Dripping the Data

Sample Size Calculator

Home / Finance Toolkit / Sample Size Calculator
Probability & Research Calculators

Sample Size Calculator

Imagine you want to survey shoppers about a new product. You cannot ask every single person. This tool tells you exactly how many people you need to ask for trustworthy results.

Find sample size
Find margin of error
You need to survey 0
Confidence level
0%
Margin of error
0%
Proportion used
50%
Your confidence range on a bell curve
How sample size changes with confidence level
90% confidence0
95% confidence0
99% confidence0

What sample size actually means

You cannot always ask everyone a question. A whole city, a whole customer base, or a whole country is too big to survey one by one. So you ask a smaller group instead. Sample size is simply how many people that smaller group needs to be, so the answer you get is close to what you would have found by asking everyone.

n = (Z² × p × (1 − p)) ÷ e²
n is the sample size you need.
Z is a fixed number tied to your confidence level, such as 1.96 for 95%.
p is the proportion you expect, usually 0.5 when you are not sure.
e is your margin of error, written as a decimal.

If your population is small and known, one more step adjusts the number down. That step uses this formula.

nadjusted = n ÷ (1 + (n − 1) ÷ N)
N is your total population size. This step only matters when your population is small enough to count.
Example. A city wants to learn how residents feel about a new park. There are many residents, so asking everyone is not realistic. Using a 95% confidence level and a 5% margin of error, the survey needs about 385 responses. That means the results will very likely match the true opinion of all residents, within 5 percentage points.

Two ideas worth understanding well

Confidence level

This is how sure you want to be that your results are correct. Think of it like a weather forecast. A 95% confidence level means that if you ran this survey 100 times, about 95 of those times the true answer would fall inside your result.

Margin of error

This is how much wiggle room your result has. If 60% of people say yes with a 5% margin of error, the true number is likely somewhere between 55% and 65%.

Why a smaller margin of error needs more people

A tighter margin of error means less room for guessing, so more responses are needed to earn that precision. Going from a 5% margin to a 3% margin can nearly triple your required sample size. This is one of the most common surprises people run into when planning a survey.

Frequently asked questions

What proportion should I use if I do not know it?

Use 50%. It gives the largest, safest sample size, since this is the point where results are hardest to predict in advance.

Why does population size sometimes barely change the result?

Once a population is large enough, adding more people to it barely affects the sample size you need. That is why surveys for a city and a whole country can need a similar number of responses.

Can a sample size be too big?

Yes, in a practical sense. A larger sample costs more time and money, even if the accuracy gained becomes smaller and smaller past a certain point.

Does this work for any kind of survey?

This formula fits simple random surveys asking yes or no style questions. Studies with more complex designs may need extra adjustments beyond this tool.

Keep exploring your data with more free tools.

Try one of these calculators next.

Basic Probability Calculator Mean, Median, Mode, & Range Calculator Standard Deviation & Variance Calculator Back to Toolkit