Simple Random Sampling Calculator

Configure the calculation

Use the fields below to estimate survey sample size, adjust for response rates, and optionally draw a reproducible random sample.

Population size

Confidence level

Custom Z score

Target margin of error (%)

Expected proportion (%)

Expected response rate (%)

Requested draw count

Sampling mode

Random seed

Population list for sample drawing

If the draw count is zero, the tool uses the recommended completed sample size, capped by the list size.

Example data table

These sample scenarios show how population size, confidence, margin, and response expectations change the required sample and invitation plan.

Scenario	Population	Confidence	Margin	Expected proportion	Response rate	Recommended completes	Invites needed
Customer satisfaction survey	5,000	95%	5%	50%	80%	357	447
Employee opinion pulse	1,200	95%	4%	45%	70%	398	569
Membership preference study	25,000	99%	3%	40%	60%	1,653	2,755

Formula used

The calculator combines the classic simple random sampling equation with finite population correction and response-rate adjustment.

1) Initial sample size

n₀ = (Z² × p × (1 − p)) / e²

Here, Z is the confidence multiplier, p is the expected proportion, and e is the margin of error in decimal form.

2) Finite population correction

n = n₀ / (1 + ((n₀ − 1) / N))

When the population is limited, this correction reduces the required sample because each selected unit carries more information.

3) Invitation planning

Invites = n / response rate

A lower anticipated response rate means more invitations are needed to reach the same number of completed observations.

4) Actual error estimate

MOE = Z × √(p(1−p)/n) × FPC

The page also estimates the realized margin of error after rounding the sample size to a whole number.

How to use this calculator

Enter your total population size, such as customers, patients, accounts, or records.
Choose a confidence level or enter a custom Z score.
Set the target margin of error and the expected proportion. Use 50% when uncertainty is high.
Add the expected response rate to estimate how many invitations are required.
Optionally paste a population list and select a draw count to generate an actual random sample.
Press Calculate Sampling Plan to show results above the form, then export them as CSV or PDF.

Frequently asked questions

1) What does simple random sampling mean?

It means every unit in the population has the same chance of selection. This reduces systematic bias when the sampling frame is complete and accurate.

2) Why does the calculator ask for expected proportion?

Expected proportion reflects the share likely to answer yes, belong to a group, or show a trait. If unknown, 50% is the most conservative choice.

3) When should I use 50% for the proportion?

Use 50% when you lack prior evidence. It produces the largest required sample, which protects against underestimating survey needs.

4) What is finite population correction?

Finite population correction lowers required sample size when the population is not extremely large. It matters most when the sample becomes a meaningful share of the population.

5) Why are invites higher than completed responses?

The calculator increases the outreach count to offset nonresponse. If only 70% are expected to respond, you must invite more people to hit the goal.

6) Can I draw a real sample from names or IDs?

Yes. Paste the population list, choose the draw count, and the page returns a random selection with or without replacement.

7) What does the random seed do?

A seed makes the random draw reproducible. The same list, settings, and seed will generate the same sample sequence again.

8) Does this calculator support continuous variables?

This version focuses on proportion-based planning. For means or continuous outcomes, use a sample size method based on standard deviation.