# 95% Confidence Interval Calculator

Table of contents

95% confidence interval - formula and interpretationInterpretation of the 95% confidence intervalUsing 95% confidence interval calculatorConfidence interval calculatorsFAQsIf you want to solve some confidence interval problems, you're in the right place. Our **95% confidence interval calculator** will help you calculate this confidence interval and provide you with the essential knowledge! Read on to learn:

- What is the
`95%`

confidence interval formula; - What is the interpretation of the
`95%`

confidence interval (or any chosen one, to be honest); and - What is the p-value for the
`95`

percent confidence interval?

## 95% confidence interval - formula and interpretation

To calculate a `95%`

confidence interval, we first need to calculate the **standard error**. We can use the formula:

where:

- $SE$ - the standard error;
- $σ$ - the standard deviation; and
- $n$ - number of measurements (the size of the sample).

Now let's estimate **the margin of error**.

- $ME$ - margin of error;
- $Z(0.95)$ - z-score for
`95%`

confidence level; you'll find this value in the statistical tables.

The only thing left is to count **the lower and upper bounds** of our confidence interval. To do this, we will add and subtract the margin of error to the mean (average) - $μ$.

## Interpretation of the 95% confidence interval

How should you understand the results? Let's imagine George wants to calculate the mean height of his family members. Some relatives live very far, and George cannot measure them all. But he managed to get `30`

measurements, and the average height of those measurements was **172 cm** (`5 ft 7 in`

). He found out, that **the 95% confidence interval range is 161-183 cm** (`5 ft 3 in`

- `6 ft`

). Based on those measurements, he can be `95%`

sure that any family member's height falls between `162-183 cm`

.

## Using 95% confidence interval calculator

To use our tool:

- Look at the calculator panel on the left side of the screen.
- First, fill in the
**sample mean**(average) - x̅. - Now, fill in the standard deviation (
`s`

). - Input the sample size (
`n`

). - As it is the
`95`

percent confidence interval calculator, the confidence interval value is already there. But remember - you might change it any time. - The Z-score row will change accordingly to your chosen confidence interval.
- Enjoy the results! You might now see the margin of error, the
`95%`

confidence interval bounds, but also**a chart displaying the data.**

## Confidence interval calculators

Check out the rest of our **confidence interval tools**.

### How do I calculate a 95% confidence interval?

To count the `95%`

confidence interval:

- First, calculate the
**standard error**(`SE`

) and the**margin of error**(`ME`

).

**SE = σ/√n**

**ME = SE × Z(0.95)**

where**σ**is the standard deviation,**n**- sample size, Z(0.95) - z-score for 95% confidence interval. - Then determine the confidence interval range, using
**ME**and**μ**- the calculated average (mean).

**upper bound = μ + ME**

**lower bound = μ - ME**

### What is the p-value at 95 percent confidence interval?

The uncorrected p-value at 95% confidence interval is **0.05**.