Confidence Interval Calculator (Mean)
Estimate a range likely to contain the true mean, using the normal (z) approximation.
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Confidence Interval Calculator (Mean) by TheCalcTools
How the Confidence Interval Calculator (Mean) works
Enter the sample mean, standard deviation and sample size, then choose a confidence level.
The standard error is the standard deviation divided by the square root of n.
The margin of error is the critical z-value times the standard error.
The formula
Worked example
Using the default values shown in the calculator:
| Sample mean | 50 |
|---|---|
| Standard deviation | 8 |
| Sample size (n) | 64 |
| Confidence level | 95% |
- SE = 8 ÷ √64 = 1.00.
- Margin of error = 1.96 × 1 = 1.96.
- The 95% interval is 48.04 to 51.96.
Result:
| Standard error | 1.0000 |
|---|---|
| Margin of error | 1.9600 |
| Lower bound | 48.0400 |
| Upper bound | 51.9600 |
Frequently asked questions
What does a 95% confidence interval mean?
If you repeated the sampling many times, about 95% of the intervals built this way would contain the true mean.
Should I use a t-value for small samples?
Yes. For samples under about 30 with an estimated standard deviation, a t-distribution gives a slightly wider interval. This calculator uses the normal approximation.
Sources and further reading
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This calculator gives estimates for information only. Check important results independently before you rely on them. See our disclaimer.