Calculate the minimum sample size needed for your survey or study. Find how many responses you need based on population size, margin of error, and confidence level. Free online sample size calculator with formula guide and real-world examples.
This calculator computes the minimum number of necessary samples to meet the desired statistical constraints.
Use 50% if not sure
Leave blank if unlimited population size.
Imagine you're making a giant pot of soup. You don't need to eat the whole pot to know if it's salty enough. You just take a spoonful. That spoonful is your sample.
The whole pot is your population - everyone you want to learn about.
A sample size is just the number of people (or things) you actually survey. The goal is to pick a sample that's big enough to represent the whole population accurately.
Too small? Your results might be random noise. Too big? You're wasting time and money.
Our calculator finds the sweet spot.
Using the calculator is pretty straightforward. You just need to know four things:
Say you run a small coffee shop with 500 regular customers. You want to know how satisfied they are with your new latte recipe.
Here's what you'd put in the calculator:
Hit calculate. The calculator says you need about 217 responses. That means if you survey 217 customers, you can be 95% confident that your results are within 5% of what you'd get if you surveyed all 500.
Here's the formula the calculator uses:
n = (ZĀ² Ć p Ć (1-p)) / EĀ²
Looks scary, right? But it's just a bunch of letters. Let's translate:
So for our coffee shop example:
n = (1.96Ā² Ć 0.5 Ć 0.5) / 0.05Ā²
That gives you about 384. But wait - that's for an infinite population. Since your population is only 500, the calculator adjusts it down to 217. That adjustment is called the finite population correction. It's a fancy way of saying "if your population is small, you don't need as big a sample."
This is the wiggle room in your results. A 5% margin of error means if 60% of your sample likes the new latte, the true number in the population is probably between 55% and 65%. For most surveys, 5% is fine. If you need more precision (like for a medical study), go with 3% or even 1%. But remember - smaller margin of error means bigger sample size.
This is how sure you want to be. 95% is the standard. It means if you ran your survey 100 times, 95 of them would give you results within your margin of error. 99% is more conservative but requires a much larger sample. For most projects, 95% is plenty.
This is your best guess for the answer. If you're asking a yes/no question and you have no idea, use 50%. That gives you the biggest (safest) sample size. But if you have a hunch - like "I think 80% of customers like the new recipe" - you can use 80%. That'll give you a smaller sample size. Just be careful - if your guess is wrong, your results might be less accurate.
Pollsters use sample sizes all the time. A national poll of 1,000 people can predict a presidential election with a 3% margin of error. That's because the population is huge, but the sample size doesn't need to be.
When testing a new drug, researchers need a sample size big enough to detect a real effect. They often use a 1% margin of error and a 99% confidence level. That's why clinical trials can have thousands of participants.
For a science fair project, you don't need a huge sample. A 10% margin of error and 90% confidence level might be fine. Just be honest about your limitations.
Here are the biggest mistakes people make with sample size calculators:
Mistake 1: Using the Wrong Population Size. Your population is the group you want to learn about. Not the whole world. If you're surveying your school, the population is the number of students, not the number of people in your city.
Mistake 2: Forgetting the Finite Population Correction. If your population is small (under 10,000), the calculator adjusts your sample size down. That's good. But some people ignore this and use the infinite population formula. That gives a sample size that's too big.
Mistake 3: Using 50% Proportion When You Know Better. If you have a good guess for the population proportion, use it. It'll save you time and money. But if you're wrong, your results might be off.
Mistake 4: Ignoring Non-Response. The calculator tells you how many responses you need. But not everyone will respond. If you expect a 50% response rate, you need to survey twice as many people.
If your population has different groups (like men and women, or different age groups), you might want to sample each group separately. That's called stratified sampling. It can give you more accurate results with a smaller overall sample.
Sometimes it's easier to sample groups (clusters) instead of individuals. For example, if you're surveying schools, you might pick a few schools and survey everyone in them. That's cluster sampling.
The sample size formula was developed by statisticians in the early 20th century. It's based on the central limit theorem, which says that if you take enough random samples, their averages will form a normal distribution. That's why the formula works.
If your population is tiny (under 100), just survey everyone. It's called a census. No calculator needed.
If your population is huge (over 100,000), the sample size doesn't change much. For a 5% margin of error and 95% confidence, you need about 384 responses. That's true whether your population is 100,000 or 100 million.
Problem: My sample size is bigger than my population.
Solution: That means you need to survey more people than exist. Either lower your confidence level or increase your margin of error. Or just survey everyone (a census).
Problem: I'm getting different results from different calculators.
Solution: Some calculators use different formulas or assumptions. Ours uses the standard formula with a finite population correction. If you're comparing results, make sure you're using the same inputs.
Problem: My sample size seems too small.
Solution: That's normal. A sample of 384 can represent a population of 100,000 with a 5% margin of error. Trust the math.
The sample size formula is used in everything from election predictions to quality control in factories. Without it, we'd have to survey everyone for everything. That would be impossible.
So next time you see a poll that says "margin of error Ā±3%," you'll know someone used a sample size calculator to figure out how many people to ask.
For most surveys, a sample size of 384 is good if your population is large (over 100,000) and you want a 5% margin of error at 95% confidence. For smaller populations, the sample size will be smaller. The key is to balance accuracy with practicality.
If you don't know your population size, just leave it blank or use a very large number (like 1,000,000). The calculator will use the infinite population formula. Just use 50% for the population proportion to get the safest sample size.
For most surveys, 5% is standard. For more precision (like medical studies), use 3% or 1%. For school projects or informal surveys, 10% might be fine. Remember: smaller margin of error = larger sample size.
95% is the standard for most research. Use 99% if you need to be very sure (like for legal or medical decisions). Use 90% for exploratory or informal surveys. Higher confidence = larger sample size.
The population proportion affects the variability in your data. A proportion of 50% gives the most variability, so it requires the largest sample. If you have a good guess (like 80%), you can use that to get a smaller sample.