Confidence Interval Calculator
Switch between mean and proportion modes to estimate population parameters from sample data.
Inputs — Mean
Common values: 90, 95, 99
Results — Mean
Inputs — Proportion
Common values: 90, 95, 99
Results — Proportion
Bounds are expressed as proportions between 0 and 1.
Use this Confidence Interval Calculator to estimate a confidence interval for a population mean or population proportion from sample data.
Calculation Method
This calculator currently uses Z-based confidence intervals.
Mean confidence interval:
x̄ ± z × (s ÷ √n)
Proportion confidence interval:
p̂ ± z × √[p̂(1 − p̂) ÷ n]
Where:
p̂ = number of successes ÷ sample size
Example
Suppose a sample has:
Mean = 50
Standard deviation = 10
Sample size = 100
Confidence level = 95%
The standard error is:
SE = 10 ÷ √100 = 1
Using z = 1.96:
Margin of error = 1.96 × 1 = 1.96
The 95% confidence interval is:
50 ± 1.96 = 48.04 to 51.96
Important Note
A 95% confidence interval does not mean there is a 95% probability that the true value lies inside one calculated interval. Under repeated sampling with the same method, approximately 95% of such intervals would contain the true parameter.
For small samples with an unknown population standard deviation, a t-based mean interval may be more appropriate. Simple normal proportion intervals may also be unsuitable for small samples or proportions close to 0 or 1.