# Sample Size Calculator

We've answered your questions about sample size in this handy guide. Use our new sample size calculator to get the right sample size for your next survey.

In survey research it is important to receive feedback that is most reflective of the population you are targeting. The more appropriate the sample size, the more accurate the results.

Using a sample size that is too low will lessen quality and a sample size that is too large complicates analysis and is not time or cost efficient. Fortunately, determining sample size is not a guessing game and can be achieved using a simple calculation.

## Sample Size Calculator

Population size
Confidence level
Margin of error
Sample proportion
Recommended Sample Size
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## Understanding Sample Size

### How do you find the minimum sample size? How do you determine sample size in research?

Your minimum sample size is the minimum number of respondents you need to get survey results that reflect the population you are studying, whilst adhering to your desired confidence interval (margin of error) and confidence level. To ensure more accurate results, you may need to increase your sample size as occurrences of “non-response” can cause biased results.

To calculate your minimum sample size, you will firstly need to consider these factors:

1. Population size

The population size is the total number of people in the population (target audience) you are looking to survey. For example, if you were surveying the general population from a city with 30,000 residents, the population size for your study is 30,000.

When surveying small populations, a finite population correction is used. You can use 100,000 with caution if you do not know the exact size of a large population; sample size remains quite static over 100,000.

2. Confidence level

The confidence level indicates the probability that your confidence interval contains the true population value, if you were to repeat your study with a random sample selection.

For example, with a confidence level of 95%, your study could be repeated several times and your population would fall within the confidence interval on 95% of these occurrences.

The accuracy of your results is determined by how high your confidence interval is. You should also note that as your confidence level increases, so does your required sample size.

3. Confidence interval (Margin of error)

The confidence interval is a range of values that are likely to contain your population value and is expressed in percentage points. For example, a confidence interval of ±2% means that your true population will lie either 2 percentage points above or below where it is shown in your results.

Your confidence interval will be higher or lower than your specified value as it is based on your actual sample proportion, rather than your estimated proportion. It also depends on how accurate the results you are seeking are (determined by your confidence level). A higher confidence level results in a wider confidence interval.

4. Sample proportion

Your sample proportion (expressed as a percentage) indicates your estimated results and is calculated using a quick feedback study or previous survey results. Otherwise, 50% is a safe sample proportion to use without hindering the accuracy of your calculated sample size.

### What is a good sample size for quantitative research? What is a good sample size for a survey?

The ideal sample size for your study will depend on your population size, confidence level, and confidence interval. The survey design and methodology you use may also require you to further adjust your sample size.

A good sample size will satisfy your criteria for accuracy in quantitative research results. It is usually determined by a combination of expected confidence, budget and resource availability for analysis.

Generally, the bigger the sample size, the more accurate your results will be. However, you should consider that large sample sizes are costlier and can complicate your study. You can use our sample size calculator to determine the minimum sample size for your project to ensure your survey is accurate and cost effective.

### What sample size do I need for 95 confidence?

Once you have selected your confidence level as 95%, you will then need to determine your confidence interval and population size to calculate the sample size required for your study.

The sample size will be larger for 95% confidence than 90%, if all other factors remain the same.

Even though we recommend using 90% confidence level to achieve the right balance between cost and precision, you can increase it up to 99 percent. However, 99% confidence more than doubles the size of the required sample, compared to 90% confidence. This might produce an unnecessary bloat of data for most quantitative research projects.

### How do you find the sample size when given the margin of error?

To calculate sample size using your margin of error (confidence interval), you must also know your confidence level and population size.

The margin of error is usually expressed as ± value. This means your survey results can represent a range of values plus or minus the value of the margin of error.

Consider a survey that indicates that 40% of car owners in the USA would not consider the colour red for their next car. With a 5% margin of error, you should express your findings as 35-45% of car owners in the USA would not consider a red car. To gain more accurate insights, you could lower your margin of error to 2%, for example, and expect your findings to lie within a smaller confidence interval of 38-42%.

### Why does the margin of error decrease as the sample size increases?

You will see in our sample size calculator, reducing your margin of error results in a large increase in recommended sample size.

It should be noted that this is not a linear relationship, increasing sample size will result in diminishing returns in margin of error reduction. For example, the following chart illustrates the relationship between margin of error and sample size, for a population of 1 million, seeking a 90% confidence interval, with a 0.5 sample proportion.

As shown above, moving from a 5% margin of error to a 1% margin of error would require a sample size over 20 times as large.

### What is the formula for determining sample size?

The formula for calculating sample size is:

$$n = \frac{ N \frac{ z^2 p(1-p) } {e^2} } { \frac{ z^2 p(1-p) } {e^2} + N - 1 }$$

where:

• n is the sample size,
• N is the population size,
• z is the confidence level (in percent, such as 90% = 0.9),
• p is the sample proportion (in percent, such as 50% = 0.5),
• e is the margin of error (in percent, such as 5% = 0.05).

### Why is a small sample size bad? Why is a larger sample size better? Why must sample size be greater than 30?

Using a sample size that is too low can affect the robustness of data, especially in surveys where respondents have strong and clear preferences. See more.

### How do you justify small sample size in quantitative research?

A small sample size can be justified when: The whole population is small. For example, if there are only 100 customers, then it is OK to sample ~30 to get a view of the opinions of the whole customer base. When the cost of sampling is prohibitive.

Please note, it is not justifiable for most consumer research.

### Why is sample size important? Why is sample size important in quantitative research?

Sample size is important because it determines the accuracy and quality of your survey results. It is especially important in quantitative research as robust data is the key to unlocking meaningful and actionable insights.

Using an appropriate sample size increases the chances that your survey results will accurately reflect the views of your target audience. Once you have determined your sample size, you can now find respondents for your study.

### How does sample size affect validity of a study?

If sample size is not large enough for your study, the internal and external validity will be compromised and it can also result in cases of bias. A higher sample size results in more accurate results. Sample size is only one of many factors that affect the validity of your study.

You should also consider that data can still be useful in some instances even if you do not meet the required sample size for your study. For example, a customer satisfaction survey with open-ended questions can still provide meaningful insights as detailed consumer feedback is indispensable to market research.

##### Written on 15 July 2020 by: ##### Catherine Chipeta
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