Finite Population Correction Calculator
Find the finite population correction factor for your survey. Enter the sample size and the total population size.
Learn how to calculate it yourselfEnter your values
Results update as you type.
Correction factor
multiply your margin of error by this
Calculate it yourself
Sample 100 people without replacement from a population of 1,000.
Follow this worked example, then repeat the steps with your own numbers.
Subtract the sample from the population
N − n = 1000 − 100 = 900.N is the population size and n is the sample size.
Divide by one less than the population
(N − n)/(N − 1) = 900/999 ≈ 0.90090.Take the square root
FPC = √(900/999) ≈ 0.94916.Apply the correction to a standard error
If the uncorrected standard error is 2 points, corrected SE = 2 × 0.94916 ≈ 1.898 points.
The correction assumes a random sample without replacement from the stated population. Multiply a standard error or margin of error by FPC, and a variance by FPC².
Check your answer in the calculatorUse your PaperSurvey.io results
A Response plan applies a population correction when you supply population size, while this calculator shows the factor itself.
When it matters
The usual margin of error formula assumes the population is effectively infinite. When your sample is a large fraction of a small population, for example surveying 300 of a 1000-member group, you already know more about the whole than that formula assumes, so the true margin of error is smaller. The correction factor captures that gain.
How to apply it
The factor is the square root of (N − n) divided by (N − 1), where N is the population and n is the sample. It requires the sample to be no larger than the population. Multiply your margin of error by this factor: at a full census the factor is 0, and for a tiny sample of a huge population it is close to 1 and can be ignored.
Frequently asked questions
When can I skip the correction?
If your sample is less than about 5% of the population, the factor is so close to 1 that it makes almost no difference and is usually left out.
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