Margin of Error Calculator

Calculate margin of error for surveys and statistical studies with confidence intervals

Survey Margin of Error Calculator

Use FPC when sample size is 5% or more of the total population

Z-score: 1.96

Number of people surveyed

Proportion as decimal (e.g., 0.57 for 57%)

Calculated Sample Proportion (p̂): 0.5000 (50.00%)

Example Calculation

Survey Scenario

Population: 5,000 people

Sample: 400 people surveyed

Responses: 260 people answered "yes"

Confidence Level: 96%

Calculation

Sample Proportion: 260/400 = 0.65

Z-score (96%): 2.05

FPC needed: 400/5000 = 8% (>5%)

Margin of Error: ±4.69%

Interpretation: 96% confident the true proportion is 65% ± 4.69%

Common Confidence Levels

90%Z = 1.645
95%Z = 1.96
96%Z = 2.05
98%Z = 2.33
99%Z = 2.58

95% is most commonly used in social sciences

MOE Guidelines

≤3%: Excellent precision
3-5%: Good precision
5-10%: Fair precision
>10%: Consider larger sample

When to Use FPC

Use FPC when:
Sample ≥ 5% of population

Effect:
Reduces margin of error for finite populations

Formula:
FPC = √((N-n)/(N-1))

Understanding Margin of Error

What is Margin of Error?

Margin of error indicates how many percentage points your survey results may differ from the true population value. It's a measure of the uncertainty in your sample estimates due to random sampling variation.

Key Applications

  • Political polling and election predictions
  • Market research and customer satisfaction
  • Quality control and manufacturing
  • Medical and clinical research studies

Factors Affecting MOE

Sample Size

Larger samples reduce margin of error. MOE decreases proportionally to the square root of sample size.

Confidence Level

Higher confidence levels increase margin of error. 99% confidence requires a larger margin than 95%.

Population Proportion

MOE is largest when proportion is near 50% (0.5), and smallest near 0% or 100%.

Important Considerations

  • • Margin of error only accounts for random sampling error, not bias
  • • Assumes random sampling from the target population
  • • Does not account for non-response bias or measurement errors
  • • FPC should be used when sample is ≥5% of finite population