Statistics & Probability

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90% Confidence Interval Calculator.

Calculate a normal-approximation confidence interval using z = 1.645.

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Set your values

Results update as you type.

lower: 47.368

lower

47.368000
upper: 52.632

upper

52.632000
marginOfError: 2.632

marginOfError

2.632000

Results update automatically as you type.

Use Cases

Assess precision of sample estimates

Determine how precise your sample mean is by seeing the width of the confidence interval. A narrower interval indicates more precise estimates, which can guide decisions on sample size.

Example: If your 90% confidence interval is wide, you might need a larger sample size to get a more precise estimate.

Frequently Asked Questions

What is a 90% confidence interval?
A 90% confidence interval is a range of values that you can be 90% confident contains the true population mean. It is calculated from your sample mean, standard deviation, and sample size, and it provides an estimate of the uncertainty around your sample mean.
How do I calculate a 90% confidence interval?
To calculate a 90% confidence interval, you need the sample mean, standard deviation, and sample size. The formula uses the critical value for 90% confidence (approximately 1.645 for a normal distribution). The margin of error is 1.645 * (standard deviation / sqrt(sample size)). The interval is sample mean ± margin of error.
What does the 90% confidence level mean?
The 90% confidence level means that if you were to take many samples and compute a 90% confidence interval from each, about 90% of those intervals would contain the true population mean. It does not mean there is a 90% chance that the true mean lies within a specific interval.

Tips & Common Mistakes

Tips

  • Ensure your sample size is large enough (typically n > 30) for the normal approximation to be valid. For smaller samples, consider using a t-distribution.
  • Use the sample standard deviation, not the population standard deviation, unless you know the population standard deviation.
  • The confidence interval is only as good as your sample. Ensure your sample is random and representative of the population.
  • Remember that a 90% confidence interval is narrower than a 95% interval, so it gives a less conservative estimate.

Common Mistakes to Avoid

  • Using the population standard deviation when only the sample standard deviation is known, which can lead to an incorrect interval.
  • Confusing the confidence level with the probability that the true mean is in the interval. The 90% refers to the long-run proportion of intervals that contain the true mean.
  • Forgetting to take the square root of the sample size when calculating the standard error, which would make the interval too wide or too narrow.

Last updated: August 12, 2026