Sample Size Calculator for Survey Researchers

What is Sample Size?

Sample size is the total number of complete survey responses a project needs to produce statistically reliable results at a given confidence level and margin of error. Essentially, it’s the minimum number of people you need to gather insights from to represent your target population.

Note: This refers to the total number of completed survey responses, not just the number of people you invite to participate in the survey.

Now when calculating sample size, there are a few definitions and parameters to understand here.

Population Size

Your population size equals the total number of the group your survey results will be representing. For example, the state of California (39.36 million), Pacific Gas & Electric (PG&E) customers (16 million), or active members of the California Bar Association (202 thousand).

Population size is notated as N in the sample size formula.

Margin of Error

This refers to the “give or take” on your results. If 60% of people in your survey pick an option and your margin of error is 5%, that means the real number for your whole audience is probably 60% give or take 5%, so somewhere between 55% and 65%.

A smaller margin of error means a more exact answer, and getting it takes more responses. So your sample size takes potential outliers into account, ensuring you have a good representation of the group of people you’re trying to analyze.

Note that in the sample size formula, margin of error is represented by e.

Confidence Level

Confidence level is how sure you can be that the truth falls inside that “give or take” range. A 95% confidence level (the most common choice) means you can be 95% sure the real answer lands within your margin of error. The higher you set it, the more responses you need.

Alpha Level

The alpha level is how much risk you’re willing to take of seeing a result that looks real but is actually just chance. In most cases, 0.05 is the standard alpha level. However, alpha levels 0.01 and 0.1 are not uncommon.

If you don’t know which alpha level to choose, set alpha = 0.05. The confidence level will be 100 minus the alpha value. If the alpha is 0.05, the confidence level is 0.95 or 95%.

Population Proportion

The population proportion is your best guess at how the answers will split. If you expect about half your audience to say yes and half to say no, that’s a 50/50 split, written as 0.5.

When you have no idea how it’ll break, you still use 0.5. An even split is considered the “safest” guess because it asks for the most responses, so you’ll never come up short. If past research tells you the split is more lopsided (say, 80% one way), you can use that instead and you’ll need fewer responses.

In the sample size formula, proportion is represented by p.

Z-Scores

Z-score is a number that stands in for how sure you want to be. You don’t calculate this. Instead, you look it up based on your confidence level.

For example, if you pick 95% confidence, your corresponding z-score is 1.96. So that’s the number you drop into the formula. A higher confidence level gives you a bigger z-score, which is part of why being more certain requires more responses.

Note that z-scores are represented by z in the formula.

The table below gives you the z-score for each common confidence level, so you can find the one that matches your survey.

Confidence Level	Z-Score
90%	1.645
95%	1.96
98%	2.33
99%	2.575

Sample Size Formula

While you can always make things easy on yourself and just use the sample size calculator we’ve created for you, let’s go ahead and cover the sample size formula.

The formula for calculating sample size is as follows:

n₀ = ( z² × p ( 1 – p ) ) / e²

Once you’ve done that calculation, you’ll use this formula to get the final sample (only if you know your specific population size):

n = n₀ / (1 + (n₀ − 1) / N)

Note: n₀ refers to your base sample size and n refers to your final sample size.

So for a population size of 1,000, margin of error of 5%, and confidence level of 95%, you’d start with the first formula:

N = ( 1.96² × .5 (1 – .5) ) / .05² = 384.16, or 384 people

This is the standard sample size for a larger population, like the total population of the United States.

But because our population size is just 1,000, from there we’d do:

384 / (1 + (384 − 1) / 1,000) = 384 / 1.384

This gets us a a final sample size of 278 people.

 

Quick Reference Guide: Sample Size at 95% Confidence

The table below shows the completed responses needed at a 95% confidence level, for three common margins of error, across different population sizes (assuming p = 0.5, the most conservative estimate).

