PROPOSIA

Sample Size Calculator

Design statistically robust studies with confidence. Calculate sample sizes, estimate margins of error, and generate professional methodology narratives for your grant proposals.

5%
1% (Precise)20% (Rough)
50%

Use 50% if you are unsure (Industry Standard).

Proposal Snippet Generator
"This study establishes a sample size of 385 participants to ensure statistical validity. Based on a confidence level of 95% and an estimated population proportion of 50%, this sample size yields a margin of error of ±5.0%. This configuration ensures that the study results are representative of an infinite population within the specified reliability thresholds."

Required Sample Size

385

To achieve a margin of error of 5% with 95% confidence, you need 385 respondents.

Visual Analysis

Diminishing Returns Curve
Study Architect Analysis

🧠 How It Works

To be 95% sure of your data, you need 385 people to take your survey.

📉 The Math Explained

  • The "Why": This number balances your desired accuracy (±5.0%) with your confidence level.
  • The Assumption: We assumed the "worst-case" variance (50/50 split) to ensure your sample is large enough for any question.

⚖️ Trade-offs

Precision is expensive. If you relaxed your error margin to ±6.0%, you would save 118 responses.

✨ Recommendation

If 385 is over budget, consider lowering your Confidence Level to 90%.

Methodology & Technical Reference

Primary Formula (Infinite Population)

This calculator uses Cochran's Formula to determine the sample size needed to estimate a population proportion with a specific margin of error and confidence level.

n₀ = (Z² × p × (1-p)) / e²
  • Z: Z-score (e.g., 1.96 for 95% confidence).
  • p: Population proportion (assumed 0.5 for max variance).
  • e: Margin of Error (e.g., 0.05 for ±5%).

Finite Population Correction

When the population size (N) is known and small relative to the sample, a Finite Population Correction (FPC) is applied to reduce the required sample size.

n = n₀ / (1 + (n₀ - 1) / N)
Note on Power Analysis: This tool calculates sample sizes for descriptive statistics (Confidence Intervals). It is distinct from Power Analysis, which is used to calculate sample sizes for hypothesis testing.

About this material

The Sample Size Calculator is a professional-grade tool designed to help researchers determine the optimal sample size for their quantitative studies. Whether you are conducting a clinical trial, a social science survey, or market research, ensuring statistical validity is crucial for funding success. This calculator uses Cochran's Formula with optional Finite Population Correction to provide precise estimates for confidence intervals and margins of error.

Robust methodology sections are a key requirement for major funding bodies like the NIH, NSF, and European Research Council (ERC). Use this tool to generate defensible sample size justifications for your grant proposal template. After designing your study, you can use our Budget Calculator to estimate recruitment costs, or the Gantt Chart Creator to plan your data collection timeline. For qualitative aspects of your proposal, explore our Citation Converter to manage your bibliography.