Sample Size Calculator
Calculate the required sample size for your survey or study with this free online calculator. Find the right sample size for your desired confidence level and margin of error.
Sample Size Calculator
Find out the sample size required for your survey or study based on confidence level, margin of error, and population proportion.
Result
Required Sample Size: ?
This is the minimum sample size needed for your specified parameters.
Sample Size Formula
\(n = \frac{z^2 \times p \times (1-p)}{e^2}\)
Where:
\(n\) = Sample size
\(z\) = Z-score for the confidence level
\(p\) = Population proportion (0.5 if unknown)
\(e\) = Margin of error
For finite population: \(n_{adjusted} = \frac{n}{1 + \frac{n-1}{N}}\)
Example
For a 95% confidence level, 5% margin of error, and 50% population proportion:
- Z-score for 95% confidence = 1.96
- Sample size = (1.96² × 0.5 × 0.5) ÷ 0.05² = 384.16
- Rounded up: 385 respondents needed
Margin of Error Calculator
Calculate the margin of error for your survey or study based on sample size, confidence level, and population proportion.
Result
Margin of Error: ?
This is the margin of error for your specified parameters.
Margin of Error Formula
\(e = z \times \sqrt{\frac{p \times (1-p)}{n}}\)
Where:
\(e\) = Margin of error
\(z\) = Z-score for the confidence level
\(p\) = Population proportion (0.5 if unknown)
\(n\) = Sample size
About Sample Size
Sample size is a critical component of any research study or survey. It determines how many subjects or respondents you need to include in your study to get results that reflect the target population as precisely as needed.
Why Sample Size Matters
- Statistical Power: Larger sample sizes provide more statistical power, making it easier to detect effects.
- Precision: Larger samples typically yield more precise estimates with narrower confidence intervals.
- Representativeness: Adequate sample sizes help ensure your sample represents the population.
- Resource Efficiency: Calculating the right sample size helps avoid wasting resources on unnecessarily large samples.
Key Concepts
- Confidence Level: The probability that your sample accurately reflects the population within your margin of error. Common confidence levels are 90%, 95%, and 99%.
- Margin of Error: The amount of error you're willing to accept in your results, typically expressed as a percentage (e.g., ±5%).
- Population Proportion: The expected proportion of the population that has the attribute you're measuring. If unknown, 50% (0.5) is used as it provides the most conservative estimate.
- Population Size: The total size of the population from which you're drawing your sample. For large populations, this has minimal impact on the required sample size.
Z-scores for Common Confidence Levels
- 90% Confidence: Z = 1.645
- 95% Confidence: Z = 1.96
- 99% Confidence: Z = 2.576
Applications
- Market Research: Determining how many consumers to survey.
- Medical Studies: Calculating the number of patients needed for clinical trials.
- Quality Control: Deciding how many products to inspect.
- Political Polling: Figuring out how many voters to poll for accurate election predictions.
- Academic Research: Planning appropriate sample sizes for research studies.