 surveyking / docs

# Sample Size Calculator

How many people do you need to take your survey? Determining sample size can be tough. Try our sample size calculator. We give you everything you need to calculate how many responses you will need to be confident in your results.

#### Calculate Sample Size:

 Population Size: Confidence Level: 80% 85% 90% 95% 99% Margin of Error (%):

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#### Needed Sample Size:Based on infinite (large) population

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* Assumes a normal distribution of 50% to calculate your sample size

### What is Sample Size

The number of respondents who take your survey is a sample size. It's a sample because it represents a part of the total group of people whose opinions or behavior you care about. As an example, you can select at random 10 out of 50 employees from a department at your job. Those 10 are the sample and the 50 are the population.

There can be two different sample sizes. One based on an infinitely large population, the other based on a smaller finite population. This finite number you can specify above.

The bigger the population is, the bigger the sample will need to be to accurately reflect the population.

### Key Terms

Population Size: This is the total number of people in the group you are trying to reach with your survey. If you were taking a random sample of people in the United States, then your population size would be about 321 million.

Confidence Level: A measure of how confident you are that your sample accurately reflects the population, including room for the margin of error. Common standards used by researchers are 90%, 95%, and 99%.

If your confidence level is 95% in the above example, you could say you're 95% certain that between 38% and 42% of the United States Population do not like their jobs.

Margin of Error (Also called percent error): A percentage that describes how closely the answer your sample gave is accurate if you were to ask the entire population. For example, let’s say you send a survey to 500 people in the United States asking them if they like their jobs. 40% say no. If your margin of error is 2% you could say you're confident the true answer is somewhere between 38% and 42%. "How" confident you are can also be described as a percent and this is called a confidence Level.

See our margin of error calculator for how to calculate your percent error.

Population Proportion: This can be described as the makeup of the population. For example, if it's well known that 60% of college students are female, you could say the population proportion of college students is 60% female. If you wanted to mainly get opinions of college females, you would use this 60 percent in the formula below (for P). Most times though these numbers are not known and 50% (.50) is used for P. This .5 number produces the largest possible sample size, as it is most conservative.

Finite Population Adjustment: If you know the exact population number for the group you are targeting, an adjustment to sample size will be made to reflect this population number. See the below formulas.

### How to Calculate Sample Size Of an Infinitely Large Population

Sample Size Equation

\begin{align*} \frac{z^2 * P * (1 - P)}{C^2} \end{align*}

Where,

z = z-score (see below)

P = Proportion of correct answer based on prior experience. (Use .5 if unknown as this creates the largest and most conservative sample)

C = Confidence interval percentage as a decimal

The z-score is the number of standard deviations a given proportion is away from the mean. To find the correct z-score to use in your calculation, refer to this table:
 Desired Confidence Interval Z-score 80% 1.28 85% 1.44 90% 1.65 95% 1.96 99% 2.58