Confidence Level Calculator
The Confidence Level Calculator builds a confidence interval around a sample mean from the standard deviation, sample size, and a chosen confidence level, returning the lower bound, upper bound, and margin of error.
What this calculator does
The Confidence Level Calculator estimates your result instantly from the values you enter, using standard statistics formulas. The Confidence Level Calculator builds a confidence interval around a sample mean from the standard deviation, sample size, and a chosen confidence level, returning the lower bound, upper bound, and margin of error. Calculations run in your browser, so nothing you type is sent to a server, and the output is an estimate rather than a certified or official figure.
Result
About Confidence Level Calculator
Enter a sample mean along with its standard deviation and sample size, choose a confidence level, and this tool returns the interval likely to contain the true population mean. It uses the standard z-score for each confidence level.
The margin of error is reported separately so you can see how far each bound sits from the sample mean.
Formula & Mathematical Calculation
Lower Bound = f(Sample mean, Standard deviation, Sample size (n), Confidence level)
Calculated according to standard stats formulas implemented in the calculator core.
Calculation Example
For a sample mean of 50, standard deviation 10, size n = 30, at 95% confidence (z = 1.96): the standard error is 10 ÷ √30 = 1.8257419, so the margin of error is 1.96 × 1.8257419 = 3.5785.
The interval runs from 50 − 3.5785 = 46.4215 to 50 + 3.5785 = 53.5785, and the Margin of Error box shows ± 3.5785.
Key Benefits
- Builds a confidence interval around any sample mean you provide
- Offers 90%, 95%, and 99% confidence levels with the matching z-scores
- Reports the margin of error separately from the interval bounds
- Uses the standard error of the mean so results scale with sample size
How to Use this Calculator
-
Enter the sample mean
Type your sample mean into the Sample mean field. -
Enter the standard deviation
Type the standard deviation into its field; it cannot be negative. -
Enter the sample size
Type the sample size n, which must be at least 1. -
Choose a confidence level
Select 90%, 95%, or 99% from the Confidence level dropdown. -
Calculate
Press Calculate and read the Lower Bound, Upper Bound, and Margin of Error boxes.
Assumptions & Limitations
What the calculation assumes
- Every value you enter is treated as an exact, known amount.
- Any rate or interval you enter is assumed to hold for the whole period unless the form asks for it separately.
- Results use standard published formulas and account only for the values entered above.
- Rounding is applied for display; the underlying calculation uses your full precision.
- Results are returned in the same units you enter, unless the tool states the output unit.
What it does not cover
- Confidence Level Calculator produces a calculated result for reference and learning, not a certified or official measurement.
- Real-world outcomes differ when tolerances, rounding rules or local standards apply.
- Definitions and standards vary by region and change over time; verify the convention that applies to your case.
- Figures are only as accurate as the inputs you supply — check them before acting on the result.
- For work where the result carries real consequences, confirm it against an authoritative source.
Frequently Asked Questions
Free to use, no account needed. Calculations run in your browser, so nothing you type is sent to a server. Results are estimates — how we build and check our calculators.