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margin of error calculator

Understanding sample sizes

It’s something most researchers understand that the larger your sample size, the more accurate your data is going to be to that for the population as a whole, but it’s harder to understand just how large the sample needs to be to give a certain level of accuracy.

Knowing how big your sample needs to be to get a given level of accuracy is very important if you’re planning to buy consumer panels, for instance.

Surveys with a too-small sample for the population size can give misleading answers, so it’s always critical to maximise the sample size where possible, and to always bear in mind that there’s always a margin of error.

If you want to calculate your margin of error, check out our calculator

Calculating Manually

We’ve provided an automatic calculator for this, but as any good researcher and student knows, it’s important to show your working.

The sample size is defined by the following formula:

Sample size = z2 x p ( 1 - p ) e2 1 + z2 x p ( 1 - p ) e2 N

After crunching all those numbers, (or using our calculator, if you’re smart), you’ll find a number that defines how many responses you need to receive for your survey to meet the criteria you’ve set for it. By playing around with the numbers (and looking at the equation) you may notice that the required sample doesn’t increase linearly with the desired measures of accuracy, with the required samples getting very large.

So, now you should be armed with all the information and numbers you need to determine how many responses you need to be able to have real confidence in your results.

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