Confidence interval for a mean or a proportion.
How to use this calculator
Every field updates the result as you type — there is no submit step. The inputs below are pre-filled with a realistic example so you can see how the tool behaves before entering your own figures.
| Field | Unit | What it means |
|---|---|---|
| Interval for | — | Select the mode that matches your situation. |
| Sample mean | — | Enter a numeric value. |
| Sample standard deviation | — | Enter a numeric value. |
| Sample proportion | — | Enter a numeric value. |
| Sample size | — | Enter a numeric value. |
| Confidence level | — | Choose one of the available options. |
| Use t-distribution (small sample) | yes / no | Toggle this on to include it in the calculation. |
Worked example
Using the default values loaded into the calculator above, the result is:
| Input | Value |
|---|---|
| Interval for | Mean |
| Sample mean | 100 |
| Sample standard deviation | 15 |
| Sample proportion | 0.45 |
| Sample size | 50 |
| Confidence level | 95% |
| Use t-distribution (small sample) | yes |
| Output | Value |
|---|---|
| 95% confidence interval | 95.737047 to 104.262953 |
| Point estimate | 100 |
| Margin of error | 4.262953 |
| Standard error | 2.12132034 |
| Critical value | 2.009575 (t (49 df)) |
| Sample size | 50 |
| Relative margin of error | 4.263% |
Precision and rounding
Calculations run in IEEE 754 double precision, giving about 15–17 significant decimal digits. Displayed values are rounded for readability while the full precision is retained internally, so intermediate rounding never accumulates into the final answer.
Very large or very small magnitudes switch automatically to scientific notation.
Sharing and saving a calculation
The "Copy link" button encodes every value you have entered into the page URL. Opening that link restores the calculation exactly, which makes it easy to bookmark a scenario, send it to someone else, or keep several variations side by side in separate tabs.
Frequently asked questions
What does the Confidence Interval Calculator do?
Confidence interval for a mean or a proportion.
What result do the default values produce?
With the values pre-loaded in the calculator, 95% confidence interval comes to 95.737047 to 104.262953.
Is this calculator free to use?
Yes. It is free, requires no account, and runs entirely in your browser — nothing you enter is transmitted or stored on a server.
Can I save or share a calculation?
Yes. The "Copy link" button builds a URL containing all your entered values. Anyone opening that link sees the same calculation.
How accurate is the result?
Calculations use double-precision floating point, accurate to roughly 15 significant digits. Displayed values are rounded for readability only.