Margin of Error Calculator

Calculate the margin of error for your survey results. Understand the precision of your data and make confident decisions.

Calculator Inputs

Enter your survey parameters below

Sample Size (n)

The number of respondents in your survey

Population Size (N) — optional

Total population size. Leave blank if unknown or very large.

Confidence Level

How confident you want to be that the true value falls within the margin

Response Distribution: 50% / 50%

Expected proportion of responses. Use 50% if unsure (worst-case scenario).

Results

Your calculated margin of error

Margin of Error

±4.38%

Lower Bound

45.62%

Upper Bound

54.38%

With a 95% confidence level and a sample of 500 respondents, the true population value is between 45.62% and 54.38%.

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What is Margin of Error?

The margin of error (also called the confidence interval) tells you how much the results of your survey might differ from the true population value. For example, if your survey shows 60% of respondents prefer option A with a margin of error of ±4%, the true value likely falls between 56% and 64%.

How is Margin of Error Calculated?

The margin of error formula is:

MOE = z × √(p(1-p) / n)

z — the z-score corresponding to your confidence level (e.g., 1.96 for 95%)
p — the expected proportion (use 0.5 for maximum margin of error)
n — your sample size

When surveying a significant portion of a finite population, a finite population correction (FPC) factor is applied to reduce the margin of error.

Tips for Reducing Margin of Error

1.Increase sample size — the most effective way to reduce your margin of error.
2.Lower confidence level — accept more risk for tighter intervals (e.g., 90% instead of 99%).
3.Use targeted surveys — focus on a specific population segment to get more relevant responses.

Frequently Asked Questions

What is a good margin of error for a survey?

Most researchers aim for a margin of error of 5% or less. Political polls typically target 3%, while academic research may require 2% or lower depending on the field.

What confidence level should I use?

The 95% confidence level is the industry standard. Use 99% for critical decisions (medical, safety) and 90% when a wider margin is acceptable.

Do I need to enter a population size?

Only if your sample represents a significant portion (more than 5%) of the total population. For large populations, it has minimal impact on the result.

What response distribution should I use?

Use 50/50 if you are unsure — this gives you the worst-case (largest) margin of error. If you already have data suggesting a skewed distribution (e.g., 80/20), use that value for a more accurate result.