Math & Science
Confidence Interval Calculator
Calculate confidence intervals for means and proportions
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Frequently asked questions
What does 95% confidence mean?
If we repeated the study 100 times, ~95 of those intervals would contain the true value.
Z or t distribution?
Use t for small samples (n<30) or unknown population standard deviation.
How to narrow the interval?
Increase sample size or accept lower confidence level.
Related tools
About this tool
Inputs
- Sample Mean
- Standard Deviation
- Sample Size
- Confidence Level
- 90%
- 95%
- 99%
Results
- Lower Bound
- Upper Bound
- Margin of Error
Before making a decision based on estimates, run the numbers through this Confidence Interval Calculator. A few seconds of input can save hours of uncertainty. You supply sample mean, standard deviation, sample size, confidence level, 90%, 95% and 99%, and the tool calculates lower bound, upper bound and margin of error from those figures. Mathematical tools turn abstract formulas into concrete answers you can verify and apply. The tool applies the exact mathematical operation to your inputs and shows the result without intermediate rounding.
The ability to calculate confidence intervals for means and proportions comes up more often than most people expect — in professional work, academic projects, and everyday planning. If the result seems implausible, work backward from the answer to see where the logic breaks. If we repeated the study 100 times, ~95 of those intervals would contain the true value. Understanding the underlying principle helps you judge whether a result is reasonable. Run the calculation with your best-case and worst-case assumptions to bracket the likely outcome.