What is Confidence Interval Calculator?
Confidence Interval Calculator helps you estimate an interval around a sample mean at a chosen confidence level.
The main result is confidence interval, with a breakdown of margin of error. The formula, example and assumptions below explain how to interpret it.
How to use Confidence Interval Calculator
Use the example to get familiar with the form, then enter your own figures. Any rates in the example are illustrative. Check the field labels and units before calculating.
- Gather sample mean, known population standard deviation, sample size and confidence level. Use values from the same situation or reporting period.
- Replace the example sample mean with your own value, then complete the other fields. Check the displayed units and each selected option.
- Select Calculate and read confidence interval with its result breakdown. Change one input and calculate again to compare a second scenario. Reset restores the original example.
- Enter sample mean, at least -1000000000000. Decimals are accepted.
- Enter known population standard deviation, at least 0.000001. Decimals are accepted.
- Enter sample size, at least 2. Use a whole number.
- Choose confidence level from 90%, 95% and 99%.
Confidence Interval Calculator: a worked example
With the inputs below, the result is 48.0400 to 51.9600 (confidence interval). Follow the example, then replace these illustrative values with your own.
| Input or output | Example value |
|---|---|
| Sample mean | 50 |
| Known population standard deviation | 10 |
| Sample size | 100 |
| Confidence level | 95% |
| Confidence interval | 48.0400 to 51.9600 |
| Margin of error | 1.959964 |
Understanding the Confidence Interval result
Read confidence interval alongside margin of error. These describe different parts of the same calculation.
Displayed results use a readable number of decimal places. When checking a result by hand, keep extra precision until the last step. To compare scenarios, change one input at a time and keep the others fixed.
- Example Margin of error: 1.959964
Confidence Interval Calculator: assumptions and common mistakes
A useful estimate starts with the right inputs. Check the following assumptions and limits before applying the result to your situation.
- This is a z interval, not a Student’s t interval for an unknown population standard deviation.
- Check the base value, sample definition and chosen operation. Display rounding should come after the calculation.
For wider guidance, visit NIST statistical handbook. The formula and scope of this specific tool are stated on this page.
