Margin of Error in Statistics

The majority of surveys that are conducted for research purposes are based on information that is collected from a sample population as opposed to the full population (a census). As the sample is only representative of the full population, it is likely that some error will occur, not in terms of the calculation, but in terms of the sampling. That is, a sampling error will emerge because the researchers did not include everyone that exists within a given population. The MOE measures the maximum amount by which the sample results may differ from the full population. As most responses to survey questions can be presented in terms of percentages, it makes sense that the MOE is also presented as a percentage.

Margin of Error Formula

The Margin of Error (MOE) Calculator uses the following formulas:

1. MOE = z * √p * (1 - p) / √n

2. MOE (with finite population correction) = z * √p * (1 - p) / √(N - 1) * n / (N - n)

Where:

MOE  is the margin of error,

z  is the z-score associated with a level of confidence,

p  is the sample proportion, expressed as a decimal,

n  is the sample size,

N is the population size.

To estimate the sample size, take a look at our sample size calculator.

Margin of Error Calculation Example:  A market research agency conducted a survey to identify how many mobile phone users use their devices to access social media. They surveyed 1000 mobile phone users and found that 540 regularly used their devices to access their social media profiles.

Let's assume that we require a 95% level of confidence; as such, the z-score = 1.96.

The sample population, p, is 540 / 1000 = 0.54. (The sample size, n, was 1000.)

As such, the margin of error in this survey is as follows:

MOE = z * √p * (1 - p) / √n

MOE = 1.96 * √0.54 * (1 - 0.54) / √1000

MOE = 0.977 / 31.623 * 100 = 3.089%

These results indicate that the market research company can conclude with 95% confidence that 54% of mobile phone users use their device to access social media, give or take 3%.

Reference: Daniel WW (1999). Biostatistics: A Foundation for Analysis in the Health Sciences. 7th edition. New York: John Wiley & Sons.