Finite Population Correction Calculator Formula

Understand the math behind the finite population correction calculator. Each variable explained with a worked example.

Use the Finite Population Correction Calculator

Formulas Used

Corrected Standard Error

corrected_se = se * fpc

FPC Factor

fpc_factor = fpc

Sampling Fraction (n/N)

sampling_fraction = n / N

SE Reduction (%)

reduction_pct = (1 - fpc) * 100

Variables

VariableDescriptionDefault
seUncorrected Standard Error2.5
nSample Size100
NPopulation Size500
fpcDerived value= sqrt((N - n) / (N - 1))calculated

How It Works

How to Apply the Finite Population Correction

Formula

FPC = sqrt((N - n) / (N - 1))

Corrected SE = SE * FPC

When sampling without replacement from a finite population, the standard error is smaller than the infinite-population formula suggests. The FPC factor accounts for this. It is close to 1 when n is small relative to N, and approaches 0 as n approaches N (census).

Worked Example

Standard error = 2.5, sample of 100 from a population of 500.

se = 2.5n = 100N = 500
  1. 01Sampling fraction = 100/500 = 0.20 (20% of population)
  2. 02FPC = sqrt((500-100)/(500-1)) = sqrt(400/499) = sqrt(0.8016) = 0.8954
  3. 03Corrected SE = 2.5 * 0.8954 = 2.2384
  4. 04The standard error is reduced by 10.5%

Ready to run the numbers?

Open Finite Population Correction Calculator