Confidence Interval Calculator - Free CI Calculator for Mean & Proportion
Confidence Interval Calculator
Calculate confidence intervals for population parameters. Find the range of plausible values with specified confidence level.
Confidence Interval for Population Mean
Results
Confidence Interval
Visual Representation
Calculation Details
Key Values
Sample Size Calculator
Find the sample size needed for a desired margin of error.
How to use this calculator
📊 How to Use This Calculator
- Choose the parameter: mean, proportion, or difference
- Enter your sample statistics (mean/proportion, sample size, etc.)
- Select your confidence level (90%, 95%, or 99%)
- Click calculate to get the confidence interval
- Use the sample size calculator to plan future studies
📐 Understanding Confidence Intervals
What is a Confidence Interval?
A range of plausible values for a population parameter, calculated from sample data.
Interpretation
A 95% CI means: if we repeated the sampling process many times, about 95% of the intervals would contain the true parameter.
Key Formulas
Mean: x̄ ± t × (s/√n)
Proportion: p̂ ± z × √[p̂(1-p̂)/n]
🌟 Real-World Examples
Example 1: Average Height
Sample mean = 170 cm, SD = 10 cm, n = 100
95% CI: [168.04, 171.96] cm
Example 2: Election Poll
Support = 52%, n = 1000
95% CI: [48.9%, 55.1%] (±3.1% margin of error)
Example 3: Treatment Effect
Difference in means = 5.2 units
95% CI: [2.1, 8.3] - significant effect
💡 Pro Tips
- • Wider CI = more uncertainty, narrower CI = more precision
- • Increase sample size to reduce margin of error
- • Higher confidence level = wider interval
- • CI that excludes 0 indicates statistical significance
- • For proportions near 0 or 1, use Wilson score interval
- • Check assumptions: random sampling, normality (for small n)
⚠️ Common Mistakes to Avoid
- • CI is NOT the probability the parameter is in the interval
- • Don't use z when n < 30 for means (use t instead)
- • Ensure data meets assumptions before calculating
- • CI for proportion requires np ≥ 5 and n(1-p) ≥ 5
- • Remember: CI is about the parameter, not individual values
- • Don't confuse confidence level with confidence interval
About this calculator
Calculate confidence intervals for population mean, proportion, and difference. Find margin of error and interpret results with visualization.
Was this helpful?
Browse more in
Related Calculators
Mean, Median, Mode Calculator - Free Online Statistics Calculator
Calculate mean (average), median (middle value), and mode (most frequent) instantly. Includes step-by-step solutions and data visualization.
Standard Deviation Calculator - Free Online Variance & SD Calculator
Calculate standard deviation, variance, and coefficient of variation. Choose between population and sample calculations with visual distribution.
Correlation Coefficient Calculator - Free Pearson's r Calculator
Calculate Pearson correlation coefficient (r) between two variables. Includes scatter plot, regression line, and coefficient of determination (r²).
Z-Score Calculator - Free Standard Score & Probability Calculator
Calculate z-scores, find probabilities, and percentile ranks. Convert between raw scores and z-scores with visual normal distribution curve.
Chi-Square Test Calculator - Free χ² Statistical Test
Perform chi-square tests for independence and goodness of fit. Calculate chi-square statistic, p-value, and visualize expected vs observed frequencies.
Linear Regression Calculator - Free Statistical Analysis Tool
Perform linear regression analysis. Calculate slope, intercept, R-squared, predictions, and residuals with scatter plot visualization.