Confidence Interval Calculator
Calculate the confidence interval for a population mean from sample data. Supports 90%, 95%, and 99% confidence levels.
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How to use this calculator
The interval is centred on the sample mean x̄. z* is the critical value for the chosen confidence level, σ is the standard deviation, and n is the sample size.
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Enter the sample mean, standard deviation, and sample size.
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Select the desired confidence level (90%, 95%, or 99%).
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The result gives the lower and upper bounds of the interval, and the margin of error.
Frequently asked questions
What does a 95% confidence interval mean?
If you repeated the sampling process 100 times, approximately 95 of the resulting intervals would contain the true population mean. It does NOT mean there is a 95% chance the true mean is in this specific interval.
How does sample size affect the confidence interval?
Larger samples produce narrower (more precise) intervals. Doubling the sample size narrows the interval by a factor of √2.
When should I use z vs t critical values?
Use z* (this calculator) when the population standard deviation is known or n > 30. Use t* when σ is unknown and n is small — the t-distribution accounts for extra uncertainty.
Confidence Interval Calculator — Margin of Error & Bounds
How to use the confidence interval
Use this confidence interval to he confidence interval for a population mean from sample data. Enter your values above and get your result in seconds. The tool is free, works on all devices, and keeps your data private — nothing is stored or shared.
How the confidence interval works
The confidence interval calculator uses standard formulas used in statistical analysis, data science, and research. Enter your inputs, and the tool calculates the result instantly in your browser. No server-side processing means your data stays on your device. Results update in real time as you change inputs.
What is a confidence interval?
A confidence interval (CI) is a range of values that likely contains the true population parameter. Rather than estimating a single-point mean, a CI provides a plausible range with an associated level of certainty — typically 90%, 95%, or 99%.
Factors that narrow a confidence interval
Three factors control the width of a CI: increasing sample size (n) narrows it proportionally to √n; decreasing variability (σ) narrows it linearly; and lowering the confidence level (e.g., from 99% to 90%) narrows it by reducing the critical value z*. In practice, collecting a larger sample is the most reliable way to improve precision.
Confidence interval: how it works
Statistical analysis underpins data science, research, quality control, and business intelligence. This tool applies established textbook formulas to your dataset and returns results instantly, eliminating manual calculation errors.
Who uses this tool?
Researchers, students, analysts, and business professionals use it to understand datasets quickly. Whether you are summarising survey responses or checking experiment results, this tool delivers the key figures instantly.
Learn more from an authoritative source:
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Results are estimates for informational purposes only and do not constitute professional financial, medical, legal, or technical advice. Read full disclaimer →