Quantitative Sample Size Calculator UX
Calculate the sample size needed for your UX research study
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Quantitative Sample Size Calculator UX
Calculate sample size for surveys, usability testing and card sorting with academically validated formulas
Cochran's Formula: Finite Population
Cochran's formula is the statistical standard for calculating sample size when you know the exact size of your population. It includes a finite population correction factor (FPC) that reduces the required sample, optimizing resources without losing precision.
n = (N * Z^2 * p * q) / ((N-1) * E^2 + Z^2 * p * q)When to use this formula?
- You know the exact size of your population (employees, registered users, clients)
- The population is less than 100,000 individuals
- Your sample represents more than 5% of the total population (5% rule)
- You need statistical rigor for publications or critical decisions
Parameters
- N
- Total population size
- Z
- Z-value for confidence level (1.96 for 95%)
- p
- Expected proportion (0.5 if unknown)
- q
- 1 - p (complement of the proportion)
- E
- Acceptable margin of error (e.g., 0.05 for +/-5%)
Practical example
You have 2,000 registered users and want to survey them with 95% confidence and +/-5% margin of error.
With Cochran's formula: n = (2,000 * 3.84 * 0.25) / (1,999 * 0.0025 + 3.84 * 0.25) = 323 participants. Without the finite correction you'd need 385.
Simplified Formula: Infinite Population
When the population is unknown or exceeds 100,000 individuals, the finite correction factor has less than 1% impact. In these cases, the simplified formula is used, which does not require knowing the population size.
n = (Z^2 * p * q) / E^2When to use this formula?
- You don't know the exact size of your population
- The population exceeds 100,000 individuals
- Your sample represents less than 5% of the total population
- Market research with broad or public audiences
Parameters
- Z
- Z-value for confidence level (1.96 for 95%)
- p
- Expected proportion (0.5 if unknown)
- q
- 1 - p (complement of the proportion)
- E
- Acceptable margin of error (e.g., 0.05 for +/-5%)
Practical example
You want to survey users of an app with millions of downloads, with 95% confidence and +/-5% margin.
With the simplified formula: n = (3.84 * 0.25) / 0.0025 = 385 participants. This result is independent of the population size.
When to use each formula?
The choice between finite and infinite formula depends on two factors: whether you know your population size and what proportion of it your sample will represent.
- Do you know the exact size of your population? If not -> use the infinite formula.
- Does the population exceed 100,000? If yes -> use the infinite formula (the result is practically identical).
- Will your sample be more than 5% of the population? If yes -> use the finite formula (Cochran) to optimize resources.
- When in doubt -> use the infinite formula. It always gives an equal or larger sample, which is more conservative.
Quick comparison
| Criterion | Finite Population | Infinite Population |
|---|---|---|
| Known population | Yes, required | Not necessary |
| Population size | < 100,000 | > 100,000 or unknown |
| Sample vs population | > 5% of population | < 5% of population |
| Correction factor | Yes (reduces sample) | Not applicable |
| Typical result | Smaller sample (optimized) | Conservative sample |
| Use case | Companies, closed communities | General market, mass apps |
Detailed Guides by Methodology
Learn more about each methodology with examples, benchmarks, and best practices