How the Confidence Interval Calculator works.
interval = x̄ ± z × (s/√n)x̄ is sample mean, s is sample standard deviation, n is sample size, and z is 1.645, 1.960, or 2.576 for the selected level.
Worked example for the Confidence Interval Calculator.
A mean of 50, standard deviation 10, sample size 100, and 95% confidence use z = 1.96, giving an interval of 48.04 to 51.96.
How to read this result.
The interval estimates a range for a population mean under the selected model; it is not the probability that a fixed parameter moves after the interval is calculated.
How the calculation works
For a mean interval with a normal approximation, margin of error is critical value × standard error, where standard error is sample standard deviation divided by √n. Formula or rule: interval = x̄ ± z × (s/√n). x̄ is sample mean, s is sample standard deviation, n is sample size, and z is 1.645, 1.960, or 2.576 for the selected level.
What this calculator does not prove
The calculator uses a z critical value and assumes an independent, representative sample with a reasonably normal sampling distribution. It does not correct bias or study design. Use the result for the mathematical question shown here; a correct calculation does not by itself establish that the source data, sample, or real-world assumption is appropriate.
Inputs and edge cases to check.
Standard deviation must be positive, sample size must be at least 2, and confidence must be 90%, 95%, or 99%.
What this tool does not include.
The calculator uses a z critical value and assumes an independent, representative sample with a reasonably normal sampling distribution. It does not correct bias or study design.
Reference guidance and methodology.
Confidence Interval Calculator questions.
What does the Confidence Interval Calculator calculate?
Estimate a normal-approximation confidence interval for a sample mean with clear assumptions and margin of error.
Which formula or algorithm does it use?
interval = x̄ ± z × (s/√n). x̄ is sample mean, s is sample standard deviation, n is sample size, and z is 1.645, 1.960, or 2.576 for the selected level.
What limitations or edge cases matter?
Standard deviation must be positive, sample size must be at least 2, and confidence must be 90%, 95%, or 99%. The calculator uses a z critical value and assumes an independent, representative sample with a reasonably normal sampling distribution. It does not correct bias or study design.