Sample Size Calculator - Slovin's Formula To Calculate Sample Size For Surveys

The accuracy of your survey results depends less on how many questions you ask and more on who you ask them to. Get your sample size wrong and even a well-designed survey produces unreliable data. 

This guide walks you through how to calculate the right sample size for your survey using Slovin's Formula, and includes a calculator you can use right now.

What’s a Sample Size?

A sample size is the number of people you survey to represent a larger population. Rather than reaching out to every single person in your target group, you select a subset that is large enough and representative enough to produce reliable results on behalf of the whole.

Think of it like a taste test. A food manufacturer launching a new product doesn't need every person in the country to try it before making a decision. They need enough people from the right demographic groups to get a reliable read on how the broader market will respond. That group of tasters is their sample.

A sample size is a group selected in a way that reflects the characteristics of the population you are trying to understand. The more representative your sample, the more accurately your results will reflect reality.

The easiest way to think about sample size for a survey is to act as a “representative” of the actual population for that study. 

Another 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, of the people of Texas.

Once you have a sample size, you'll have to distribute the questionnaire for your survey. 

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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.

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.

Sample Size Calculator

Use This Template

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.

Term 1 – Population Size (N)

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 had 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.

Term 2 – Margin of Error (e)

The margin of error, also known as the confidence interval is an upper limit of how much your survey results, based on the sample size for the survey, can differ from the actual truth of 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.

Term 3 – 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) fall 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 the 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, a confidence level should not be confused with a confidence interval, which is just another term for margin of error.

Term 4 – 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.

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Slovin's Formula for Sample Size 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.

How to Choose Your Margin of Error and Confidence Level

Before you can calculate your sample size, you need to decide on two numbers: your margin of error and your confidence level. They are not independent decisions. They work together, and understanding how they relate to each other is the key to choosing the right inputs for Slovin's Formula.

Start with your confidence level

Your confidence level is the starting point. It answers one question: "How many times out of 100 do I need my results to be accurate?"

If you need to be right 95 times out of 100, use a 95% confidence level. If you need to be right 99 times out of 100, use 99%. If 90 times out of 100 is sufficient, 90% works.

Most business surveys default to 95%. It is the industry standard because it is precise enough to make reliable decisions without requiring an impractically large sample size.

Then set your margin of error

Once you have decided your confidence level, your margin of error follows naturally from the stakes of your decision. Your margin of error reflects how much variance you are willing to accept between your sample results and the true values of your full population. A lower margin of error means more precise results but requires a larger sample size. A higher margin of error reduces the sample size you need but makes your results less precise.

In simple terms, your margin of error is how much you are willing to be off by. The higher the stakes of your decision, the smaller it should be.

Here is how confidence level and margin of error work together in practice:

High stakes decision — 99% confidence, 1% to 3% margin of error

You need to be very sure and very precise. This applies to clinical research, major financial decisions, or public policy studies where the cost of being wrong is significant.

Medium to high stakes decision — 95% confidence, 4% to 6% margin of error

This is the standard for most business surveys. A company deciding whether to permanently roll out a new product feature, restructuring a team, or entering a new market needs reliable data without requiring an unrealistically large sample size.

Low stakes or exploratory research — 90% confidence, 7% to 10% margin of error

A startup validating an early idea just needs a directional signal. Precision matters less than speed and cost at this stage.

Examples

A retail brand wants to survey its 50,000 customers to understand satisfaction with a new checkout experience before deciding whether to keep it. This is a significant business decision but not a critical one.

They decide they need to be right at least 95 times out of 100, so they choose a 95% confidence level. Given the medium-to-high stakes, they are comfortable with a 5% margin of error, meaning their results could be 5% higher or lower than the true figure across all 50,000 customers.

Together those two numbers, 95% confidence and 5% margin of error, tells they are 95% confident that their survey results will fall within 5% of the true answer. Plugging those into Slovin's Formula gives them the exact sample size they need to make a reliable decision without surveying every customer.

Meanwhile, You can use this free margin of error calculator.

Wrapping Up …

Getting your sample size right is the foundation of any reliable survey. With the right population size, margin of error, and confidence level in hand, you have everything you need to collect data that actually reflects your audience.

The next step is building the survey itself. SurveySparrow's conversational survey format achieves up to 40% higher completion rates, which means your carefully calculated sample is more likely to respond. Start your free trial and build your first survey in minutes.