Margin of Error Calculator | Statistical Resources

Margin of Error Calculator

Can you rely on your survey results? By calculating your margin of error (also known as a margin of error or a confidence interval), you can tell how much the opinions of the sample you survey is likely to deviate from the total population. Our margin of error calculator makes it easy.

Calculate Margin of Error:

Confidence Level:

Sample Size

Margin of Error:

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* Assumes a normal distribution of 50% to calculate your error

What is Margin of Error?

Your margin of error is the possible range that your sample survey data is correct when compared to the population.

As an example, let's say you were trying to decide between color A and color B for a new muffin your company planned to sell, and your target customer base (the "population") consists of 200,000 potential customers. If you surveyed 600 of them (your "sample size"), and 30% of them liked color A could you rely on your survey results?

Using the margin of error calculator with a confidence level of 99% (meaning there's a 99% chance that your sample accurately reflects the attitudes of your potential customer base), you’ll see that the margin of error is 5%. That means a 99% likelihood that between 25% and 35% of your customer base will prefer muffin color A.

Key Terms

Confidence Level: A measure of how confident you are that your sample accurately reflects the population, within its margin of error. Common standards used by researchers are 90%, 95%, and 99%.

If your confidence level is 95% in the above example, you could say your 95% certain that between 38% and 42% of the United States Population do not like their jobs.

Sample Size: The number of completed responses your survey receives is your sample size. It's called a sample because it represents a part of the group of the total group people whose opinions or behavior you care about. As an example, you can select at random 10 out of 50 employees from a department at your job. Those 10 are the sample and the 50 are the population.

There can be two different sample sizes. One based on an infinitely large population, the other based on a smaller finite population. This finite number you can specify above.

The bigger the population is, the bigger the sample will need to be to accurately reflect the population. See our sample size calculator for how to calculate your needed sample size.

Population Proportion: This can be described as the makeup of the population. For example, if it's well known 60% of college students are female you could say the population proportion of college students is 60% female. If you wanted to mainly get opinions of college females, you would you this 60% number in the formula below (for P). Most times though these numbers are not known and 50% (.50) is used for P. This .5 number produces the largest possible sample size, as it is most conservative.

How to Calculate Margin of Error



The z-score is the number of standard deviations a given proportion is away from the mean. To find the right z-score to use, refer to the table below:
Desired Confidence IntervalZ-score
80%1.28
85%1.44
90%1.65
95%1.96
99%2.58

Is Your Error Too Big?

If you calculate your margin of error and it feels too big, you'll need to increase your sample size by sending your survey to more people. SurveyKing makes collecting responses easy. Send out a weblink on social media or do an email campaign to send it to people you know directly!

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