Confidence Interval Calculator

When to use

• Use it to estimate uncertainty around a mean or proportion from valid summary inputs.
• Use it when the sample design and distribution conditions match the selected z or t method.
• Use model-based or exact methods when data are clustered, highly discrete, or outside normal-approximation conditions.

How to use

1. Select mean or proportion and enter the estimate, sample size, and required variability information.
2. Choose the confidence level and confirm whether population standard deviation is known.
3. Calculate the interval and inspect standard error, critical value, and bounds.
4. Interpret the interval in the units and sampling context of the original measure.

Inputs

Point estimate

The sample mean or observed proportion at the center of the interval.

Sample size

The number of independent observations used for the estimate.

Standard deviation or successes

Variability input for a mean or event count for a proportion.

Confidence level

The long-run coverage level that selects the z or t critical value.

Notation

Interpretation

• The interval gives values compatible with the estimate and method assumptions; it is not the probability that a fixed parameter lies inside this one computed interval.
• Width reflects sample size, variability, and selected confidence.
• For proportions near zero or one, a normal-approximation interval may be unsuitable.

Effect-size guidance

• Report point estimate, interval, confidence level, n, and units together.
• Judge whether the interval includes practically important values, not only a null value.
• Do not narrow an interval by choosing a lower confidence level after seeing the data.

Worked examples

Assumptions

• Inputs are finite numeric values after parsing, with missing or invalid values handled according to the selected workflow.
• The selected interval method matches the parameter and data structure.
• Observations are independent unless the chosen summary method accounts for dependence.

Practical guidance

• Check independence and sampling design before using a textbook standard error.
• Retain unrounded inputs until final reporting.
• Use exact or model-based software when method conditions are doubtful.

Common mistakes

• Saying a specific interval has a 95% probability of containing the true mean.
• Using z when sigma is not known.

Limitations

• Coverage depends on method assumptions.
• Bootstrap intervals are out of scope.

Related workflow links