How many respondents do I need to survey for my results to be representative? You can answer this question — and calculate the sample size — quickly and easily with the QUESTIONSTAR sample size calculator. This article explains, in plain terms, what each of the parameters you need actually means.
If you're interested in the math behind it, you'll find it on our technical page on calculating sample size. Here we focus on how to use the calculator in practice and on what the parameters you need to enter actually mean.
The QUESTIONSTAR sample size calculator
With the sample size calculator, you can work out in a few seconds how large your sample needs to be for your survey results to be representative of the population you're studying. Choose a margin of error and a confidence level, enter the size of the population (if known) and the proportion of the characteristic you're studying (if known) — and you get the required sample size.
The calculator is freely accessible, with no registration and no data storage. You can use it as often as you like — including for other people's projects.
What do the calculator's parameters mean?
The calculator asks for four inputs. Two of them are required — margin of error and confidence level. The other two are optional: the size of the population and the proportion of the characteristic in the population. What exactly do these values mean?
Margin of error
The margin of error (also called the tolerance for error) indicates by how many percent the value measured in your sample may deviate from the true value in the population. Values between 3% and 5% are common.
For example: your survey finds that 60% of respondents prefer brand X. A margin of error of 5% then means that the true proportion in the population may deviate from your measured value by 5% up or down — so it lies between 55% (60% minus 5 percentage points) and 65% (60% plus 5 percentage points). This range is also called the confidence interval.
The smaller the margin of error, the larger the sample has to be — and the relationship is not linear but quadratic. Halving the margin of error quadruples the required sample size.
Confidence level
The confidence level indicates the probability with which you want to be certain that the sample is representative of the population — that is, that the true value lies within the calculated range. 95% or 99% are common.
A confidence level of 95% means: if you ran the survey 100 times, the result would fall within the stated margin of error in 95 of them. In 5 cases the true value would fall outside this range — and the survey results would then not be transferable to the population.
For the example above, this means: we are 95% certain that the proportion of people who prefer brand X in the population lies between 55% and 65%.
Here, too: the higher the confidence level, the larger the required sample. For most practical applications, 95% is perfectly sufficient.
Population size
The population comprises all the people whose opinions, attitudes or behaviors you want to represent in your survey.
If the survey results are meant to be representative of your company's employees, the population size equals the number of all employees at your company. If the results are meant to apply to all of Germany, the population is roughly 83 million.
The smaller the population, the smaller the sample you need for a representative result.
In many cases the population size is not known. That's not a big problem: leave the field empty, and the sample size calculator will assume an infinite population. You'll then have to survey somewhat more respondents, but at the same time you have the assurance that the survey results are representative.
Proportion of the characteristic in the population
Sometimes you know from earlier studies or general statistics how often a particular characteristic occurs in the population — for example, that roughly 30% of the population are vegetarians. If you know this proportion, you can enter it into the calculator and thereby determine the required sample size more precisely.
If you don't know the proportion, leave the field empty. The calculator will then assume 50% — the value that yields the largest required sample. That way you're on the safe side.
Required sample size
The required sample size is the result of the calculation — it tells you how many respondents you need to survey at a minimum for your survey to be representative of the population.
Note: the required sample size is not the number of people invited, but the number of fully completed questionnaires. Since the response rate is rarely 100%, you usually have to invite considerably more people than the number of usable responses you need.
It's a different matter if you survey fewer respondents than the required sample size demands. In that case you have no basis whatsoever for claiming that the statements from your survey also apply to the population. Neither the margin of error nor the confidence level can remedy this — if the minimum sample size wasn't reached, they are meaningless.
Does my survey really have to be representative?
Representativeness is a demanding goal — and not always necessary. Before you launch the survey, it's worth considering whether your research question really calls for a representative sample, or whether it's enough for you to gather tendencies, hypotheses or individual opinions.
Representativeness makes sense when you want to make statements about an entire population — say, about all employees, all customers in a market or all students at a university. It matters less when you want to collect feedback or gather ideas and suggestions from your employees or customers, in exploratory studies where you're first developing hypotheses, or in qualitative surveys where the depth of the answers counts rather than their spread.
Representativeness is necessary, for example, in market research studies that segment target markets, assess the reception of a new product or measure responses to advertising messages. Without representativeness, the survey results can't be transferred to the population — and you don't know whether the market actually responds the way your data suggest.
The same applies to employee surveys ahead of a planned restructuring, and especially to opinion polls and electoral research — here representativeness is the prerequisite for sound conclusions.
A representative sample requires not only the right size but also the right composition. If, for example, you want to measure employee satisfaction at a company but only survey the staff of one branch, the sample — no matter how large — is not representative of the whole company. The selection method is at least as important as the count.
How can I calculate the sample size myself?
If you want to understand the calculator and follow the math behind it yourself, you'll find all the formulas, variables and worked examples in our technical article on calculating sample size.
In brief: for infinitely large populations we use Cochran's formula n = z² · p · (1 − p) / E². For finite populations, a correction is added that adjusts the sample size downward. The variables z, p and E correspond to the confidence level, the characteristic proportion and the margin of error — that is, the inputs the calculator asks you for.