Margin of error-formula, definition and calculator

Calculate your survey’s margin of error in moments and ensure the accuracy of insights collected for your research.

Margin of error calculator 

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Your Margin of Error

What is margin of error?

Margin of error helps you estimate how close your survey results are to the truth. Think of it as a built-in honesty check for your data. A smaller margin of error signifies more precise results. Whether you’re conducting academic research or analyzing market trends, checking the margin of error helps you measure how much wiggle room there is between your sample results and the real-world numbers.

How to calculate NPS

Margin of error-formula

Margin of Error=
Zx
p(1-p)n

Z : Z - score (based on your confidence level, e.g., 1.96 for 95%)

P : Sample proportion (as a decimal)

n : Total sample size

  • Confidence LevelZ-score
  • 80%1.28
  • 85%1.44
  • 90%1.65
  • 95%1.96
  • 99%2.58

Confidence interval

A confidence interval is like a safety net for your survey results. It gives you a range of numbers that your true result is likely to fall into. For example, if your survey says 60% of people prefer chocolate with a confidence interval of ±5%, it means the real number is likely between 55% and 65%. It’s not an exact figure, but it gives you a reliable range to work with.

Confidence level

Confidence levels tell you how certain you can be that your results fall within the confidence interval. Think of it as your trust factor. A 95% confidence level means that if you repeated the survey 100 times, 95 of those times, your results would stay within the same range. It’s a way of saying, “I’m this confident my data is accurate."

What is the relationship between confidence interval and margin of error? 

Think of confidence interval and margin of error as two elements that go together like puzzle pieces. The margin of error determines the width of your confidence interval.

For example, if your survey shows that 60% of people prefer chocolate with a margin of error of ±4%, your confidence interval is 56% to 64%.

In simple terms, the confidence interval is the visible boundary, and the margin of error is the measurement that sets that boundary. Together, they ensure your survey results are both reliable and actionable.

What factors affect a survey's margin of error? 

The margin of error is influenced by a few key factors that shape the accuracy of your survey results. Let’s take a closer look.

  • How does sample size affect margin of error? 

    The larger your sample size, the smaller your margin of error. Collecting more data gives you a clearer picture of your audience with reduced variability.Example: Surveying 1,000 people instead of 100 gives you more precise results.

    Read more on sample size calculator

  • How does population variability affect margin of error? 

    If your audience has mixed opinions or diverse characteristics, your margin of error will naturally increase. Greater variability means more room for uncertainty.Example: If preferences are split between chocolate, vanilla, and strawberry, the margin of error will be larger compared to a group where nearly everyone picks chocolate.

  • How does confidence level affect margin of error? 

    Choosing a higher confidence level means widening your margin of error. It’s the trade-off for being more certain about your results.
Example: A 99% confidence level will have a broader margin of error compared to 90% confidence.

  • How does survey design affect margin of error? 

    Poorly phrased or leading questions, sampling errors, and low response rates can inflate your margin of error. Biases—whether intentional or not—can skew your results and increase uncertainty.

    Read more on survey biases

How Zoho Survey can help

Whether you’re conducting market research, academic studies, or quick opinion polls, Zoho Survey has everything you need to simplify the process and deliver results

With intuitive DIY features, Zoho Survey empowers you to design and manage your research effortlessly, saving both time and costs while maintaining complete control over your projects.

Access a global audience panel to reach the right respondents and pair it with powerful analytics to uncover meaningful insights. Zoho Survey puts the power of research in your hands.

Balance accuracy with the costs of surveying using Zoho Survey.