📉 Margin of Error Calculator

Calculate the margin of error for your surveys and polls. Understand how accurate your survey results are and determine confidence intervals. Perfect for market research, political polling, and customer surveys.

Number of people surveyed
Leave blank for large populations (applies finite population correction if provided)
50% gives maximum margin (conservative estimate)

📚 Understanding Margin of Error

What is Margin of Error?

Margin of error tells you how accurate your survey results are. If your survey shows 60% of people prefer option A with a Âą5% margin of error, the true population value is likely between 55% and 65%. It's a measure of the uncertainty in your survey results.

Key Concepts

  • Confidence Level: How certain you want to be (95% is standard - means 95 out of 100 times, the true value falls within the margin).
  • Sample Size: Larger samples = smaller margin of error = more accurate results.
  • Population Size: Only matters for small populations (if sampling >5% of population).
  • Sample Proportion: 50% gives the maximum margin (worst case scenario).

The Formula

For large populations:

Margin of Error = Z × √(p(1-p)/n)

Where:

  • Z = Z-score for confidence level (1.96 for 95%)
  • p = sample proportion (as decimal)
  • n = sample size

Common Margins by Sample Size (95% Confidence)

  • 📊 100 respondents: Âą9.8% margin of error
  • 📊 200 respondents: Âą6.9% margin of error
  • 📊 400 respondents: Âą4.9% margin of error
  • 📊 600 respondents: Âą4.0% margin of error
  • 📊 1,000 respondents: Âą3.1% margin of error
  • 📊 1,500 respondents: Âą2.5% margin of error

Best Practices

  1. Use 95% confidence level (industry standard)
  2. Aim for Âą3-5% margin for professional surveys
  3. Use 50% proportion if you don't know expected results (conservative approach)
  4. Report your margin of error alongside survey results
  5. Remember: margin only accounts for sampling error, not response bias

Common Mistakes

  • ❌ Confusing margin of error with confidence level
  • ❌ Not reporting margin of error with survey results
  • ❌ Ignoring non-response bias (margin only accounts for random sampling error)
  • ❌ Using too small samples for subgroup analysis
  • ❌ Assuming smaller margin is always better (cost vs. precision tradeoff)

❓ Frequently Asked Questions

What's a good margin of error?

For professional surveys, Âą3-5% is typical. Political polls often use Âą3%. Market research may accept Âą5-7% for cost efficiency. Academic research might require Âą2-3%. The "right" margin depends on your budget, how critical the decision is, and your population size.

How many respondents do I need?

For Âą5% margin at 95% confidence: ~400 respondents. For Âą3% margin: ~1,100 respondents. For Âą2% margin: ~2,400 respondents. Use our calculator's "Sample Size" mode to determine exact numbers for your requirements.

Does population size matter?

Only for small populations. If you're sampling more than 5% of your population, use the finite population correction. For example, surveying 100 people from a population of 500 requires correction. But surveying 400 people from millions doesn't - the margin is the same whether your population is 1 million or 300 million.

Why use 50% proportion?

Using 50% gives you the maximum possible margin of error (worst-case scenario). If you don't know what results to expect, use 50% to be conservative. If you know results will be extreme (like 10% or 90%), the actual margin will be smaller.

What about subgroup analysis?

When analyzing subgroups (like age ranges or regions), your effective sample size is much smaller, increasing your margin of error. If you have 400 total respondents and want to analyze just females (say, 200 people), your margin for that subgroup is larger - calculate separately using n=200.

🔗 Related Tools

📊 Confidence Interval Calculator 📏 Sample Size Calculator 📈 A/B Test Significance