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Margin of Error Calculator

How to calculate your survey's margin of error, what it tells you, and how to tighten it.

Enter your sample size and confidence level to calculate your survey's margin of error.

The total number of people you could possibly survey. Leave blank if unknown or very large.
Margin of Error Calculator
± 0%
Assumes a 50% response distribution (the most conservative, widest-margin estimate). Formula: MoE = z x sqrt(p(1-p)/n), adjusted for population size when provided.
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What is margin of error?

Margin of error tells you how much your survey results might differ from the true opinion of your entire target population, simply because you surveyed a sample of people rather than everyone. It's expressed as a plus-or-minus percentage around your result.

For example, if 60% of respondents say they prefer Product A with a margin of error of ±4%, the real figure across your whole population most likely falls somewhere between 56% and 64%. The smaller the margin of error, the more precisely your sample reflects the full population.

Margin of error vs. confidence interval vs. confidence level

These three terms are often confused, but they describe different pieces of the same statement:

  • Margin of error — the size of the plus-or-minus range (e.g. ±4%).
  • Confidence interval — the actual range your true result falls in (e.g. 56%-64%), calculated as your result ± the margin of error.
  • Confidence level — how sure you are that the confidence interval contains the true value, typically 90%, 95%, or 99%.

Put together: "We are 95% confident (confidence level) that the true value falls between 56% and 64% (confidence interval), a margin of error of ±4%."

Formula for calculating margin of error

MoE = z × √( p(1-p) / n )
z = z-score for your confidence level · p = expected response distribution (0.5 is the most conservative default) · n = sample size

When you also know your total population size, a finite population correction is applied so the margin of error shrinks slightly for smaller populations — which is exactly what the calculator above does automatically.

Confidence levelZ-score
90%1.645
95%1.96
99%2.576
Worked example

You survey 400 people from a large population at a 95% confidence level:

  • z = 1.96, p = 0.5, n = 400
  • MoE = 1.96 × √(0.5 × 0.5 / 400) = 1.96 × 0.025 = 0.049
  • Margin of error ≈ ±4.9%

What affects your margin of error

Sample size

Larger samples produce a smaller margin of error, but with diminishing returns — doubling your sample from 400 to 800 respondents only tightens a ~4.9% margin of error to roughly ~3.5%, not half of it. This is why chasing extremely large samples usually isn't worth the extra time and cost.

Confidence level

A higher confidence level (say 99% instead of 95%) means you want to be more certain your interval captures the true value — which requires a wider range, and therefore a larger margin of error, for the same sample size.

Population variability

Using p = 0.5 (a 50/50 split) is the standard, most conservative assumption because it produces the widest possible margin of error. If you already have good reason to expect a lopsided result (e.g. 80/20), your real-world margin of error will typically be smaller than the calculator's default estimate.

How to reduce your margin of error

  • Collect more responses. Use our Sample Size Calculator to see exactly how many you need for your target margin of error.
  • Choose a representative sample. A random, well-targeted sample reduces bias that a bigger margin-of-error number alone can't fix.
  • Accept a slightly lower confidence level (e.g. 90% instead of 99%) if your use case allows it — it directly narrows the margin of error without collecting a single extra response.
  • Keep response quality high. Short, clear surveys reduce drop-off and rushed answers, so your effective sample stays close to your target.

Frequently asked questions

What's a good margin of error for a survey?

±5% at a 95% confidence level is the widely used industry standard for general audience research. Higher-stakes decisions (elections, product launches) often target ±3% or tighter.

Does margin of error apply to every question in my survey?

Technically each question has its own margin of error based on how many people answered it and how their responses were distributed — so a question with more skipped answers will have a wider margin of error than the survey's headline number.

Why does population size barely change the result for large populations?

The finite population correction has almost no effect once your population is much larger than your sample (roughly 20x or more) — this is why national surveys with millions of people in the population use sample sizes similar to those for a population of just 100,000.

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