Confidence Interval Calculator Calculate confidence intervals from summary statistics or raw data with multiple confidence levels.
Confidence Interval Calculator
Calculate confidence intervals from summary statistics or raw data with multiple confidence levels.
Choose Input Type
Enter summary statistics or paste raw data values.
Select Confidence Level
Choose from 80% to 99.9% confidence.
View Confidence Interval
See the interval bounds, margin of error, and standard error.
What Is Confidence Interval Calculator?
The Confidence Interval Calculator computes the range within which the true population mean is likely to fall, based on sample data. You can input summary statistics (mean, standard deviation, sample size) or paste raw data for automatic computation. The calculator supports multiple confidence levels and shows the complete calculation breakdown including standard error, margin of error, and z-score. Confidence intervals are fundamental to statistical inference — they quantify the uncertainty in sample-based estimates and are used in virtually every field of research.
Why Use Confidence Interval Calculator?
-
Accepts both summary statistics and raw data input
-
Multiple confidence levels from 80% to 99.9%
-
Shows complete calculation breakdown (SE, margin of error, z-score)
-
Essential for statistical inference and research reporting
Common Use Cases
Research Reporting
Report confidence intervals alongside point estimates in academic papers.
Quality Control
Establish confidence bounds for manufacturing process measurements.
Survey Analysis
Report survey results with appropriate confidence intervals.
Medical Studies
Calculate confidence intervals for treatment effect estimates.
Technical Guide
The confidence interval for a population mean is: CI = x̄ ± Z × (s/√n), where x̄ is the sample mean, s is the sample standard deviation, n is the sample size, and Z is the critical value for the desired confidence level. The standard error SE = s/√n measures the precision of the sample mean. The margin of error E = Z × SE. For raw data, the calculator computes s using the sample standard deviation formula: s = √(Σ(xᵢ-x̄)²/(n-1)). This uses the z-distribution; for small samples (n < 30), the t-distribution would be more appropriate, though the difference becomes negligible for larger samples.
Tips & Best Practices
-
1Higher confidence levels produce wider intervals — there is a trade-off between confidence and precision
-
2Increasing sample size narrows the confidence interval (proportional to √n)
-
3A 95% CI means: if we repeated sampling many times, 95% of intervals would contain the true mean
-
4Report both point estimates and confidence intervals for complete statistical communication
Related Tools
Sample Size Calculator
Calculate required sample size for surveys based on confidence level, margin of error, and population.
🔢 Math & Calculators
Z-Score Calculator
Calculate Z-scores and percentiles, or find values from Z-scores using the standard normal distribution.
🔢 Math & Calculators
P-Value Calculator
Calculate p-values from Z or t test statistics with one-tailed and two-tailed options.
🔢 Math & Calculators
Prime Factorization
Find the prime factors of any number with expanded form and divisor count.
🔢 Math & CalculatorsFrequently Asked Questions
Q What does a 95% confidence interval mean?
Q How do I make my confidence interval narrower?
Q Should I use z or t distribution?
Q Can I calculate CI for proportions?
Q What is standard error?
About This Tool
Confidence Interval Calculator is a free online tool by FreeToolkit.ai. All processing happens directly in your browser — your data never leaves your device. No registration or installation required.