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Margin of Error Calculator

The calculator considers various parameters like Confidence Level, Proportion Percentage, Sample Size, and Population Size to estimate the overall Margin of Error accurately.

Confidence Level (α)

Sample Size (n)

Proportion Percentage (p)

Margin of Error

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Margin of Error Calculator

Quickly calculate the margin of error (MOE) for surveys using confidence level, sample proportion, sample size, and population size.

What Is Margin of Error?

The margin of error represents the potential difference between a sample statistic and the true population value. Expressed as a percentage, it shows how much the survey result may vary due to sampling error. For example, a 95% confidence level with a 4% MOE means the true population value lies within ±4% of the sample statistic 95% of the time.

Margin of Error Formulas

Basic formula:

MOE = z × √(p × (1 − p) / n)

With finite population correction:

MOE = z × √(p × (1 − p) / n) × √((N − n) / (N − 1))

Where:

MOE = margin of error
z = z-score for desired confidence level
p = sample proportion (decimal)
n = sample size
N = population size

Example

Calculate MOE for p = 0.3, 95% confidence, n = 1000:

z = 1.96
MOE = 1.96 × √(0.3 × 0.7 / 1000)
MOE ≈ 0.028 (2.8%)

How to Use the Calculator

Select confidence level.
Enter proportion percentage (p).
Enter sample size (n).
Enter population size (N), if applicable.
Click Calculate.

Manual Calculation Steps

Alternative formula using population standard deviation:

MOE = z × σ / √n

Determine σ and n.
Compute √n.
Divide σ by √n.
Multiply by z-score for confidence level.

FAQs

Acceptable Margin of Error

Typically 4%–8% at 95% confidence level is considered acceptable.

Reducing Margin of Error

Increase sample size
Reduce variability
Use one-sided confidence intervals
Lower confidence level

Purpose of Margin of Error

Shows reliability of survey results. Smaller MOE indicates higher accuracy.

Slovin’s Formula

Calculate sample size with known population and desired MOE: n = N / (1 + N × e²).

Effect of Sample Size

Larger samples reduce MOE, improving representation of the population.

References

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