Sample Size Calculator
How many responses your study actually needs.
Sample Size Calculator
Find the number of responses needed for a survey or study at a chosen confidence level and margin of error.
How close the estimate must be to the true value.
Use 50% when you have no prior estimate — it needs the largest sample.
Leave blank for an unlimited population; enter it to apply the finite population correction.
Required sample
385
completed responses
- Cochran estimate (n₀)
- 385
- Finite population correction
- Not applied
- Critical value (z)
- 1.96
Expected precision: ±5 percentage points at 95% confidence.
This is the number of completed responses. If your response rate is lower than 100%, invite more people than this figure.
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What This Calculator Does
The Sample Size Calculator estimates how many completed responses a survey or study needs to reach a chosen margin of error at a chosen confidence level. It uses Cochran's formula and applies the finite population correction when you know the size of the population.
How It Works
Cochran's formula multiplies the squared critical value by the expected proportion and its complement, then divides by the squared margin of error. A 95% confidence level and a 5% margin of error with a 50% expected proportion gives about 385 responses. If the population is small, the finite population correction reduces that number.
Example
For 95% confidence, a ±5% margin of error, and a 50% expected proportion, the unadjusted requirement is 385 responses. In a population of 1,000 the finite population correction lowers it to 278; in a population of 100,000 it stays effectively at 385.
Formula
n₀ = z² × p(1 − p) / e²p = 0.5 maximises the required sample when no prior estimate exists.
n = n₀ / (1 + (n₀ − 1) / N)Reading the Results
Required sample
Completed responses needed. This is not the number of people to invite — divide by your expected response rate to get that.
Finite population correction
A reduction applied when the population is small relative to the sample, because sampling without replacement is more precise.
Sources and References
Cochran, W. G. (1977), Sampling Techniques, 3rd ed.
n₀ = z²pq/e²
The standard reference for the sample size formula and its finite population correction.
NIST/SEMATECH e-Handbook of Statistical Methods
Sample size for a specified margin of error
References identify the method or data behind this calculator. Where a standard or tariff changes, the current edition applies, and the assumptions stated above take precedence over a remembered figure.
Frequently Asked Questions
What sample size do I need for a survey?
It depends on the precision you need. For a ±5% margin at 95% confidence, budget about 385 responses regardless of population size; for ±3%, about 1,067. Smaller margins need disproportionately larger samples.
Why does a 50% proportion need the largest sample?
The term p(1−p) is largest at p = 0.5. If you expect a very one-sided result, the required sample is smaller — but using 50% is the safe choice when you have no prior estimate.
Should I allow for people who do not respond?
Yes. The figure here is completed responses. If you expect a 20% response rate, invite roughly five times as many people, and monitor whether non-response is biased.
Does a big population always need a bigger sample?
Not much. Beyond a few thousand, population size barely changes the requirement; the finite population correction matters mainly for small, closed populations such as a single company or school.