Population Size	±3% margin	±5% margin	±10% margin
500	341	218	81
5,000	880	357	95
50,000	1,045	382	96
500,000+	1,065	384	97

You’ll notice that as the population grows, the required sample barely moves. This is because sample size is driven more by how precise you want to be versus overall population size. And tightening precision is expensive: going from ±10% to ±3% at a large population multiplies the requirement by more than ten (97 to 1,065).

 

When the Formula Breaks Down

This formula helps answer one specific question: how many completes are needed for a given precision on a single population. But it doesn’t account for situations where you can’t actually obtain a random, representative sample of that population.

Here are three examples of when the formula might not paint the entire picture.

Small Populations and Subgroup Analysis

While the formula gives you a valid total, the situation changes if you need to compare subgroups.

For example, you need to reach 384 completes for a nationally representative sample. But if you’re looking at a subgroup that’s just 15% of the population, that might look like you need only 58 respondents, but that’s too small of a group for reliable conclusions.

To account for this, many published national studies will field 1,000-2,000 completes, even if the formula says they need just 384.

B2B and Niche Audiences

The formula also assumes the sample size exists in reachable numbers. For a narrow B2B audience, like IT decision-makers at mid-size manufacturers or a particular medical specialty, the statistically required sample may exceed the number of such people you can realistically reach and qualify.

The math might say 384, but feasibility says the qualified universe is small and expensive to access. Here the binding constraint isn’t statistics, it’s incidence and reach.

Low-Incidence Targets

When your target is a small fraction of the general population, there’s a lot of screening involved to find the right people. Reaching 384 qualified respondents at a 2% incidence could mean screening roughly 19,000 people.

This can quickly drive up costs and make the project take a long time just to get the number of completes you need. Something to keep in mind as you consider your next research study.

 

Why Sample Size Alone Isn’t Enough

Having a target number of completes will only get you so far. This assumes that every single response coming in is genuine and from a real member of your target group.

So there’s a secondary layer to this. You’ve calculated how many genuine, accurate responses you need. Now, you need to have the parameters in place to maximize those responses.

To do this, you need to consider factors like:

• Panel quality: Are your respondents actually who they say they are, and are they willing to provide you with authentic answers to your survey questions?
• Respondent verification: You (or your market research partner) need a way to verify respondents actually fit your audience, especially for B2B and specialist audiences.
• Data integrity: No matter your vetting process, not every complete will be real. Having a way to identify and remove those fraudulent completes ensures your final results only consist of real and valid responses.

While the calculator plays an important role in telling you how many responses you need, the next part is making sure you end up with that many verifiable responses to get accurate insights.

 

Get Help With Complex Sample Planning

Need help calculating sample for a complex B2B or healthcare study, or confirming whether your target audience is reachable at the precision you need? Our team can assess feasibility before you commit. Talk to us about your study.

 

Frequently Asked Questions

How do I calculate sample size?

Sample size is calculated in two steps. First, use the base formula n₀ = (z² × p (1 − p) ) / e², where z is the z-score for your confidence level (1.96 for 95%), p is your expected response split (use 0.5 if unknown), and e is your margin of error as a decimal (0.05 for ±5%). At those standard values, the base sample size is 384. Second, if your population is a known, limited size, apply the finite population correction n = n₀ / (1 + (n₀ − 1) / N) to trim that number down. For a population of 5,000, it lowers 384 to 357. Or skip the math and use the calculator above.

What sample size do I need for a survey?

It depends on how precise you want to be and how sure you want to be, not mainly on how big your audience is. For most surveys, a good starting point is 384 completed responses. That gives you 95% confidence with a give-or-take of 5% for a large audience. Want a tighter give-or-take? You’ll need more responses. Surveying a small, known group? You’ll need fewer. The calculator above gives you the exact number for your inputs.

What is margin of error?

Margin of error is the “give or take” on your results. If 60% of people in your survey pick an option and your margin of error is 5%, the real figure for your whole audience is probably 60% give or take 5, or somewhere between 55% and 65%. A smaller margin of error means a more exact answer, and getting it takes more responses.