Confidence Interval for a Mean
Confidence Interval for a Mean with explicit assumptions and reproducible inputs.
Formula
- Use the units shown beside each field.
- Results update automatically whenever you change an input.
- Displayed values use up to four decimal places, or scientific notation for very small or large numbers. Calculations use standard floating-point arithmetic; exact integer and fraction tools identify their own precision rules.
- Independent observations; the t interval assumes a normal population or an adequate large-sample approximation. The z method requires a genuinely known population SD. Numerical results are approximate. Extremely small probabilities can underflow to zero. No personal, clinical or financial decision rule is inferred.
Example Calculation
- Sample mean: 50
- Standard deviation: 10
- Sample size: 25
- Confidence level: 95 %
- Method: Sample SD: Student t
Mean50, sample SD10, n25 and 95% confidence give approximately [45.8722,54.1278].
Method references
Frequently asked questions
How do I use this calculator?
Enter sample mean, standard deviation, sample size, confidence level, method. The result updates automatically. Use Reset to restore the example values.
What method does it use?
mean ± critical value × SD/√n; t uses df=n−1.. Independent observations; the t interval assumes a normal population or an adequate large-sample approximation. The z method requires a genuinely known population SD. Numerical results are approximate. Extremely small probabilities can underflow to zero. No personal, clinical or financial decision rule is inferred.
Why might a rounded result differ?
The calculation keeps full numeric precision internally, then rounds the displayed result. Rounding intermediate steps by hand can produce a slightly different answer.
Are my inputs saved online?
No. This calculator processes your inputs in your browser. A recently used list stores only calculator names on this device, not your entered values.
Check the assumptions and units before using this result. Read about calculation methods.