Sample Size Calculator
Choose a confidence level and margin of error to calculate the minimum sample size needed for a survey or study.
Last updated: September 5, 2026
Frequently asked questions
How is sample size calculated?
n = (z² × p × (1−p)) / e², where z is the z-score for your confidence level, p is the estimated proportion (50% is the most conservative/largest assumption if unknown), and e is your margin of error as a decimal. Higher confidence and lower margin of error both increase the required sample size.
Why use 50% for the estimated proportion if I don't know it?
50% produces the largest possible required sample size (p×(1−p) is maximized at p=0.5), so it's the safe, conservative default when you have no prior estimate - using it guarantees your sample is large enough regardless of the true proportion.
How does population size affect the required sample size?
For very large or unknown populations, sample size depends only on confidence level and margin of error, not population size. For a known, finite population, the finite population correction reduces the required sample size somewhat, since sampling a larger fraction of a smaller population reduces uncertainty faster.
Is 'calculating sample size online' or 'determine sample size calculator' the same as this tool?
Yes - all of these describe finding the minimum sample size needed for a survey or study at a chosen confidence level and margin of error, which is exactly what this calculator does.
How much does doubling the margin of error change the required sample size?
It cuts the required sample size to roughly a quarter, since sample size is inversely proportional to the square of the margin of error (n ∝ 1/e²) - halving your desired margin of error, conversely, roughly quadruples the sample you need.
What sample size is needed for a 95% confidence level and 5% margin of error with an unknown proportion?
About 385 - using n = (1.96² × 0.5 × 0.5) / 0.05² = 0.9604 / 0.0025 ≈ 384.16, rounded up to 385, the commonly cited figure for a general population survey.
Why does the calculator ask for an estimated response proportion if I don't have survey results yet?
The proportion affects how much variability the formula assumes exists in responses - if you have a rough prior estimate (from past research or a pilot study), entering it can lower the required sample size compared to the conservative 50% default, since p×(1−p) is smaller the further p is from 0.5.