Sample Size Calculator
Confidence Level
5.0%
Required Sample Size385
Before running a survey you need to know how many responses make the results trustworthy. This calculator applies Cochran’s formula to find the minimum sample size for a chosen confidence level and margin of error, then applies a finite population correction when you supply the total population. It assumes maximum variability (p = 0.5) for a conservative, worst-case estimate.
Formula
n0 = z² × 0.25 / e² ; with population N: n = ceil( n0 / (1 + (n0 − 1) / N) )
- z
- Z-value for the confidence level (90% = 1.645, 95% = 1.96, 99% = 2.576)
- e
- Margin of error as a proportion (5% becomes 0.05)
- 0.25
- Maximum variability p(1−p) at p = 0.5, the most conservative assumption
- N
- Total population size (omit for an effectively infinite population)
- n
- Required sample size, rounded up to the next whole respondent
How it works
- Select a confidence level — 90%, 95%, or 99% — which sets the z-value (1.645, 1.96, or 2.576 respectively).
- Enter the margin of error as a percentage (for example 5 for ±5%); the calculator divides it by 100 internally.
- Optionally enter the total population size. With no population, the infinite-population formula is used; with one, the result is reduced by the finite population correction. The required sample size is always rounded up to a whole number.
Worked examples
How many people must you survey for 95% confidence and a ±5% margin of error, with no population limit?
- z = 1.96 for 95% confidence; e = 0.05.
- n0 = 1.96² × 0.25 / 0.05² = 3.8416 × 0.25 / 0.0025 = 384.16.
- Round up to the next whole respondent.
Required sample size ≈ 385
Same 95% confidence and ±5% margin, but for a finite population of 1,000 people.
- Start from n0 = 384.16 as above.
- Apply the correction: 384.16 / (1 + (384.16 − 1) / 1000) = 384.16 / 1.38316 ≈ 277.8.
- Round up to the next whole respondent.
Required sample size ≈ 278
Frequently asked questions
- Why does the formula assume p = 0.5?
- The variability term p(1−p) is largest at p = 0.5, where it equals 0.25. Using that value gives the most conservative (largest) sample size, so your survey stays valid no matter how the responses actually split.
- What does the finite population correction do?
- When you survey a closed group, you do not need as many responses as for an unlimited population. Supplying the population size shrinks the required sample — for a population of 1,000 the ±5%/95% requirement drops from 385 to 278.
- Which confidence levels are supported?
- This calculator supports 90%, 95%, and 99% confidence, mapped to z-values of 1.645, 1.96, and 2.576. The 95% level is the most common default in market research and academic surveys.
- How is margin of error different from confidence level?
- The margin of error is how far your sample result may sit from the true value (the ± band), while the confidence level is how often that band would contain the true value over repeated samples. Tightening either one raises the required sample size.