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

Population Size (Optional)

Margin of Error:
(Based on infinitely large population)

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Margin of Error:
(Based on your population)

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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 usually just a sample of the total population. 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 a range that your sample survey data is accurate 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 userbase is 200,000 total people. If you surveyed 600 users (your "sample size"), and 70% of them liked color scheme A could you rely on those 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 65% and 75% of your userbase will prefer color scheme A.

Key Terms

Confidence Level: A measure of how confident you are that your sample accurately reflects the population. 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.

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). Often these numbers are not known and 50% (.50) is used for P. This .5 number produces the largest possible sample size, as it is the most conservative estimate.

Population Size:This is the size of your total population. Often this will be an extremely large number (such as the number of people in the United States). If you do not know your population size, it will be assumed that is infinitely large, and margin of error will be calculated using the first equation blow. If you do know your population size, such all the employees at your workplace, the margin of error will be calculated using the second equation below.

How to Calculate Margin of Error (MOE)

Margin of Error Equation (Infinity large population):

\begin{align*} MOE = \sqrt{\frac{P * (1 - P)}{n} } * 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)

Margin of Error Equation (Finite population):

\begin{align*} MOE = \sqrt{\frac{P * (1 - P)}{\sqrt{(N-1)*n / (N-n)}} } * 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 = Population size

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!