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Sample Size Calculator – Slovin’s Formula To Calculate Sample Size For Surveys

Kate Williams

22 February 2023

7 min read

In the early days of the pandemic, we’d often hear someone from our friends or family complaining, “Where’s COVID? Nobody I know has it. This is just all a big conspiracy.” Of course, as the pandemic spread and affected all our lives, the reality dawned on everyone. What’s the mistake that the virus deniers made? Their sample size was too small.

For example, to get to the bottom of customer engagement or employee satisfaction, you need to conduct a survey. But of course, surveying each and every one of your customers or even employees is not always a realistic option. That is why you need a sample size for a survey, and we’re going to help you with a sample size calculator.

People conducting market research through online surveys often face the challenge of striking the right sample size for a survey. The quality of your results will be directly proportional to the quality of your sample size for a survey. You could even say that the well-chosen sample size is the backbone of a successful survey.

Sample Size Calculator – Applying Slovin’s Formula

So, to apply the Sample size formula, you’ll need two things:

N – Population Size

e – Margin of Error

We’ve explained what population size (N) and margin of error (e) mean in the section below. But if you already have those in hand, feel free to apply the Slovin’s Formula here.

n = N / (1+Ne^2)

Where n is your sample size.

  • The margin of error (e) is a percentage, but we’ll express it as a decimal for the formula. Remember how we talked about the 5% margin of error? In this formula, that would be expressed as 0.05 (5/100)
  • Let’s say that you want a survey that represents approximately 10,000 people. You’re alright with a margin of error of 6%. Using just this much information, we can undertake the sample size calculation using Slovin’s Formula. Let’s try it out.

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Sample Size Formula with Example

In our example:

N= 10,000

e= 0.06

n = N / (1+N*e^2)

n = 10,000 / (1+ 10,000*0.06^2)

n = 270.27

And there you go. For this particular survey, we need a sample size of 270 people. That’s how easy it is to apply Slovin’s formula. There are other formulas for calculating sample sizes in more specific scenarios that will use variables like confidence level and standard deviation.

What’s a Sample Size?

Before we get into how sample sizes can make or break your survey (they really can!), we need to talk about what precisely a sample size is. Is it just a bunch of people you pick at random to fill out surveys? Well, sometimes. Or is it a carefully chosen group of people based on different aspects? Well, sometimes. It all depends on what your survey is trying to find.

The easiest way to think about sample size for a survey is to act as a “representative” of the actual population for that study. For example, if you’re trying to survey all the people residing in Texas, you wouldn’t literally survey all of them. You would pick out a sample size for the survey that would be representative, roughly speaking, for the people of Texas.

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The power of sample sizes is that they can give you accurate results about a large group of people. You will never have to contact each of them individually. Yet, you could come to understand things like what products they like to buy, how engaged they are at work, or what they think about your brand. That’s why everyone conducting a large-scale survey needs to have a sample size calculator in place.

The Terms Used In Sample Size Calculation

One of the trickiest parts of conducting a successful online survey is sample size calculation. But thankfully, there are well-trusted sample size calculation formulas that have been adapted to give you just the right sample size. The formula, though, relies on a bunch of terms that you would need to know beforehand.

Population Size

For calculating sample size, this is a metric you need to have. What does population size refer to? While calculating the sample size for a survey, population size is the number of people represented in your sample. A different way to think about it is: population size is the number of people your results will be about.

Let’s take an example. You’re in the HR team of an organization, and you’re trying to figure out your level of employee engagement. You use SurveySparrow’s templates for employee engagement surveys and design yourself a good-looking, effective survey. In this case, your population size will be the number of employees at your company.

You might not survey all your employees, but your sample size for the survey might consist of employees in different departments. You could get a rough estimate of the overall engagement levels of your workforce. But we’re getting ahead of ourselves. For now, if someone asks, population size is the number of people you want to get results about.

Now, does this have to be an exact number? Not necessarily. It would be nice if you have a precise idea of your population size. For example, you’re trying to do a market study about the interests of teenagers, and you’re not going to have an exact number. A ballpark figure will work just fine in such cases.

