±Free
Mean confidence interval
Normal-approximation interval using a supplied z critical value; assumes independent observations.
Enter the mean, standard deviation, sample size and chosen positive z critical value. The tool calculates SE = SD / √n, then returns the interval mean ± z × SE and its error margin.
How to use
- Enter your text, values, or image.
- Adjust the options and run the tool.
- Copy or download your result.
Worked example
Example input
Sample mean: 100 Standard deviation: 10 Sample size: 100 Critical z (1.96 ≈ 95%): 1.96
Example result
{
"standardError": 1,
"margin": 1.96,
"lower": 98.04,
"upper": 101.96
}Limitations and details
Uses a normal approximation with independent observations; it does not select a confidence level or use Student’s t distribution.
Inputs and options
- Sample mean
- Number
- Standard deviation
- Number · Minimum: 0
- Sample size
- Number · Minimum: 1
- Critical z (1.96 ≈ 95%)
- Number · Minimum: 0
Frequently asked questions
Is this tool free and private?
Yes. All 300 tools are free in this phase. Processing happens in your browser; your input and files are not sent to our servers.