Sample Size Calculator

Estimate required sample size for proportions or means using confidence level, margin of error, and optional finite population correction

Example Results

2 examples

Estimate survey sample size for a proportion

Compute the required sample size for a 95% confidence survey with a 5% margin of error using a conservative 50% proportion

{
  "result": {
    "recommendedSampleSize": 385,
    "infinitePopulationSampleSize": 384.16,
    "zCriticalValue": 1.96
  }
}
View input parameters
{ "calculatorMode": "proportion", "confidenceLevel": "0.95", "marginOfError": "0.05", "estimatedProportion": "0.5", "estimatedStandardDeviation": "1", "populationSize": "", "precision": 2 }

Adjust sample size for a finite population

Apply finite population correction when the total population is known and relatively small

{
  "result": {
    "recommendedSampleSize": 125,
    "infinitePopulationSampleSize": 138.3,
    "finitePopulationAdjustedSampleSize": 124.64
  }
}
View input parameters
{ "calculatorMode": "mean", "confidenceLevel": "0.95", "marginOfError": "2", "estimatedProportion": "0.5", "estimatedStandardDeviation": "12", "populationSize": "500", "precision": 2 }

Key Facts

Category
Math, Date & Finance
Input Types
select, text, number
Output Type
json
Sample Coverage
4
API Ready
Yes

Overview

The Sample Size Calculator helps you determine the statistically significant number of participants needed for your research, surveys, or experiments. By inputting your desired confidence level and margin of error, you can ensure your data collection is robust and reliable.

When to Use

  • •Before launching a survey to ensure your results are representative of the target population.
  • •When planning a scientific experiment to determine the minimum number of subjects required for valid conclusions.
  • •When you need to adjust your sample size based on a known, finite population size to avoid over-sampling.

How It Works

  • •Select your calculation mode: choose 'Proportion' for categorical data or 'Mean' for continuous numerical data.
  • •Input your target confidence level (e.g., 95%) and the acceptable margin of error.
  • •Provide optional parameters like estimated standard deviation or total population size for more precise results.
  • •Click calculate to receive the recommended sample size based on statistical formulas.

Use Cases

Market researchers determining the number of customers to survey for a new product launch.
Academic researchers calculating the required participants for a clinical study or behavioral experiment.
Quality control teams estimating the number of units to inspect from a production batch.

Examples

1. General Survey Planning

Market Researcher
Background
Planning a customer satisfaction survey for a large user base.
Problem
Needs to know how many users to contact to achieve a 95% confidence level with a 5% margin of error.
How to Use
Set mode to 'Proportion', confidence level to 95%, and margin of error to 0.05.
Example Config
calculatorMode: proportion, confidenceLevel: 0.95, marginOfError: 0.05
Outcome
The tool recommends a sample size of 385 participants.

2. Finite Population Study

Operations Manager
Background
Auditing a specific batch of 500 manufactured parts.
Problem
Needs to determine the sample size for an inspection with a 2-unit margin of error.
How to Use
Set mode to 'Mean', confidence level to 95%, margin of error to 2, and population size to 500.
Example Config
calculatorMode: mean, confidenceLevel: 0.95, marginOfError: 2, populationSize: 500
Outcome
The tool provides an adjusted sample size of 125 units, accounting for the finite population.

Try with Samples

barcode
Nginx Log Parser Samples
Comprehensive Nginx log samples for testing log-parser tool, including access logs and error logs with various formats and scenarios
task process
sample
ELK Stack Log Analysis Samples
Comprehensive ELK Stack (Elasticsearch, Logstash, Kibana) samples for log aggregation, processing, and visualization in distributed systems
task process
sample
Copyright-Free M4A Audio Samples
Apple iTunes compatible M4A audio samples with AAC encoding, optimized for quality and file size balance
keywords sample,size
sample
Server Logs Samples
Server log files with IP addresses for testing extraction
task process
sample

Related Hubs

Barcode, QR Code, and Label Tools
Compare barcode generation, QR code creation and decoding, UPC/EAN validation, WiFi QR sharing, and printable label tools in one hub.

FAQ

What is a confidence level?

It represents how certain you want to be that the true population parameter falls within your margin of error, typically set at 95%.

What is the margin of error?

It is the range of values above and below your sample result that you expect the true population value to fall within.

When should I use the finite population correction?

Use this when your total population is small and known, as it allows for a smaller sample size while maintaining the same level of accuracy.

What is the difference between Proportion and Mean modes?

Proportion mode is for binary outcomes (e.g., yes/no), while Mean mode is for measuring averages of continuous variables.

Why is the recommended sample size sometimes a decimal?

Calculations often result in fractions; always round up to the nearest whole number to ensure your sample size meets the minimum statistical requirement.

API Documentation

Request Endpoint

POST /en/api/tools/sample-size-calculator

Request Parameters

Parameter Name Type Required Description
calculatorMode select No -
confidenceLevel select No -
marginOfError text Yes -
estimatedProportion text No -
estimatedStandardDeviation text No -
populationSize text No -
precision number No -

Response Format

{
  "key": {...},
  "metadata": {
    "key": "value"
  },
  "error": "Error message (optional)",
  "message": "Notification message (optional)"
}
JSON Data: JSON Data

AI MCP Documentation

Add this tool to your MCP server configuration: 

{
  "mcpServers": {
    "elysiatools-sample-size-calculator": {
      "name": "sample-size-calculator",
      "description": "Estimate required sample size for proportions or means using confidence level, margin of error, and optional finite population correction",
      "baseUrl": "https://elysiatools.com/mcp/sse?toolId=sample-size-calculator",
      "command": "",
      "args": [],
      "env": {},
      "isActive": true,
      "type": "sse"
    }
  }
}

You can chain multiple tools, e.g.: `https://elysiatools.com/mcp/sse?toolId=png-to-webp,jpg-to-webp,gif-to-webp`, max 20 tools.

If you encounter any issues, please contact us at [email protected]