Confidence Interval Calculator
Calculate the confidence interval for a population mean using the z-distribution. Specify the sample mean, standard deviation, sample size, and confidence level to get the interval bounds.
This free online confidence interval calculator provides instant results with no signup required. All calculations run directly in your browser — your data is never sent to a server. Enter your values below and see results update in real time as you type. Perfect for everyday calculations, homework, or professional use.
The average value from your sample.
Population or sample standard deviation.
Number of observations in your sample.
Z critical value: 1.645 for 90%, 1.96 for 95%, 2.576 for 99%.
How to Use This Calculator
Enter your input values
Fill in all required input fields for the Confidence Interval Calculator. Most fields include unit selectors so you can work in your preferred unit system — metric or imperial, whichever matches your problem.
Review your inputs
Double-check that all values are correct and that you have selected the right units for each field. Incorrect units are the most common source of calculation errors and can produce results that are off by factors of 2, 10, or more.
Read the results
The Confidence Interval Calculator instantly computes the output and displays results with units clearly labeled. All calculations happen in your browser — no loading time and no data sent to a server.
Explore parameter sensitivity
Try adjusting individual input values to see how the output changes. This is a quick and effective way to develop intuition about how different parameters influence the result and to identify which inputs have the largest effect.
Formula Reference
Confidence Interval Calculator Formula
See calculator inputs for the governing equation
Variables: All variables and their units are labeled in the calculator interface above. Input fields accept values in multiple unit systems — select your preferred unit from the dropdown next to each field.
When to Use This Calculator
- •Use the Confidence Interval Calculator when you need accurate results quickly without the risk of manual computation errors or unit conversion mistakes.
- •Use it to verify calculations made by hand or in spreadsheets — an independent check can catch errors before they lead to costly decisions.
- •Use it to explore how changing input parameters affects the output — a quick way to develop intuition and identify the most influential variables.
- •Use it when collaborating with others to ensure everyone is working from the same numbers and applying the same assumptions.
About This Calculator
The Confidence Interval Calculator is a free, browser-based calculation tool for engineers, students, and technical professionals. Calculate the confidence interval for a population mean using the z-distribution. Specify the sample mean, standard deviation, sample size, and confidence level to get the interval bounds. It implements standard formulas and supports both metric (SI) and imperial unit systems with automatic unit conversion. All calculations are performed instantly in your browser with no data sent to a server. Use this calculator as a quick reference and sanity-check tool during design, analysis, and learning. Always verify results against primary engineering references and applicable standards for any safety-critical application.
About Confidence Interval Calculator
The confidence interval calculator computes an interval estimate for a population mean based on sample data. Instead of a single point estimate, a confidence interval provides a range within which the true population parameter is likely to fall, along with a level of confidence (typically 90%, 95%, or 99%). Confidence intervals are indispensable in scientific research, clinical trials, opinion polls, quality control, and business analytics. A 95% confidence interval means that if you repeated the sampling process many times, approximately 95% of the resulting intervals would contain the true population mean. The width of the interval depends on the variability of the data, the sample size, and the desired confidence level.
The Math Behind It
Formula Reference
Confidence Interval for Mean
CI = x_bar +/- z* * (sigma / sqrt(n))
Variables: x_bar = sample mean; z* = critical value; sigma = standard deviation; n = sample size
Worked Examples
Example 1: Average height survey
A sample of 36 adults has mean height 170 cm with sigma = 6 cm. Find the 95% CI.
The 95% confidence interval is (168.04, 171.96) cm.
Example 2: Battery life test
50 batteries tested have mean life 48.5 hours with sigma = 3 hours. Find the 99% CI.
The 99% CI for battery life is (47.41, 49.59) hours.
Common Mistakes & Tips
- !Interpreting the CI as a probability statement about a single interval rather than a long-run frequency property.
- !Using z* when the sample size is small and sigma is unknown; use the t-distribution instead.
- !Forgetting that increasing confidence level widens the interval, reducing precision.
Related Concepts
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Frequently Asked Questions
What does 95% confidence mean?
It means that if you were to take many samples and compute a CI from each, approximately 95% of those intervals would contain the true population mean. It does not mean there is a 95% probability that this specific interval contains the mean.
How do I make a confidence interval narrower?
Increase the sample size (n), accept a lower confidence level, or reduce the variability in your data. Of these, increasing n is the most common approach.
When should I use a t-interval instead of a z-interval?
Use a t-interval when the population standard deviation is unknown and you are estimating it with the sample standard deviation, particularly when n < 30.