Margin of Error Calculator

Can you rely on your survey results? By calculating your margin of error (also known as a confidence interval), you can tell how much the opinions of the sample you survey are 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?

The number of respondents who take your survey is a sample size. It's a sample because it represents a part of the total group of 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.

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 scheme A and color scheme B for a new version of your company’s website. Your user base is 200,000 total people. If you surveyed 600 users (your "sample size"), and 30% of them liked color scheme A could you rely on your survey results?

Using our margin of error calculator with a confidence level of 99% (meaning there's a 99% chance that your sample correctly reflects the opinions of your user 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 color scheme 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%.

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 total group of 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 use this 60 percent 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

Margin of Equation:

\begin{align*} \sqrt{\frac{P * (1 - P)^2}{6} } * Z \end{align*}

Where,

P = Proportion of correct answer based on prior experience. (Use .5 if unknown as this creates the largest and most conservative sample)

N = Sample size

z = Z-Score (see below)

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's too big for your liking, you'll need to increase your sample size by collecting more responses. SurveyKing makes collecting responses easy. Send out a web link on social media or do an email campaign to send it to people you know directly!

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