# Calculator: Calculate Your Survey’s Minimum Sample Size Developing a survey and ensuring you have a valid response that you can base your business decisions on requires quite a bit of expertise. First, you have to ensure that your questions are asked in a manner that doesn't bias the response. Second, you have to ensure that you survey enough people to get a statistically valid result.

You don't need to ask every person, this would be labor-intensive and quite expensive. Market research companies work to attain a high level of confidence, low margin of error while reaching the minimum quantity of recipients necessary. This is known as your sample size. You are sampling a certain percentage of the overall population that to attain a result that provides a level of confidence to validate the results. Utilizing a widely accepted formula, you can determine a valid sample size that will represent the population as a whole.

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### The Formula for Determining The Minimum Sample Size

The formula to determine the minimum sample size necessary for a given population is is as follows: $S=\frac{\frac{z^2\times p\left ( 1-p \right )}{e^2}}{1+ \left (\frac{z^2 \times p\left (1-p\right )}{e^2N}\right )}$

Where:

• S = Minimum sample size you should survey given your inputs.
• N = Total population size. This is the size of the segment or population that you are wishing to evaluate.
• e = Margin of Error. Whenever you sample a population, there's going to be a margin of error in the results.
• z = How confident you can be that the population would select an answer within a certain range. The confidence percentage translates to the z-score, the number of standard deviations a given proportion is away from the mean.
• p = Standard deviation (in this case 0.5%).

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