Mr Calcu | Find the right number of survey responses to gain accurate insights and make smarter decisions—fast, easy, and statistically sound.
Quickly calculate your ideal survey sample size. Boost accuracy and build trust with this easy-to-use tool designed for confident decision-making.
Survey Sample Size Calculator Description
Why Sample Size Matters
- Ensures accurate and reliable survey results
- Balances statistical rigor with time and budget constraints
- Prevents over- or under-sampling
How the Calculator Works
Sample Size Formula
n = (Z^2 * p * (1 - p)) / E^2
Where:
- n: required sample size
- Z: Z-score (e.g., 1.96 for 95% confidence)
- p: estimated population proportion (default: 0.5)
- E: margin of error (as a decimal, e.g., 0.05 for 5%)
Finite Population Correction (FPC)
If your total population (N) is small, use:
n_adj = n / (1 + (n - 1) / N)
- This adjusts the sample size downward to avoid oversampling
Pro Tip: If you expect a low response rate, increase your sample size by dividing by the expected response rate.
Real-World Examples
Example 1: City Council Survey
- Population: 10,000
- Confidence Level: 95%
- Margin of Error: 5%
- Estimated p: 0.5 (no prior knowledge)
Calculation:
n = (1.96^2 * 0.5 * 0.5) / 0.05^2
n_adj = 384.16 / (1 + (384.16 - 1)/10000) ≈ 370
Final Sample Size: 370 participants
Example 2: Niche Market Research
- Population: 800
- Confidence Level: 99%
- Margin of Error: 3%
- Estimated p: 0.5
Calculation:
Z = 2.576, E = 0.03
n = (2.576^2 * 0.5 * 0.5) / 0.03^2 ≈ 1842.67
n_adj = 1842.67 / (1 + (1842.67 - 1)/800) ≈ 292
Final Sample Size: 292 participants
Edge Case Considerations
- Small Populations: Always apply FPC when N < 10,000.
- High Confidence Levels: 99%+ levels require significantly larger samples.
- Rare Outcomes: Adjust p accordingly (e.g., 0.1 or 0.01).
- Non-Response Rates: Multiply your sample size to compensate for low response rates.
- Cluster Sampling: Multiply sample size by the design effect (e.g., 1.5 to 2.0).
Take control of your survey success—use this calculator now to build confidence in every response you collect.