Margin of Error

If you thought population size was easy to understand, things are about to get a little trickier. But we’ll break it down for you, so there’s no need to worry. What’s the margin of error, also known as the confidence interval, about? It’s an upper limit of how much your survey results, based on the sample size for the survey, can differ from the actual truth from your population size.

In other words, a margin of error represents the confidence with which you trust your sample size for a survey to reflect the opinions of the population size. For example, if you measure customer experience, let’s assume that if we were to average out the satisfaction score of all your customers, that number out of 10 would be an 8. Now, we obviously cannot survey all your customers, so let’s say we surveyed your sample.

Would you be alright with getting a customer satisfaction score in your survey of 7.5? Or perhaps 8.5? It wouldn’t be precise, but it would be somewhere in the ballpark. In the above example, your margin of error is about 0.5, expressed in percentage as 5%. Usually, a margin of error between 4% and 8% is acceptable and still gives you meaningful results.

Since the margin of error is intuitively about how detailed your survey is, the higher you allow your margin of error to be, the smaller your sample size for the survey. In cases where you’re constrained by not having many participants, increasing the margin of error by a bit can reduce the sample size you need. You compromise on precision, but at least get some meaningful data out of it.

Confidence Level

Wait, you thought the margin of error expressed the confidence you have in your survey’s results. So what’s this confidence level all about? That’s on point. Confidence level is the term used to express how confident you are that your sample size for the survey represents the population size.

Another way to think about confidence level is how confident you want to be that the actual results (ideally the average taken from your total population size) falls within the margin of error. Your level of confidence, of course, would depend on how well your sample size for the survey represents the population size.

Let’s work with the case of the customer satisfaction survey we talked about earlier. Let’s say that your survey results show a 7.5/10 satisfaction score, and your margin of error is 5% (which is 0.5/10). How confident can you be that your actual customer satisfaction score is 7.5, give or take 0.5? That’s your confidence level.

The accepted confidence level for surveys is anywhere between 90% to 99%. Below that, the data can be unreliable. Like margin of error, your confidence level will also impact your sample size for the survey. For a higher score, you will need more people in your sample survey and vice versa. Also, confidence level should not be confused with a confidence interval, which is just another term for margin of error.

Standard Deviation

The last term you need to understand for the sample size formula to make sense is the standard deviation. Let’s take an example. You are conducting an employee engagement survey for a multinational company, and you need a sample size for the survey. How much do you think the results you receive from different employees will vary from each other and the average? That’s the standard deviation.

If your standard deviation is low, that means that your responses will be clustered roughly around the mean number. So if the mean engagement level is 7/10, most responses from your sample size will be somewhere around there. If you expect more erratic results, though, then your standard deviation would be higher.

We know what you’re thinking. Where will I find this out from? Don’t worry. For now, you can use a standard deviation of 0.5. That’ll give you a large enough sample size to conduct a rigorous and meaningful survey.

We understand that this can be confusing, but hang on. The way it all comes together to give you your ideal sample size for the survey is nothing short of beautiful. At SurveySparrow, we’re particularly fond of how you can calculate your sample size for a survey by knowing just these few metrics.

You can try it here for FREE!

Wrapping Up …

When you think about it, the idea of having a sample size seems ingenious. Why go through the trouble of reaching out to everyone? You could pick out a few people to represent them, and voila. But having a sample size for a survey also opens a can of worms. There are many mistakes to be made that will make you arrive at the wrong results.

If you’re having trouble getting reliable results from your survey, you could consider an advanced online survey tool like SurveySparrow. It helps you craft beautiful surveys that your sample size will love to fill. But Surveysparrow is not just about aesthetics. It also gives you powerful tools to analyze the responses once they come in.

We hope we were able to help you with this guide for sample size calculation. It’s tricky at first, but once you get the hang of the terminology and formulas, you’ll have no trouble determining your ideal sample size. Having a perfect sample size for the survey is not too far off from having a superpower. It’ll help you generate insights and reach your goals faster. Happy surveying!


Kate Williams

Content Marketer at SurveySparrow

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