Confidence Interval for a Proportion Calculator
Confidence interval around a sample proportion.
Enter your values
Enter the sample proportion you are working with.
Enter the sample size you are working with.
Choose one of: 90%, 95%, 99%.
Results update instantly as you type — no submit needed. Your values are remembered on this device, and the shareable link reopens the calculator with exactly these numbers.
- Confidence interval
- 0.341 to 0.499
- Margin of error
- ±0.079
- Standard error
- 0.0403
Quick answer
The confidence interval for a proportion is p̂ ± z*sqrt(p̂(1-p̂)/n), using the z critical value for the chosen confidence level.
CI = p̂ ± z*sqrt(p̂(1-p̂)/n)
At a glance
| What it does | Confidence interval around a sample proportion. |
|---|---|
| Category | Statistics |
| Inputs needed | Sample proportion, Sample size, Confidence level |
| Main output | Confidence interval |
| Formula | CI = p̂ ± z*sqrt(p̂(1-p̂)/n) |
| Cost | Free — no sign-up, no download |
How to use the Confidence Interval for a Proportion Calculator
- 1Enter your sample proportion (successes divided by sample size).
- 2Enter the sample size and desired confidence level.
- 3The margin of error uses the z critical value times the standard error.
Inputs explained
- Sample proportion
- Enter the sample proportion you are working with.
- Sample size
- Enter the sample size you are working with.
- Confidence level
- Choose one of: 90%, 95%, 99%.
Worked example
Using the values the calculator loads with:
Inputs
- Sample proportion0.42
- Sample size150
- Confidence level95%
Results
- Confidence interval0.341 to 0.499
- Margin of error±0.079
- Standard error0.0403
Frequently asked questions
Which confidence level should I use?
95% is the most common default in research and reporting.
What if n is small?
For small samples, consider an exact binomial confidence interval instead of this normal approximation.
What do I need to enter into the Confidence Interval for a Proportion Calculator?
Just 3 values: sample proportion, sample size, confidence level. Every field starts with a realistic example, so you can change one number at a time and watch the result update instantly.
How does the Confidence Interval for a Proportion Calculator work out the answer?
The confidence interval for a proportion is p̂ ± z*sqrt(p̂(1-p̂)/n), using the z critical value for the chosen confidence level. It applies the formula CI = p̂ ± z*sqrt(p̂(1-p̂)/n) and shows the working so you can check each step by hand.
Is the Confidence Interval for a Proportion Calculator free, and do I need an account?
It is completely free with no sign-up, no download and no usage limit. Everything is calculated in your browser, so the numbers you type never leave your device.
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.