# Margin of error calculator

What is margin of error and what does it mean for your survey data?

Will your survey results ever perfectly match the population you’re studying? Probably not.

But you can get a good idea of how close you are by using a margin of error calculator. This handy tool will help you to find the margin of error and will tell you if the amount of people you’re surveying is enough for you to feel confident about the accuracy of the data you collect.

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## What is margin of error in a survey?

Margin of error, also called confidence interval, tells you how much you can expect your survey results to reflect the views from the overall population. Remember that surveying is a balancing act where you use a smaller group (your survey respondents) to represent a much larger one (the target market or total population).

You can think of margin of error as a way of measuring how effective your survey is. The smaller the margin of error, the more confidence you may have in your results. The bigger the margin of error, the further they can stray from the views of the total population.

As the name implies, the margin of error is a range of values above and below the actual results from a survey. For example, a 60% “yes” response with a margin of error of 5% means that between 55% and 65% of the general population think that the answer is “yes”.

## How to calculate margin of error

n = sample size • σ = population standard deviation • z = z-score

1. Get the population standard deviation (σ) and sample size (n).
2. Take the square root of your sample size and divide it into your population standard deviation.
3. Multiply the result by the z-score consistent with your desired confidence interval according to the following table:

Let’s see the margin of error formula at work with an example.

Imagine you're trying to decide between Name A and Name B for a new product and your target market consists of 400,000 potential customers. This is your total population.

You decide to survey 600 of those potential customers. This is your sample size.

If you want to calculate your sample size, check out our sample size calculator.

When you get the results, 60% of respondents say they prefer Name A. You need to input a confidence level in the margin of error calculator.

This number expresses how certain you are that the sample accurately reflects the attitudes of the total population. Researchers commonly set it at 90%, 95% or 99%. (Do not confuse confidence level with confidence interval, which is just a synonym for margin of error.)

Try inputting the numbers from this example in the margin of error calculator above. The calculator gives you a margin of error of 4%.

Remember that 60% of your respondents chose Name A? This margin of error means that now you know with 95% likelihood that 56% to 64% of the total population (your target market) prefer Name A for your product.

We arrive at 56 and 64 by adding and subtracting the margin of error from your sample’s response.

## How sample size affects margin of error

As we said, knowing your margin of error helps you understand whether the sample size of your survey is appropriate.

If your margin of error looks too big, you will want to increase the size of the sample so that the attitudes of the population surveyed match those of the total population more closely.

What this means is that you will need to send your survey to more people.

The Sample Size Calculator can help you easily determine how many people you need to take your survey.

Need to calculate your statistical significance? Check out our A/B testing calculator.

## 5 steps to increase your data’s reliability

Now that you know how margin of error is calculated and how it affects your results, let’s review the steps that you need to follow to use these concepts in your survey design.

You can also find a more detailed explanation in this article on how to estimate your population.