Confidence Interval for a Proportion Calculator

Parameters

Sample Size (n)

Successes (x)

Confidence Level

80% 85% 90% 95% 98% 99% 99.9%

Decimal Places

2 3 4 5 6

Continuity Correction

None Yates' Correction

Method

Results

Enter parameters and click Calculate to see results.

Confidence Interval

—

Sample Proportion (p̂)

—

Margin of Error

—

Method

—

z* Score

—

Std. Error

—

n Check

—

p̂ — —

How This Was Calculated

Guide

Confidence Interval for a Proportion estimates the range that likely contains the true population proportion based on sample data. Enter your sample size (n) and number of successes (x), choose a confidence level and method, then click Calculate. The tool shows the interval, margin of error, and step-by-step workings.

Facts

• The Wald interval is the classic formula but performs poorly for small samples or proportions near 0 or 1.
• The Wilson interval is more accurate and recommended for most applications.
• Agresti–Coull adjusts Wald by adding two successes and two failures.
• Clopper–Pearson (exact) guarantees at least the nominal coverage but can be conservative.
• Continuity correction improves normal approximation for discrete data.

Tips

• Use Wilson by default — it balances accuracy and simplicity.
• Check the n check badge: both np̂ and n(1−p̂) should be ≥ 10 for Wald.
• For rare events (p̂ < 0.1 or p̂ > 0.9), prefer Wilson or Clopper–Pearson.
• Export results as JSON for reporting or further analysis.

Use Cases

• Market Research — estimating customer satisfaction rates.
• Clinical Trials — proportion of patients responding to treatment.
• Quality Control — defect rate in a production batch.
• Political Polling — support percentage for a candidate.
• A/B Testing — conversion rate confidence intervals.

About

This tool computes confidence intervals for a population proportion using four widely adopted statistical methods. It is designed for researchers, analysts, students, and professionals who need fast, accurate, and well-documented interval estimates. Built with pure JavaScript — no external libraries required for computation.

Examples

• Example 1: n=100, x=40, 95% Wilson → CI ≈ (0.307, 0.499)
• Example 2: n=500, x=350, 99% Wald → CI ≈ (0.656, 0.744)
• Example 3: n=30, x=2, 95% Clopper–Pearson → CI ≈ (0.008, 0.202)
• Example 4: n=2000, x=1600, 90% Agresti–Coull → CI ≈ (0.786, 0.814)

Feature	Details
Price	Free
Rendering	Client-Side Rendering
Language	JavaScript
Paywall	No

Open This Tool

Checkout More Maths Tools!

Advertise here

About This Tool

How It Works?