Confidence Calculator

Confidence Interval Calculator is the Best Online Confidence Interval Calculator Tool, free without app. Confidence Interval Calculator Tool helps to management, analysis, editing, generate and convert data. Use this calculator to compute the confidence interval or margin of error, assuming the sample mean most likely follows a normal distribution.

What is the confidence interval?

In statistics, a confidence interval is a range of values that is determined through the use of observed data, calculated at a desired confidence level that may contain the true value of the parameter being studied. The confidence level, for example, a 95% confidence level, relates to how reliable the estimation procedure is, not the degree of certainty that the computed confidence interval contains the true value of the parameter being studied. The desired confidence level is chosen prior to the computation of the confidence interval and indicates the proportion of confidence intervals, that when constructed given the chosen confidence level over an infinite number of independent trials, will contain the true value of the parameter.

Confidence intervals are typically written as (some value) ± (a range). The range can be written as an actual value or a percentage. It can also be written as simply the range of values.

Best Confidence Interval Calculator Tool

What is the confidence interval? The definition says that, "a confidence interval is the range of values, derived from sample statistics, that is likely to contain the value of an unknown population parameter." But what does that mean in reality?

Imagine that a brick maker is concerned whether the mass of bricks he manufactures is in line with specifications. He has measured the average mass of a sample of 100 bricks to be equal to 3 kg. He has also found the 95% confidence interval to be between 2.85 kg and 3.15 kg. It means that he can be 95% sure that the average mass of all the bricks he manufactures will lie between 2.85 kg and 3.15 kg.

Of course, you don't always want to be exactly 95% sure. You might want to be 99% certain, or maybe it is enough for you that the confidence interval is correct in 90% of cases. This percentage is called the confidence level.

95% confidence interval formula

Calculating the confidence interval requires you to know three parameters of your sample: the mean (average) value, μ, the standard deviation, σ, and the sample size, n (number of measurements taken). Then you can calculate the standard error and then the margin of error according to the following formulas:

standard error = σ/√n

margin of error = standard error * Z(0.95)

where Z(0.95) is the z-score corresponding to the confidence level of 95%. If you are using a different confidence level, you need to calculate the appropriate z-score instead of this value. But don't fret, our z-score calculator will make this easy for you!

How to find the Z(0.95) value? It is the value of z-score where the two-tailed confidence level is equal to 95%. It means that if you draw a normal distribution curve, the area between the two z-scores will be equal to 0.95 (out of 1).

How to calculate confidence interval?

To calculate a confidence interval (two-sided), you need to follow these 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 it! That was quite of a lot of computations, wasn't it? Luckily, our confidence level calculator can perform all of these calculations on its own.