Advanced Margin of Error Calculator

Margin of Error Calculator

Calculate the margin of error for your survey or study with confidence levels and detailed explanations.

Input Parameters

Sample Size (n)

The number of observations in your sample.

Population Size (N)

The total size of the population. Leave empty if unknown.

Confidence Level

Sample Proportion (p)

The percentage value from your sample (0-100%). Default is 50% for maximum variability.

Results

Enter your parameters and click “Calculate” to see results

About Margin of Error

What is Margin of Error?

The margin of error is a statistic expressing the amount of random sampling error in a survey’s results. It represents the radius of a confidence interval for a given statistic.

Formula

For a proportion, the margin of error (MOE) is calculated as:

MOE = z × √[p(1-p)/n] × FPC

Where:
z = z-score for confidence level
p = sample proportion
n = sample size
FPC = Finite Population Correction (if applicable)

Common Z-Scores

90% Confidence Level: z = 1.645
95% Confidence Level: z = 1.96
99% Confidence Level: z = 2.576

Tips

• Larger sample sizes reduce the margin of error
• Higher confidence levels increase the margin of error
• A 50% proportion gives the maximum margin of error
• Use the finite population correction when sampling more than 5% of the population