"How many people do I need?" is the question supervisors are asked most often and the one students most often answer by guessing. A sample size is not a matter of taste — it follows from how precise you need to be, how confident you want to be in that precision, and how large the population is.
This calculator uses Cochran's formula with the finite population correction, the approach cited in most methodology chapters. It shows the arithmetic and the reasoning alongside the number, so you can defend the figure rather than just quote it.
n₀ = z²·p·(1−p) / e². The z value comes from your confidence level (1.96 for 95%), p is the expected proportion, and e is the margin of error as a decimal. For 95% confidence, ±5% and p = 0.5, that gives 385.
Where you know the population size N, the finite population correction applies: n = n₀ / (1 + (n₀−1)/N). For a population of 1,000 this brings 385 down to 278. The correction matters because sampling 278 from 1,000 already covers a large share of the group — precision does not require the same absolute number as it would from a population of millions.
The margin of error is how wide your answer is: ±5% means a finding of 60% could reasonably be anywhere from 55% to 65%. The confidence level is how often that interval would contain the true value if you repeated the study many times: 95% confidence means it would 19 times in 20.
Tightening either one costs you sample size, and the cost is not linear. Halving the margin of error from ±5% to ±2.5% quadruples the sample, because e is squared in the denominator. This is why ±5% at 95% is so nearly universal — it is the point where precision and feasibility meet for most student projects.
The term p·(1−p) is the variance of a proportion, and it reaches its maximum at p = 0.5. Using 50% therefore produces the largest sample the formula will ever ask for, which makes it the safe default when you do not know what to expect.
If prior research gives you a solid estimate — say 20% of a population uses a service — entering 20% will reduce the required sample. Only do this when you can cite the source of the estimate, because an optimistic guess here quietly weakens your study. Entering 0% or 100% implies no variability at all, so this tool substitutes 50% and tells you it has.
The calculated sample is the number of usable responses you need, not the number of people to contact. If you need 278 responses and expect 70% of those approached to reply, you must approach around 398.
Student surveys routinely return far less than 70%, particularly online. Plan for the rate you can actually justify from a pilot or from comparable studies, and record it in your methodology. Discovering the shortfall after fieldwork has closed is expensive and often impossible to fix.
It sizes a sample for estimating a single proportion from a random sample. If you plan to compare subgroups, each subgroup needs enough cases in its own right — a total of 278 split across eight districts leaves roughly 35 per district, too few for most tests.
It also assumes probability sampling. Convenience and snowball samples do not support a margin of error at all, however many people you recruit, because the mathematics rests on every member having a known chance of selection. If your sampling is non-probability, report the sample size but drop the precision claim, and say so in your limitations. For power-based sizing of experiments, a power analysis is the right tool instead.
At 95% confidence with a ±5% margin of error and 50% expected proportion, 278. Change any of those three inputs and the answer changes.
It is the result for 95% confidence, ±5% margin of error and maximum variability with a large or unknown population. Entering a population size will usually reduce it.
50%, unless prior research gives you a defensible estimate. 50% maximises the variance term and so gives the largest, safest sample.
You can use the number as a target, but a margin of error only has meaning for probability sampling. With a convenience sample, report the size and acknowledge the limitation.
Yes. Enter your expected response rate and the tool shows how many people to approach to end up with the sample you need.