Sample Size Calculator

How to use the sample size calculator

1. Choose your confidence level.
2. Enter the margin of error you will accept.
3. Enter the population size, or leave it blank for a large group.
4. Read how many people to survey.

What sample size means

A survey sample size is how many people you need to survey so the result reflects the whole group within a stated accuracy, in other words a statistically significant sample. Two things set it: the confidence level, how sure you want to be that the true answer falls within your range, and the margin of error, how wide that range is. A 95% confidence level with a 5% margin of error is a common choice, and it means that if you repeated the survey many times, about 95% of the results would land within 5 points of the truth.

The formula

The tool uses Cochran's formula. The base size is n0 equals z squared times p times one minus p, divided by the margin of error squared, where z comes from the confidence level and p is the response distribution. For a limited population it then applies the finite-population correction, which lowers the number when the group is small. The response distribution defaults to 50%, which demands the largest sample and is the safe choice when you cannot estimate it.

Source: Cochran, W. G., Sampling Techniques.

Confidence and margin of error

Raising the confidence level or shrinking the margin of error both increase the sample you need, and the margin of error has a strong effect because it is squared in the formula. Halving the margin of error roughly quadruples the required sample. A larger population barely changes the number once it is big, which is why national surveys often need only around a thousand people.

FAQ

How many people do I need to survey?

It depends on your confidence level and margin of error. For 95% confidence and a 5% margin of error, you typically need around 385 responses from a large population. Enter your figures for an exact number.

What is the margin of error?

The margin of error is how far your survey result might be from the true value, as a percentage. A smaller margin needs a much larger sample, since it is squared in the formula.

What confidence level should I use?

95% is the common standard. Use 99% when you need extra certainty, at the cost of a larger sample, or 90% when a rougher estimate is acceptable.

Why does the response distribution default to 50%?

Because 50% requires the largest sample, so it is the safest assumption when you cannot guess how answers will split. If you know the split is lopsided, a different value lowers the number needed.

Is my information private?

Yes. Everything is calculated in your browser and nothing you enter is uploaded or saved.