About the Sample Size Calculator
Sample Size Calculator tells you how many responses you need before you can trust a survey or a measurement. Choose whether you are estimating a percentage, such as the share of customers who are satisfied, or an average, such as the mean height or time. Pick your confidence level, usually 95 percent, and the margin of error you can accept. For a percentage, add the expected share, or leave 50 percent if you do not know, which is the safe choice. For an average, add the expected standard deviation. If your whole group is small, enter its size and the tool reduces the sample with the finite population correction. Add an expected response rate to see how many people to invite. Calculations use Cochran's formula and run in your browser.
Updated September 2026
How to use the Sample Size Calculator
- 1Choose A percentage (survey) or An average (measurement).
- 2Pick a confidence level, such as 95 percent, and your margin of error.
- 3Enter the expected percentage (50 if unknown) or the expected standard deviation.
- 4Optional: enter the size of the whole group and the response rate you expect.
- 5Read the sample size, the margin of error it gives and the number of people to invite.
Why sample size matters
A small sample can give a result that looks convincing and is only luck, and a huge sample wastes time and money. The right size depends on how precise you need to be, how sure you want to be and how varied the thing you are measuring is. A sample size calculation makes those choices visible before you start, instead of after the results come in.
The three inputs are simple. The confidence level is how often you want the method to be right, the margin of error is how close you need to be and the variation is how much answers differ from person to person.
Percentages and averages
- For yes or no questions and shares, use A percentage and 50 percent if unsure.
- For numbers such as height, price, time or score, use An average and enter the expected standard deviation.
- Take the standard deviation from a small pilot study or earlier research.
- If you plan to compare groups or study subgroups, plan the sample size for the smallest group.
From sample size to invitations
Not everyone you ask will answer, so invite more people than you need. Online surveys often get 10 to 30 percent, and postal or phone surveys can be higher or lower. Enter your expected response rate to see how many to send. If the response is lower than you hoped, follow up with reminders rather than accepting a smaller sample, because the people who answer late are often different from the first responders.
Choose participants at random from the group you want to describe. Random selection is what makes the margin of error meaningful.
Related tools
Confidence Interval Calculator turns your results into an interval, Standard Deviation Calculator finds the spread of your data, Z-Score Calculator finds critical values and normal probabilities, Percentage Calculator handles response rates and Random Number Generator can pick people from a numbered list at random.
Features
- Sample size for a percentage or for an average
- Confidence levels of 80, 90, 95 and 99 percent
- Finite population correction for small groups
- Expected response rate to work out invitations
- Margin of error the result gives
- Z value shown
- Copy the result
- Runs in your browser
Frequently asked questions
What sample size do I need for a survey?
For a 95 percent confidence level and a 5 percent margin of error, you need about 385 responses when the group is large. For a 3 percent margin you need about 1,068. Enter your own numbers in the tool and it works out the exact figure.
What formula does the tool use?
For a percentage it uses Cochran's formula n = z² × p × (1 − p) ÷ e², where z is the value for your confidence level, p the expected proportion and e the margin of error. For an average it uses n = (z × standard deviation ÷ margin) squared. Both are rounded up.
Why is 50 percent used when I do not know the expected share?
The formula gives the largest sample when p is 50 percent, so it is the safest choice. If you are fairly sure the true share is far from 50 percent, for example around 10 percent, entering that gives a smaller sample and saves effort.
What is the finite population correction?
When your sample is a large part of a small group, you learn more than the plain formula suggests, so fewer responses are needed. For a group of 1,000 the sample drops from 385 to 278. For large groups the correction is tiny and changes nothing.
How does the population size change the result?
Very little unless the group is small. Surveying 385 people gives the same precision for a city of 100,000 as for a country of millions. The group size matters only when it is a few thousand or less.
How many people should I invite?
Divide the sample size you need by the response rate you expect. If you need 385 answers and about 30 percent of people reply, invite 1,284. Enter your expected response rate and the tool does it for you.
Does a big sample guarantee accurate results?
No. The formulas measure random error only. If the people who answered are not like the people who did not, for example only enthusiastic customers replied, the results will be biased and a bigger sample will not fix it.