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.

Confidence Level

Margin of Error5%

1% (Precise)20% (Rough)

Population Proportion50%

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

Population Size (Optional)

Proposal Snippet Generator

"We propose a target recruitment of 385 respondents. This sample volume is calculated to achieve a precision of ±5.0% at the 95% confidence level. By securing this number of completed surveys, the project minimizes the risk of sampling bias and ensures actionable data for decision-making regarding the target population."

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

🚀 Executive Summary

Requirement: Recruit 385 participants.

📊 Key Metrics

Confidence Level: 95%
Precision: ±5.0% (Margin of Error)
Volume Risk: Low Volume

💡 Efficiency Opportunity

Accepting a slightly higher error margin of ±6.0% would reduce the target by 118 people.

✅ Action Item

Proceed with 385 subjects to ensure decision-making data stays within the ±5.0% reliability threshold.

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.