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Sample Size Calculator

Sample Size Calculator

Get to know the appropriate sample size to meet a given set of constraints correctly and swiftly by using the sample size calculator.

Infinite Population
Finite Population

Is Given:

Confidence Level:

Margin of Error:

Standard Deviation:

Population Proportion:



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Find out the target population you need to interview as the representative of the whole population through this sample size calculator.

The tool provides you with accurate results each time without any human intervention.

What Is Sample Size?

Sample size means to calculate the number of people that you will have to interview to reach a result that can reflect the needs of the population. In general, a simple size is the subset of subjects taking part in a survey from the whole population.

Why Calculate Sample Size?

For performing the survey in a large population, the sample size is very important. This is because it’s not feasible to reach out to everyone and know their opinion about a product or activity.

So it’s good to calculate the part of a population and know the opinion of all the people included in this part. Therefore, the statistical sample distribution is a vital factor for scientists, marketers, government agencies, economists, and research groups.

The calculation of sample size requires you to go through a long calculation but what if you don’t have the time? In this case, you can get the assistance of our minimum sample size calculator. As it will let you perform the whole calculation in no time.

How To Calculate Sample Size?

The following essential factors need to be known for calculating sample size. Let’s take a look at them:

Margin Of Error:

This is the level of precision you require. It can be a positive or negative number that is shown with an estimated proportion. In general, this is the range in which the population proportion is estimated and is expressed in percentages such as ±5%. It is also known as a confidence interval.

Confidence Level:

This is the probability of error contained by the margin of error. Meanwhile, the higher confidence level indicates you are near the real proportion.

Population Size:

The size of the population is the actual number of individuals in the population. If you have a large population but you don’t know the exact figure then use 100,000 because the samples are not too much different for larger populations. So you can use this figure as your population size.

Standard Deviation:

It shows the variation between the individual responses and the mean. If it’s low then the score will be considered near the mean and a higher value will show that when you plot it on the graph the response will be spread out too much.


Z-score shows your confidence level in percentages such as 90%, 95% and 99 % etc.

z = (x – μ) / σ

Sample Size Formula:

For calculating the sample size you need to know the above-mentioned variables. If you don’t know the exact population, then you can still find the sample size. Let’s see the following formula:

Sample size formula for infinite population:

\(\left(\dfrac{\text{Confidence Level}* \text{Standard Deviation}}{\text{Margin of Error}}\right)^2\)

Sample size formula for finite population:

Sample Size = (n x N) / (n+N-1)


n = sample size..
MOE is Margin Of Error.
N is the population size

Rather than performing this complex calculation, you can simply get the help of a free population proportion calculator. With it, you will be able to perform the precise calculation of the appropriate sample size quickly.

You can also use our sampling distribution calculator to get the probability of getting a certain value rapidly.

Confidence level z-score
80% 1.28
85% 1.44
90% 1.65
95% 1.96
96% 2.05
98% 2.33
99% 2.58


Let’s suppose the value of the standard deviation is 2, the confidence level is 95 % and the margin of error is 5 then how to find sample size for infinite population?


Given that:

Confidence level = 95%

We will put the value of the confidence according to z-score in which 95% = 1.96

Margin of Error = 5

Standard Deviation = 2

\(\left(\dfrac{\text{Confidence Level}* \text{Standard Deviation}}{\text{Margin of Error}}\right)^2\)



\(Sample Size = (78.4)^2\)

\(Sample size = 6146.56\)

Working Of Our Statistical Sample Size Calculator:

Calculate sample size effortlessly with the help of our online population calculator. It just requires the users to follow a couple of simple steps to precisely perform the calculation. Let’s take a look:


Choose “Infinite Population or Finite Population.
Add the values of the “confidence level”, “margin of error”, “population proportion”, and “population size” in the specified fields.
Tap on the “calculate” button.


Sample size calculation.
Step-by-step calculation.


From the source of Confidence Interval

From the source of Wikipedia: Sample size, Introduction