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Margin of Error Calculator

Calculate the precision of your survey results. Given your sample size and confidence level, determine an interval estimate around your observed proportion under the assumptions below.

Input Parameters

%

Apply finite population correction

Margin of Error

±5.0%

margin of error

Confidence Interval
45.0% — 55.0%
Confidence
95%
Sample Size
385

How We Calculate

Standard Error Formula:

e = Z × √((p × q) / n)
Z = 1.96 (for 95% confidence)
p = 0.50 (expected proportion)
q = 0.50 (1 - p)
n = 385 (sample size)

Built by Lensym — focused on valid, reliable survey research.

Understanding Margin of Error

Margin of error quantifies the uncertainty in your survey results due to sampling. A ±5% margin means if your survey shows 60% agreement, the interval estimate is 55%–65% under the assumptions listed.

When to Use This Calculator

  • You've completed a survey and want to report the precision of your findings
  • You need to determine if your sample is large enough for meaningful conclusions
  • You're comparing results across groups and need to check for overlap

What Margin of Error Does NOT Tell You

  • Bias — If your sampling method is flawed, your results may be systematically off even with a small margin of error
  • Non-response effects — People who didn't respond may differ from those who did
  • Question wording effects — How you ask affects what people answer

Method Note

This calculator uses the normal approximation (Wald interval). For small samples or proportions near 0% or 100%, Wilson score or exact binomial methods may be more appropriate.

Relationship to Sample Size

Margin of error and sample size are inversely related. Doubling your sample size does not halve your margin of error — you'd need to quadruple it due to the square root relationship. This is why there are diminishing returns on larger samples.

Need to work backwards? Calculate the sample size needed for your target margin of error.