Confidence Interval Calculator
Margin of error and interval around a sample mean.
Enter your values
Enter the sample mean you are working with.
Enter the standard deviation 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
- 66.4636 to 70.3364
- Margin of error
- ± 1.9364
- Standard error
- 0.98796
- Relative margin
- 2.83%
Working
- 1SE = 12.1 ÷ √150 = 0.98796
- 2MOE = 1.96 × 0.98796 = 1.9364
Quick answer
A confidence interval is the sample mean plus or minus z × the standard error, giving a plausible range for the population mean.
CI = x̄ ± z·(s ÷ √n)
At a glance
| What it does | Margin of error and interval around a sample mean. |
|---|---|
| Category | Statistics |
| Inputs needed | Sample mean, Standard deviation, Sample size, Confidence level |
| Main output | Confidence interval |
| Formula | CI = x̄ ± z·(s ÷ √n) |
| Cost | Free — no sign-up, no download |
How to use the Confidence Interval Calculator
- 1Enter your sample mean and standard deviation.
- 2Add the sample size.
- 3Pick a confidence level.
Inputs explained
- Sample mean
- Enter the sample mean you are working with.
- Standard deviation
- Enter the standard deviation 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 mean68.4
- Standard deviation12.1
- Sample size150
- Confidence level95%
Results
- Confidence interval66.4636 to 70.3364
- Margin of error± 1.9364
- Standard error0.98796
- Relative margin2.83%
- SE = 12.1 ÷ √150 = 0.98796
- MOE = 1.96 × 0.98796 = 1.9364
Frequently asked questions
What does 95% confidence mean?
If you repeated the study many times, about 95% of the intervals produced would contain the true population mean.
How do I halve the margin of error?
Quadruple the sample size — the margin shrinks with the square root of n.
What do I need to enter into the Confidence Interval Calculator?
Just 4 values: sample mean, standard deviation, 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 Calculator work out the answer?
A confidence interval is the sample mean plus or minus z × the standard error, giving a plausible range for the population mean. It applies the formula CI = x̄ ± z·(s ÷ √n) and shows the working so you can check each step by hand.
Is the Confidence Interval 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.