Survey Sample Size Calculator

How to use the sample size calculator

1. Population size: the number of people in the group you want to describe, such as every dentist in your city or every customer on your email list. Leave it empty if the group is very large or you do not know its size.
2. Confidence level: how sure you want to be that the true figure sits inside your margin of error. 95% is the usual choice. Pick 90% for a quick check and 99% when a wrong answer would be costly.
3. Margin of error: how many percentage points your result may be off. With a 5% margin, a survey result of 40% means the true figure is probably between 35% and 45%.
4. Expected result: your best guess at the share of people who will give the answer you care about. Keep 50% if you have no idea. It produces the largest sample, so it is the safe choice.
5. Expected response rate: of the people you invite, the share you expect to finish the survey. The calculator uses it to tell you how many people to invite.

The result updates as you type. The headline is the number of completed responses you need. Below it you see the sample for a very large population, the number of people to invite and the z-score used.

The sample size formula

Here z is the z-score for your confidence level (1.645 for 90%, 1.96 for 95%, 2.576 for 99%), p is the expected result as a decimal and e is the margin of error as a decimal. Step 1 is known as Cochran's formula. Step 2 is the finite population correction, which lowers the sample when your group is small. If you leave population size empty, the calculator stops after step 1.

A worked example

Say you plan to open a co-working space and there are 2,000 freelancers in your town. You want to know what share would pay for a desk. You choose 95% confidence and a 5% margin of error, keep the expected result at 50%, and expect 20% of the people you invite to answer.

You need 323 completed responses, which means inviting 1,615 of the 2,000 freelancers. That is most of the town. If you accept a 10% margin of error instead, you need 92 responses and 460 invitations, which is far easier to reach.

How population and margin of error change the answer

Both tables use 95% confidence and an expected result of 50%. The first shows that population size stops mattering once the group is large.

The second shows the cost of precision for a very large population. Each time you tighten the margin, the sample grows much faster than the margin shrinks.

How to use the result when you are testing a business idea

• Decide what the number is for. A survey is good for counting: what share of people have a problem, how often, what they pay today. It feeds your market research and your market size estimate in the TAM SAM SOM calculator.
• Talk to people first. A survey can only measure answers you already thought to ask about. Run a handful of customer interviews to learn the right questions, then use a survey to see how common each answer is. Interviews do not need a statistical sample. See how to validate a startup idea for the order to do things in.
• Pick a margin that matches the decision. If the choice is the same whether 30% or 40% of people have the problem, a 10% margin is enough and costs a quarter of the responses.
• Sample the right people. Responses must come from your target group, your ideal customer profile, and not from friends or whoever follows you online.
• Do not treat stated interest as sales. People who say they would buy often do not. Treat survey answers about future purchases as a ceiling, and check them with a real offer such as a pre-order page.

A survey is one input, not the whole test. In Fonda, the Validate phase covers Market, Key risks and Interviews, and you talk to real customers before you get a Verdict of go, refine or pivot. It is free to start.

What the calculator leaves out

• How you pick people. The formula assumes a simple random sample, where everyone in the group has the same chance of being asked. A link posted in one online community is not random, and the margin of error does not apply to it.
• Who chooses not to answer. If the people who reply differ from those who ignore you, the result is skewed however large the sample. A higher response rate reduces this risk.
• Subgroups. The sample covers one overall figure. If you want to compare groups, such as renters and owners, each group needs its own sample of the full size.
• Question type. The formula is for yes or no style questions reported as a percentage. Averages, such as mean monthly spend, use a different formula that needs an estimate of how spread out the answers are.
• Question quality. Leading or unclear questions produce wrong answers at any sample size.