# Sample Size Calculator - Slovin's Formula To Calculate Sample Size (2023)

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.

(Video) COMPUTING SAMPLE SIZE USING THE SLOVIN'S FORMULA

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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.

(Video) How to Use Slovin's Formula - Calculate Sample Size | Research and Thesis Writing

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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.

(Video) How to determine the Sample Size || Slovin's Formula || Sample 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.

(Video) Calculate Sample Size using Excel w CI

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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## 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! (Video) Determining the Sample Size Using Slovin's Formula

##### Kate William

Content Marketer at SurveySparrow

## FAQs

### How do you calculate sample size using Slovin's formula? ›

1. Slovin's Formula. - is used to calculate the sample size (n) given the population size (N) and a margin of error (e). -It is computed as n = N / (1+Ne2).

What is N in Slovin's way of determining your sample size? ›

n = Number of samples, N = Total population and. e = Error tolerance (level).

How do you find population size with margin of error and sample size? ›

How to calculate margin of error
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:

What is the sample size of 200 populations? ›

Determining Sample Size
PopulationSamplePopulation
17011830 000
18012340 000
19012750 000
20013275 000
28 more rows

How do you determine sample size based on population size? ›

A good maximum sample size is usually around 10% of the population, as long as this does not exceed 1000. For example, in a population of 5000, 10% would be 500. In a population of 200,000, 10% would be 20,000. This exceeds 1000, so in this case the maximum would be 1000.

What are the 4 ways to determine the sample size? ›

There are many methods that researchers use to find the right sample size, but all of them can be boiled down into the following four steps:
• Step 1 Find out the size of the population. ...
• Step 2 Determine the margin of error. ...
• Step 3 Set confidence level. ...
• Step 4 Use a formula to find sample size.
Jul 14, 2022

Why do we calculate sample size? ›

Why sample size calculations? The main aim of a sample size calculation is to determine the number of participants needed to detect a clinically relevant treatment effect. Pre-study calculation of the required sample size is warranted in the majority of quantitative studies.

Do you use N or N for sample size? ›

N usually refers to a population size, while n refers to a sample size.

Is sample size big N or little n? ›

The sample size is very simply the size of the sample. If there is only one sample, the letter "N" is used to designate the sample size. If samples are taken from each of "a" populations, then the small letter "n" is used to designate size of the sample from each population.

Is N sample size or number of observations? ›

We will use Y to denote the value of an observation. The total number of observations, i.e., the sample size, will be denoted as n.

### What sample size is needed to give a margin of error? ›

To obtain a 3 percent margin of error at a 90 percent level of confidence requires a sample size of about 750. For a 95 percent level of confidence, the sample size would be about 1,000. Determining the margin of error at various levels of confidence is easy.

What sample size is needed for a 95 confidence interval? ›

To be 95% confident that the true value of the estimate will be within 5 percentage points of 0.5, (that is, between the values of 0.45 and 0.55), the required sample size is 385. This is the number of actual responses needed to achieve the stated level of accuracy.

Can you calculate sample size from standard error? ›

By calculating standard error, you can estimate how representative your sample is of your population and make valid conclusions. A high standard error shows that sample means are widely spread around the population mean—your sample may not closely represent your population.

What is the sample size for 1000 population? ›

Sampling ratio (sample size to population size): Generally speaking, the smaller the population, the larger the sampling ratio needed. For populations under 1,000, a minimum ratio of 30 percent (300 individuals) is advisable to ensure representativeness of the sample.

What is a good sample size for 300 people? ›

You would need at least 169 samples (with 95% confidence and with 5%- Margin of error) which is a most common requirement. With your current sample size you are having 11.3% margin of error (with 95% confidence). Use this on-line sample size calculator to calculate sample.

Why is 30 the minimum sample size? ›

A sample size of 30 often increases the confidence interval of your population data set enough to warrant assertions against your findings.4 The higher your sample size, the more likely the sample will be representative of your population set.

What is Slovin's formula? ›

This formula is used when you don't have enough information about a population's behavior (or the distribution of a behavior) to otherwise know the appropriate sample size. Slovin's formula is written as: n= N / (1+Ne2) Where: n= the number of samples N=the total population.

What are 3 factors that determine sample size? ›

In general, three or four factors must be known or estimated to calculate sample size: (1) the effect size (usually the difference between 2 groups); (2) the population standard deviation (for continuous data); (3) the desired power of the experiment to detect the postulated effect; and (4) the significance level.

What is the correct way to calculate population size? ›

The best way to measure the size of a population is to count all the individuals in that popula- tion. When determining the population sizes of trees or other relatively immobile organisms, this method is practical. If the organism is mobile, however, such as a fish, counting every individual would be difficult.

What is the simple random sampling formula for sample size? ›

The Formula of Random Sampling

(N-n/N-(n-1)). Here P is a probability, n is the sample size, and N represents the population. Now if one cancels 1-(N-n/n), it will provide P = n/N. Moreover, the chance of a sample getting selected more than once is needed: P = 1-(1-(1/N)) n.

### What is sample size examples? ›

In statistics, the sample size is the measure of the number of individual samples used in an experiment. For example, if we are testing 50 samples of people who watch TV in a city, then the sample size is 50. We can also term it Sample Statistics.

