Sample Size Calculator
Instantly calculate the ideal sample size for your survey. Ensure statistically significant results by balancing your population, confidence level, and margin of error with our precision tool.
Updated December 2025
Calculator
● LIVELeave blank if unknown or > 20k.
Required Sample Size
385
Units needed for 95% Confidence
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Sample Size vs. ErrorCost of Precision
Sample Size
n = 385
Margin of Error (%)
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Exponential Cost: Notice how the curve shoots up as you move left. Halving your Margin of Error (e.g., 10% to 5%) often requires quadrupling your sample size.
The Science of Sampling
Why do we only need 385 people to represent millions? Understanding the Law of Large Numbers.
The Law of Large Numbers
If you take a small sample, luck plays a huge role. If you take a large sample, patterns emerge. Below is a "Population" of 200 marbles (50% Teal, 50% Grey).
Teal Found: 50%
Error: 0%
Click a button to start sampling.
The Three Variables
To calculate a sample size, you need to make three assumptions. Here is what they actually mean.
Confidence Level
"How sure do I need to be?"
95% is the industry standard. It means if you repeated the survey 20 times, the results would match reality 19 times.
Margin of Error
"How much wiggle room?"
Also called the Confidence Interval. If you get 48% with a +/-5% error, the truth is somewhere between 43% and 53%.
Population Size
"Who are we measuring?"
Unless your population is very small (under 5,000 people), the math barely changes. 100k people and 100M people require almost the same sample size.
The Population Paradox
Common logic suggests you need to sample 10% of your population. Statistics disagrees. Watch how the required sample size (yellow line) hits a "ceiling," even as the population grows massively.
Small Population: To represent 100 people accurately, you need to survey 80% of them.
The Magic Number
385
The maximum units needed for any infinite population at 95% Confidence.
Cochran's Formula
Why 385? It comes from the "Worst Case Scenario" assumption (50% Proportion) in this formula:
n=
Z2 • p(1-p) e2
Z
Z-Score (1.96 for 95%)
e
Margin of Error (0.05)
Common Questions
Clarifying Sample Sizes
Why do I use 50% for the Proportion?
50% is the most conservative estimate (the "Worst Case Scenario"). It requires the largest sample size. If you don't know what your results will be, assuming 50% ensures your sample is big enough to handle any outcome.
Example: It is harder to predict a coin flip (50/50) than a sunrise (100% chance). Uncertainty requires more data.
Example: It is harder to predict a coin flip (50/50) than a sunrise (100% chance). Uncertainty requires more data.
Does a larger population need a larger sample?
Surprisingly, No (mostly). Once your population exceeds ~20,000, the sample size stops growing. This is why a poll of 1,000 people can accurately predict the opinion of 300 Million Americans.
Think of it like a soup. Once you've stirred the pot well, one spoonful tastes the same whether the pot is 1 gallon or 100 gallons.
Think of it like a soup. Once you've stirred the pot well, one spoonful tastes the same whether the pot is 1 gallon or 100 gallons.
What happens if my sample is too small?
Your Margin of Error increases drastically. If you need 385 people but only ask 50, your Margin of Error jumps from ±5% to roughly ±14%. Your results become statistically meaningless noise.
Verified Expert
Disclaimer: This tool is for informational and educational purposes only. Calculations are based on standard formulas but may not account for unique business variables. We do not accept liability for decisions made based on these results.