Confidence Interval Calculator
Calculate a confidence interval for a mean or a proportion. Enter your sample stats and confidence level for the margin of error and bounds.
Independently verified for accuracy
Calculator by Toolsloft ↗- Confidence interval
- 95.10009 to 104.89991
- Margin of error
- 4.89991
- z value
- 1.959964
Build a confidence interval for a mean or a proportion using the normal (z) method. Enter your sample statistics and pick a confidence level to get the margin of error and the lower and upper bounds. Suited to large samples where the normal approximation applies.
How this is calculated
The interval is the estimate plus or minus a margin of error. For a mean the margin is z times the standard deviation divided by the square root of the sample size. For a proportion it is z times the square root of p times (1 minus p) over n. The z value is the standard normal critical value for the chosen confidence level, for example 1.959964 for 95 percent.
How to use
- Choose a mean or a proportion.
- Enter your sample statistics and sample size.
- Pick a confidence level and read the interval.
Examples
- Mean:
mean 100, sd 15, n 36, 95% gives 95.1 to 104.9 - Proportion:
p 0.4, n 500, 95% gives 0.357 to 0.443
FAQ
- What confidence levels are supported?
- The tool supports 80, 90, 95, 98, and 99 percent, using the standard normal critical value for each.
- Does this use z or t?
- It uses the normal (z) method, which fits large samples or a known population standard deviation. For small samples with an unknown sigma, a t-based interval would be slightly wider.
- What is the margin of error?
- It is the half-width of the interval. The confidence interval is the point estimate minus and plus the margin of error.