What is total sample size? ›

Sample size is the number of completed responses your survey receives. It's called a sample because it only represents part of the group of people (or target population) whose opinions or behavior you care about.

When sample size is 30 or less than 30 which sample test is used? ›

Z-tests are closely related to t-tests, but t-tests are best performed when the data consists of a small sample size, i.e., less than 30. Also, t-tests assume the standard deviation is unknown, while z-tests assume it is known.

When the sample size is than 30 you should use? ›

If the sample size is greater than 30, then we use the z-test. If the population size is small, than we need a bigger sample size, and if the population is large, then we need a smaller sample size as compared to the smaller population. Sample size calculation will also differ with different margins of error.

What is the best sample size for quantitative research? ›

Summary: 40 participants is an appropriate number for most quantitative studies, but there are cases where you can recruit fewer users.

What is the smallest acceptable sample size? ›

“A minimum of 30 observations is sufficient to conduct significant statistics.” This is open to many interpretations of which the most fallible one is that the sample size of 30 is enough to trust your confidence interval.

What is the minimum sample size for quantitative research? ›

If the research has a relational survey design, the sample size should not be less than 30. Causal-comparative and experimental studies require more than 50 samples. In survey research, 100 samples should be identified for each major sub-group in the population and between 20 to 50 samples for each minor sub-group.

How many observations do you need for a large sample? ›

Some researchers do, however, support a rule of thumb when using the sample size. For example, in regression analysis, many researchers say that there should be at least 10 observations per variable. If we are using three independent variables, then a clear rule would be to have a minimum sample size of 30.

How large a sample size is needed if I want my 95% confidence interval to have a 4% margin of error? ›

We want to construct a 95% confidence interval for with a margin of error equal to 4%. Because there is no estimate of the proportion given, we use for a conservative estimate. This is the minimum sample size, therefore we should round up to 601.

How do you know if a sample size is large enough? ›

Often a sample size is considered “large enough” if it's greater than or equal to 30, but this number can vary a bit based on the underlying shape of the population distribution. In particular: If the population distribution is symmetric, sometimes a sample size as small as 15 is sufficient.

### How do you find the sample size given confidence level? ›

Then we can find the sample size to yield an interval with that confidence level and with a half width not more than the specified one. The crude method to find the sample size: n = ( z α / 2 σ E ) 2 Then round up to the next whole integer.

How do you calculate the number of samples needed? ›

Follow these steps to calculate the sample size needed for your survey or experiment:
1. Determine the total population size. First, you need to determine the total number of your target demographic. ...
2. Decide on a margin of error. ...
3. Choose a confidence level. ...
4. Pick a standard of deviation. ...
5. Complete the calculation.
Feb 25, 2020

What is the smallest sample size for a 95% confidence interval? ›

Find the estimated minimum sample size required. Solution: Confidence level 95% means that α=1−0.95=0.05 so α∕2=0.025. From the last line of Figure 12.3 "Critical Values of " we obtain z0.025=1.960.

What is the minimum sample size needed for a 95? ›

Answer: To find an 95% CI with a margin of error no more than ±3.5 percentage points, where you have no idea of the true population proportion, you must survey at least 784 people.

What is sample size equation? ›

n = Z2p(1 – p)/m2

n is the sample size, Z is the z-value, p is the proportion of population (generally taken as 0.5), m is the margin of error.

How do you find size of sampling error? ›

Calculating Sampling Error

The sampling error is calculated by dividing the standard deviation of the population by the square root of the size of the sample, and then multiplying the resultant with the Z-score value, which is based on the confidence interval.

What does N mean in sample size? ›

Sample size refers to the number of participants or observations included in a study. This number is usually represented by n.

What is N in Slovin's formula? ›

This formula is used when you don't have enough information about a population's behavior (or the distribution of a behavior) to otherwise know the appropriate sample size. Slovin's formula is written as: n= N / (1+Ne2) Where: n= the number of samples N=the total population.

What is N in sample size formula? ›

To recall, the number of observation in a given sample population is known as sample size. Since it not possible to survey the whole population, we take a sample from the population and then conduct a survey or research. The sample size is denoted by “n” or “N”.

What does N stand for in sampling? ›

Sample Mean

The symbol 'n,' represents the total number of individuals or observations in the sample.

### What if the sample size is more than 30? ›

If the sample size is greater than 30, then we use the z-test. If the population size is small, than we need a bigger sample size, and if the population is large, then we need a smaller sample size as compared to the smaller population. Sample size calculation will also differ with different margins of error.

Why should sample size be 30? ›

A sample size of 30 often increases the confidence interval of your population data set enough to warrant assertions against your findings.4 The higher your sample size, the more likely the sample will be representative of your population set.

What formula is used to calculate sample size in research? ›

The Cochran formula allows you to calculate an ideal sample size given a desired level of precision, desired confidence level, and the estimated proportion of the attribute present in the population. Cochran's formula is considered especially appropriate in situations with large populations.

What is the symbol for sample size? ›

The symbol n represents the sample size (n = 10). The capital letter X denotes the variable.

What does μ mean in statistics? ›

m (the greek letter "mu") is used to denote the population mean. The population mean is worked out in exactly the same way as the sample mean: add all of the scores together, and divide the result by the total number of scores. In journal articles, the mean is usually represented by M, and the median by Mdn.

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