Polaris' Help Center:
Survey DesignTool for Calculating the Appropriate Sample Size
Probably the most frequent question we get is "How many
people do I need to survey to get good results?" It often
comes as a surprise that the number is less than they might expect. Our response is to ask them "Well, what degree of accuracy do you need?" And that level of accuracy is expressed as the margin of error or sampling variation or the degree to which a given response is due to blind luck.
Here are some rules of thumb for sample size calculating:

Use a confidence level of 95 percent. It's the standard choice and won't be questioned.

When you are interested in the results for the total sample and it's not critical to get reliable results for individual subsegments, a sample size of 400 will yield a margin of error of +/ 5%.

When you want to have reliable results when comparing specific segments in your sample (e.g., males v. females), you want at least 150 (MoE=8%) to 200 (MoE=7%) surveys for each segment of interest.
Click on your button choice below to launch the appropriate calculator.(Click on the button again to close the calculator)
You will need to have the following data points to calculate your desired sample size:
 Your chosen confidence interval ^{(1)}
 The size of the two sample segments you are testing ^{(2)}
 The estimated size of the population ^{(3)}
 The estimated survey result that you're testing expressed either as a proportion or percentage or as a mean or average. If you don't have a good estimate (like results from a past survey), a good rule of thumb is to use the worst case odds of a 50% chance.
Note: If you are comparing means, you will also need to know the standard deviation of the mean for both segments.
Footnotes:
^{(1)} The confidence interval, almost always in the range of 90 to 99 percent (most often 95%), is used to indicate the reliability of an estimate (in this case the margin of error). For example, a margin of error of +/ 5.0 percent at a 95 percent confidence level can be interpreted to mean that if you were to repeat the survey, 95 out of 100 times the results would come back with the same result within +/ 5.0 points.
^{(2)} Along with the confidence level, the sample size determines the magnitude of the margin of error. A larger sample size produces a smaller margin of error, all else remaining equal.
^{(3)} By population, we mean the larger body of people of interest that is too large to take a census. For example, the population of interest might be all females in Georgia between the ages of 2550. As a rule of thumb, if a population is more than a couple of hundred people, we can consider it as "infinite" in size for the purpose of the calculator. The calculator can be adjusted for very small size populations (<150).