Confidence Interval Calculator

Our confidence interval calculator is a tool that allows you to find the confidence interval of a sample. Simply just enter sample mean, Size & standard deviation & get value of confidence interval.

Sample Mean (x)
Sample Size (n)
Standard Deviation (s)
Confidence Level

The confidence interval calculator on SearchEngineReports is an easy-to-use utility that requires minimal efforts from the users’ end. There is no need to memorize the formula or the z-values for confidence intervals anymore, as this automated confidence limit calculator is here for your rescue. You can calculate the confidence interval for population mean by following the few easy steps mentioned below.

  • Access the confidence interval calculator by visiting
  • Enter the sample mean, size, and standard deviation in the boxes provided on this confidence interval calculator.
  • Set the confidence level.
  • Click on the “Calculate” button and get results.

A confidence interval is naturally connected to the confidence level. In simple words, the confidence interval is the level of uncertainty existing in any particular statistic. The confidence interval includes a range of values that has the confidence to include the population value at a particular degree of confidence. A margin of error is used alongside the confidence intervals to calculate the confidence level you have in the results of a survey or poll. The results are considered to reflect the expectancy to find if it was possible to conduct a survey on the entire population.

Confidence Interval Formula

The formula for calculating confidence interval is:

X ± ZS√n

Each symbol in this formula represents the following factors:

X = Sample Mean

Z = Z score from the table

S = Standard deviation

n = Sample size

Sample size

The sample size is denoted as “n” in the formula of the confidence interval. The confidence intervals’ width decreases as the sample size is increased, given that all other quantities remain the same. The increase in sample size implies better inference as it contains more information.

Standard deviation

In the above formula, the standard deviation is abbreviated as S. As the standard deviation increases, the width of the confidence intervals also increases. Standard deviation is basically an estimate of how much data differs naturally, and it becomes difficult to estimate but possible with the help of population mean calculator where every member of a population can be sampled. The population if the standard deviation is more, but large amounts of data aren’t available.

Confidence level

It is essential to improve the data quality while using a higher confidence level, as, without it, the margin of error would be greater. If all the constraints remain fixed, the confidence level decrease will cause a decrease in the confidence interval.

The confidence intervals mainly used for solving a particular statistic are 95% and 99%. For each confidence interval, there is a z-value or score used in the confidence interval formula. The common z-values for confidence intervals are described in the table below.

Confidence Interval Z
80% 1.282
85% 1.440
90% 1.645
95% 1.960
99% 2.576
99.5% 2.807
99.9% 3.291

Calculate 95 Confidence Interval Manually

The manual calculation of confidence interval is a lengthy and complex process. You might need a notepad, pen, and calculator to write down the formula and solve the data to calculate the confidence interval manually. Let’s look at an example of calculating confidence intervals manually.

n = 40

S = 15

X = 160

Confidence interval = 95%

While having these stats, you can use the formula and the Z-value table to calculate the confidence interval. At the confidence interval of 95%, the z score is 1.960 if you look at the table above. The next thing is to put these values in the formula.

=X ± ZS√n

= 160 ± 1.960 15√40

= 160 ± 4.6485

The confidence interval for this problem is from 155.3515 to 164.6485.

This whole process can end up consuming an ample amount of time. Therefore, the easy way out of this nuisance is the 95% confidence interval calculator. In the example above, you were asked to calculate 95 confidence interval, and it ended up taking a lot of time and effort. If you use an online confidence level calculator instead of relying on the manual calculation, you can get the same results within a matter of seconds.

If we look at the confidence intervals’ width, they could be either wide or narrow. More information can be obtained about the value of a population parameter with a narrow confidence interval. Hence, it’s essential to have confidence intervals as narrow as possible. By looking at the 95 confidence interval formula mentioned above, we can figure out the factors that affect confidence intervals.