STATISTICS

Sample Size Calculator

Determine the number of subjects needed for a survey or experiment. Calculate required sample size based on confidence level, margin of error, and population.

Parameters
95% (Standard)
±5%
%

Use 0.5 if you do not know the likely yes/no split. It gives the largest safe sample size.

Required Sample Size
385
subjects
Confidence
95%, z=1.96
Expected proportion
50%
Population
Very large or unknown

The result is rounded up because you cannot survey part of a person.

No finite population correction is applied for a very large or unknown population.

The formula uses a normal approximation for one proportion and assumes a simple random sample.

Saved on this device

Recent sample-size scenarios stay in this browser only.

No data
No saved sample sizes yet.
Sample Size vs. Margin of Error
The red marker shows the sample size for your current confidence level and margin of error.*The chart compares sample sizes required for 90%, 95%, and 99% confidence levels as the acceptable error margin increases.

Understanding Sample Size

How to use this calculator

  • Confidence Level: Use 95% for most surveys. Use 90% when a rougher estimate is acceptable and 99% when you need a wider safety margin.
  • Margin of Error: Enter the range you can accept around the survey result. A smaller margin needs many more responses.
  • Population: Enter this only when the group is known and limited, such as 500 employees. Leave it blank for a large or unknown group.

Formula and assumptions

The calculator uses Cochran's formula for a single proportion. When you enter a known population size, it applies the finite population correction.

n = (Z² × p(1-p)) / e²

The default expected proportion is 0.5 because it gives the largest sample size when you do not know how responses will split.

Common mistakes, tips, and examples

Plan for nonresponse
The result is completed responses. Invite more people if only some of them are likely to answer.
Use 0.5 when unsure
If you do not know the likely response split, keep the expected proportion at 0.5. It is the conservative choice.
Small fixed groups
For a group of 500 people, a 95% confidence level and 5% margin of error gives 218 completed responses.
Large surveys
For a very large population, 95% confidence and 5% margin of error gives 385 completed responses.

FAQ

Why use 50% (0.5) for expected proportion?

A 50/50 split has the most variability, so it gives the largest sample size. Use a different value only when you have a reliable prior estimate.

Does population size always matter?

No. Population size matters most for small fixed groups. For large or unknown groups, the required sample size changes very little.

Is this the number of invitations to send?

No. It is the number of completed responses you need. If you expect a 40% response rate, divide the result by 0.4 to estimate invitations.

What does confidence level mean?

In repeated random sampling, the chosen confidence level describes how often the interval method would capture the true population value.