Statistics & Probability

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Confidence Interval Calculator.

Calculate a mean interval using an explicitly supplied critical value.

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Set your values

Results update as you type.

Margin of error: 1.96

Margin of error

1.960000
Lower bound: 48.04

Lower bound

48.040000
Upper bound: 51.96

Upper bound

51.960000

Results update automatically as you type.

Use Cases

Estimate population mean from sample data

Use this calculator to estimate the range in which the true population mean likely falls, based on your sample statistics. It's useful in research, quality control, and data analysis.

Example: If sample mean = 50, SD = 10, n = 100, z = 1.96, the 95% CI is [48.04, 51.96].

Determine margin of error for surveys

Calculate the margin of error for survey results by entering the sample mean, standard deviation, sample size, and critical value. This helps in understanding the precision of your estimates.

Example: For a survey with mean = 70, SD = 15, n = 200, z = 1.96, the margin of error is ±2.08.

Frequently Asked Questions

What is a confidence interval?
A confidence interval is a range of values, derived from sample statistics, that is likely to contain the true population parameter. It is calculated using the sample mean, standard deviation, sample size, and a critical value (z) that corresponds to the desired confidence level.
How do I choose the critical value (z)?
The critical value (z) is based on your desired confidence level. For example, for a 95% confidence level, use z = 1.96; for 90%, use z = 1.645; for 99%, use z = 2.576. This calculator requires you to input the z-value directly.
What does the debounced result mean?
Debounced results mean the calculator updates the confidence interval after you stop typing for a short delay, preventing constant recalculations. This ensures smooth and accurate output as you adjust your inputs.

Tips & Common Mistakes

Tips

  • Ensure your sample size is large enough (typically n > 30) for the z-distribution to be appropriate. For smaller samples, consider using a t-distribution instead.
  • Use the correct critical value (z) for your desired confidence level. Common values: 1.645 (90%), 1.96 (95%), 2.576 (99%).
  • Double-check that your standard deviation is from the sample, not the population, unless you are using a z-interval for a known population standard deviation.
  • Remember that the confidence interval width increases with higher confidence levels and larger standard deviations, but decreases with larger sample sizes.

Common Mistakes to Avoid

  • Using the population standard deviation instead of the sample standard deviation when the population SD is unknown.
  • Entering the variance instead of the standard deviation. The calculator expects the standard deviation, which is the square root of the variance.
  • Forgetting to use the absolute value of the critical value (z). The z-value is always positive for confidence intervals.

Last updated: August 13, 2026