Confidence Interval Calculator
Calculate confidence intervals for proportions with ease, including margin of error and confidence level adjustments.
📊 Calculation Results
🔍 What this tool does?
This Confidence Interval Calculator helps users determine the range within which a population proportion likely falls, based on a sample proportion, sample size, and confidence level. This is essential in statistics for estimating uncertainty and reliability of survey or experiment results.
⭐ Key Features
- Calculate confidence intervals for proportions accurately
- Select from common confidence levels (90%, 95%, 99%)
- Instant calculation and dynamic results display
- Copy results easily to clipboard
- Responsive design for all device types
⚙️ How to use?
- Enter the sample proportion as a decimal (e.g., 0.45) or percentage (45%).
- Input the sample size (must be a positive integer).
- Choose your confidence level from the dropdown.
- Click "Calculate" to view the confidence interval and margin of error.
- Use "Copy Result" to copy the output or "Reset Form" to clear inputs.
💡 Creative Use Cases:
📊 Market Research
Estimate customer satisfaction rates from survey data with statistical confidence.
🏥 Medical Studies
Calculate treatment success rates and their confidence intervals for clinical trials.
🗳️ Political Polling
Determine voting intention ranges and margin of error for election predictions.
📈 Quality Control
Monitor defect rates in manufacturing with confidence interval analysis.
✨ Tool Description
Our Confidence Interval Calculator uses the standard normal distribution (Z-distribution) to compute confidence intervals for population proportions. The calculator automatically determines the appropriate Z-score based on your selected confidence level and applies the formula: CI = p ± Z × √[(p×(1-p))/n], where p is the sample proportion, n is the sample size, and Z is the critical value.
📚 FAQs
A confidence interval is a range of values that likely contains the true population parameter. For example, a 95% confidence interval means we're 95% confident the true population proportion falls within this range.
The margin of error represents the maximum expected difference between the sample proportion and the true population proportion. A smaller margin of error indicates more precise estimates.
95% is most common for general research, 99% for critical decisions requiring high certainty, and 90% when broader ranges are acceptable. Higher confidence levels create wider intervals.
Generally, you need at least 30 observations, and both np and n(1-p) should be at least 5 for the normal approximation to be valid. Larger samples provide more accurate confidence intervals.
Yes! You can enter proportions as decimals (0.45) or percentages (45%). The calculator automatically converts percentages to decimals for calculations.
Wide confidence intervals typically result from small sample sizes, proportions near 0.5 (maximum variability), or high confidence levels. Increase sample size to narrow the interval.