Confidence Interval Calculator
Calculate the confidence interval for a population mean. Determine the margin of error and range where the true population parameter likely falls.
Inputs
Results
Margin of Error (±)
1.96
How to Use This Calculator
- Enter your Sample Mean (x̄) — the average of your collected data points.
- Enter the Standard Deviation (σ) of your sample and the Sample Size (n, number of observations).
- Choose a Confidence Level: 90%, 95%, or 99% — higher confidence produces a wider interval.
- The calculator uses the z-score for the chosen level (e.g., 1.96 for 95%) and computes: margin of error = z × (σ / √n).
- Lower Bound and Upper Bound define the range where the true population mean is expected to fall with the stated confidence.
- Increase sample size to narrow the interval without changing confidence level.
How the result changes with Standard Deviation (σ)
| Standard Deviation (σ) | Margin of Error (±) |
|---|---|
| 100,000 | 19,600 |
| 350,000 | 68,600 |
| 650,000 | 127,400 |
| 900,000 | 176,400 |
What each input means
- Sample Mean (x̄)
- The average of your sample data
- Sample Size (n)
- The number of observations in your sample
- Standard Deviation (σ)
- The standard deviation of the population (or sample)
- Confidence Level
- How confident you want to be in the interval
How this is calculated
Formula
CI = x̄ ± z × (σ / √n)Engine last updated . Checked against 1 independently-derived test — how we verify calculators.
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