Sample Size for a Proportion Calculator

This calculator works out how large a sample you need to estimate a proportion to a chosen margin of error, the essential planning step before running a survey or study. When you measure a proportion from a sample, your estimate carries a margin of error that shrinks as the sample grows. Turning that around, if you decide in advance how precise you want to be, you can calculate the minimum sample size required to achieve it. This is the calculation behind every well-designed opinion poll and survey, and getting it right avoids both under-sampling, which leaves your result too imprecise to be useful, and over-sampling, which wastes time and money. This calculator does it. You enter the confidence level, your target margin of error as a percentage, your best estimate of the proportion (use 50 percent if unsure, as it requires the largest sample and so is the safe choice), and optionally the size of the population you are sampling from, and it returns the required sample size, the size without any population correction, the z-value used, and the margin of error. The results update as you type. Use it to plan a survey, to size a study, or to check whether a sample is large enough for the precision you need. The base sample size is the z-value squared, times the proportion times one minus it, divided by the margin of error squared. If you enter a population, a finite population correction reduces the required size, since sampling a meaningful fraction of a small population gains precision; for very large populations the correction makes little difference. Using a proportion estimate of 50 percent gives the most conservative, largest sample, which is why pollsters default to it when the true proportion is unknown. Round the result up, since you cannot survey a fraction of a person.

Sample size = z² x p(1-p) / E². A finite population correction reduces it if a population is entered. Use 50% proportion if unsure (largest, safest). Round up.