Confidence Interval Calculator

Calculate confidence intervals for a sample mean or proportion using either raw data or summary statistics

Example Results

2 examples

Estimate a mean confidence interval from raw data

Provide a sample dataset and use the t critical value to estimate the range for the true mean

{
  "result": {
    "center": 50.5,
    "lowerBound": 48.6888,
    "upperBound": 52.3112,
    "marginOfError": 1.8112,
    "criticalValue": 2.3646
  }
}
View input parameters
{ "intervalType": "mean", "numbersInput": "48, 52, 47, 50, 53, 49, 51, 54", "meanInput": "", "standardDeviationInput": "", "sampleSize": 0, "successCount": "", "trialCount": "", "confidenceLevel": "0.95", "precision": 4 }

Estimate a proportion confidence interval

Use successes and total trials to compute a confidence interval for a conversion rate or pass rate

{
  "result": {
    "proportion": 0.7,
    "lowerBound": 0.5998,
    "upperBound": 0.8002,
    "marginOfError": 0.1002,
    "criticalValue": 1.96
  }
}
View input parameters
{ "intervalType": "proportion", "numbersInput": "", "meanInput": "", "standardDeviationInput": "", "sampleSize": 0, "successCount": "56", "trialCount": "80", "confidenceLevel": "0.95", "precision": 4 }

Key Facts

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

Overview

The Confidence Interval Calculator allows you to estimate the range for a population mean or proportion based on your sample data. Whether you have raw datasets or pre-calculated summary statistics, this tool provides precise margin of error and boundary calculations to support your statistical analysis.

When to Use

  • •When you need to estimate a population parameter from a sample mean or proportion.
  • •When you want to determine the margin of error for a survey or experiment result.
  • •When you need to validate findings using specific confidence levels like 95% or 99%.

How It Works

  • •Select the interval type: choose 'Mean' for numerical averages or 'Proportion' for percentage-based data.
  • •Input your data: paste raw numbers directly or enter summary statistics like mean, standard deviation, and sample size.
  • •Configure settings: select your desired confidence level and set the decimal precision for the output.
  • •Calculate: click to generate the lower and upper bounds, margin of error, and critical value.

Use Cases

Analyzing A/B test conversion rates to determine if the results are statistically significant.
Estimating the average response time of a system based on a sample of server logs.
Calculating the reliability of survey results by determining the margin of error for a specific sample size.

Examples

1. Mean Interval from Raw Data

Data Analyst
Background
An analyst has a set of 8 performance test results and needs to find the range for the true mean performance.
Problem
Calculate the 95% confidence interval for the mean of the provided dataset.
How to Use
Select 'Mean', paste the numbers into the dataset field, set confidence level to 95%, and calculate.
Example Config
intervalType: mean, numbersInput: 48, 52, 47, 50, 53, 49, 51, 54, confidenceLevel: 0.95
Outcome
The tool provides a 95% confidence interval with a margin of error of 1.8112, estimating the true mean between 48.6888 and 52.3112.

2. Proportion Interval for Conversion Rate

Marketing Manager
Background
A marketing campaign resulted in 56 conversions out of 80 total clicks.
Problem
Determine the 95% confidence interval for the conversion rate to understand the campaign's reliability.
How to Use
Select 'Proportion', enter 56 as success count and 80 as trial count, then calculate.
Example Config
intervalType: proportion, successCount: 56, trialCount: 80, confidenceLevel: 0.95
Outcome
The tool calculates a 70% conversion rate with a 95% confidence interval ranging from 59.98% to 80.02%.

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FAQ

What is a confidence interval?

It is a range of values derived from sample data that is likely to contain the true population parameter with a specified level of confidence.

Can I use this tool with raw data?

Yes, you can paste raw numbers separated by commas, spaces, or new lines into the dataset field for mean calculations.

What confidence levels are supported?

The tool supports common confidence levels including 80%, 85%, 90%, 95%, 98%, and 99%.

How do I calculate a proportion interval?

Select 'Proportion' as the interval type and enter the number of successes and the total number of trials.

What does the margin of error represent?

It represents the range above and below the sample statistic, indicating the potential deviation from the true population value.

API Documentation

Request Endpoint

POST /en/api/tools/confidence-interval-calculator

Request Parameters

Parameter Name Type Required Description
intervalType select No -
numbersInput textarea No -
meanInput text No -
standardDeviationInput text No -
sampleSize number No -
successCount text No -
trialCount text No -
confidenceLevel select 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-confidence-interval-calculator": {
      "name": "confidence-interval-calculator",
      "description": "Calculate confidence intervals for a sample mean or proportion using either raw data or summary statistics",
      "baseUrl": "https://elysiatools.com/mcp/sse?toolId=confidence-interval-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]