Mean interval
Mean 68, SD 3, n = 36, 95%67.02 to 68.98 with margin about 0.98
Confidence Interval Calculator
Use this free confidence interval calculator to build a z interval for a sample mean or sample proportion, then check the point estimate, standard error, margin of error, lower bound, upper bound, copy result, and recent tab-only history.
Inputs to checkExample numbersCopyable answerTab-only history
95% confidence interval67.02 to 68.98
- Margin
- 0.98
- Z-score
- 1.96
- Point estimate
- 68
Recent answers
Recent answers will appear here.
Input tips
Mean mode uses a z interval with a known or estimated standard deviation.
Proportion mode uses successes divided by sample size as the point estimate.
How to use the Confidence Interval Calculator
- Choose mean interval or proportion interval mode.
- Choose a confidence level, then enter the sample values requested for that mode.
- Press Calculate interval to see the lower bound, upper bound, margin of error, and steps.
- Use examples, recent answers, or copy the interval while checking estimates.
What people use it for
Calculate a mean confidence interval from a sample mean, standard deviation, sample size, and confidence level.
Calculate a proportion confidence interval from successes, sample size, and confidence level.
Compare how 80%, 90%, 95%, 98%, and 99% confidence levels change the interval width.
Check the point estimate, standard error, margin of error, z-score, lower bound, and upper bound before copying the result.
Use the visible steps to check homework, survey, lab, or quick statistics notes without sending the history to a server.
Quick examples
Proportion interval
52 successes, n = 100, 95%42.2% to 61.8% with margin about 9.8 points
Narrower confidence level
Mean 68, SD 3, n = 36, 90%67.1775 to 68.8225
Wider confidence level
Mean 68, SD 3, n = 36, 99%66.7121 to 69.2879
Large survey check
610 successes, n = 1000, 95%58.0% to 64.0%
Need the guide or a nearby tool?
Need a slower walkthrough, a related calculator, or the full library? These links keep you close to the task you started.
- How to use the Confidence Interval CalculatorSee slower examples, input meanings, formula notes, result limits, and mistakes to avoid.
- CalculatorsBrowse related calculators and utilities in the same category.
- Calculator and utility guidesFind more guides that use real tool inputs and example numbers.
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Frequently asked questions
Quick answers about formulas, inputs, examples, result copying, and private in-browser history.
What is a confidence interval?
A confidence interval is a range around a sample estimate. It gives a plausible range for the population mean or proportion using the confidence level and the sample information you entered.
What interval types are supported?
This page supports z intervals for one sample mean and one sample proportion. Mean mode uses sample mean, standard deviation, and sample size. Proportion mode uses successes and sample size.
What do the main Confidence Interval Calculator inputs mean?
The main inputs are the numbers, operation, mode, or known values the calculator needs. Keep units consistent, enter percentages the way the page label shows, and use the examples as a quick check before trusting the answer.
How should I read the Confidence Interval Calculator answer?
Read the headline answer, then check the supporting lines and examples to understand how the calculator got there. If one input changes, rerun the tool and compare the new answer instead of guessing.
What formulas does the calculator use?
Mean mode uses standard error = standard deviation / sqrt(sample size), then margin of error = z x standard error. Proportion mode uses p-hat = successes / sample size, standard error = sqrt(p-hat x (1 - p-hat) / sample size), then margin of error = z x standard error.
What is margin of error?
Margin of error is the amount added to and subtracted from the point estimate to create the lower and upper bounds.
Should I use mean or proportion mode?
Use mean mode for numeric averages, such as average score, height, time, or measurement. Use proportion mode for successes out of a total, such as yes responses, defect counts, signups, or pass/fail results.
How does confidence level change the answer?
A higher confidence level uses a larger z value, so the interval gets wider. For the same sample, a 99% interval is wider than a 95% interval, and a 90% interval is narrower.
What sample size should I enter?
Enter the number of observations in the sample. For mean mode, that is the count behind the sample mean and standard deviation. For proportion mode, it is the total trials or responses, and successes must be between 0 and that sample size.
Why can a proportion interval stop at 0% or 100%?
The calculator clamps proportion bounds to the possible range of 0% to 100%. When the sample is small or the success rate is very close to 0% or 100%, a different method such as Wilson or exact intervals may be more appropriate.
Can this replace advanced statistical software?
No. It is a quick educational calculator for common z intervals. Advanced studies may need t intervals, paired data, design effects, finite population corrections, exact methods, or statistical review.
What should I double-check before copying the interval?
Check that the mean and standard deviation came from the same sample, the sample size is correct, successes do not exceed sample size, and the confidence level matches your assignment or report.
Is my confidence interval history private?
Yes. Recent confidence interval answers stay only in the current browser tab while you use the page. They are not sent to a server.