Random Sampling Calculator

Work out random sampling instantly with clear inputs, formula shown and shareable results.

About Random Sampling Calculator

In simple random sampling every individual has an equal chance k/N of selection. When the sample is a large fraction of the population the finite population correction √((N−k)/(N−1)) shrinks the margin of error.

Formula

Margin of error

E = z·√(0.25/n)·√((N − n)/(N − 1))

Worked example

With the default values below, Random Sampling Calculator returns Margin of error of 6.790193. Change any input above and every figure here is recalculated in your browser.

Inputs used

Population sizeminimum 1: 5,000
Sample sizeminimum 1: 200
Confidence levelaccepts 50–99.99 %: 95 %

Results

Margin of error: 6.790193 %
Chance any individual is selected: 0.04000000
Finite population correction: 0.97989389
Effective sample size: 208.2917

Step by step

1Values used
2Margin of error
3Margin of error= 6.790193 %
4Chance any individual is selected= 0.04000000
5Finite population correction= 0.97989389
6Effective sample size= 208.2917

Assumptions and limits

The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 8 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

For 200 sampled from 5000 at 95%?

The uncorrected margin is 6.93%, and the correction factor 0.9800 brings it to about 6.79%.

When can I ignore the correction?

When the sample is under about 5% of the population; then the factor is above 0.975 and barely matters.