Confidence Interval Calculator

This confidence interval calculator will assist you in determining the confidence interval for a sample if you provide the mean, standard deviation, and sample size. It can be used with any arbitrary level of confidence. If you're wondering what a confidence interval is and how to calculate it, or if you're looking for the 95% confidence interval formula with no margin of error, this article is for you.

The purpose of the Confidence Interval Calculator is to compute the confidence interval or margin of error, assuming that the sample mean follows a normal distribution.

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What Is The Confidence Interval?

"A confidence interval is the range of values derived from sample statistics that are likely to contain the value of an unknown population parameter," according to the definition. But what does that actually mean?

Assume a brickmaker is concerned about whether the quantity of bricks he produces meets specifications. He determined that the average mass of a sample of 100 bricks was 3 kg. He also discovered that the 95% confidence interval is between 2.85 kg and 3.15 kg. It means he can be 95% certain that the average mass of all the bricks he makes will be between 2.85 kg and 3.15 kg.

Of course, you don't always want to be 95% certain. You may want to be 99% certain, or you may be satisfied if the confidence interval is correct in 90% of the cases. This percentage is referred to as the confidence level.

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How To Calculate Confidence Interval?

To compute a confidence interval (two-sided), perform the following steps:

1. Let's say the sample size is 100
2. Find the mean value of your sample. Assume it's 3.
3. Determine the standard deviation of the sample. Let's say it's 0.5.
4. Choose the confidence level. The most common confidence level is 95%.
5. In the statistical table find the Z(0.95)-score, i.e., the 97.5th quantile of N(0,1) – in our case, it's 1.959.
6. Compute the standard error as σ/√n = 0.5/√100 = 0.05.
7. Multiply this value by the z-score to obtain the margin of error: 0.05 × 1.959 = 0.098.
8. Add and subtract the margin of error from the mean value to obtain the confidence interval. In our case, the confidence interval is between 2.902 and 3.098.

That's all! That was a lot of calculations, wasn't it? Fortunately, our confidence level calculator can perform all of these calculations automatically.