## What is the ATANH Function in Excel?

The **ATANH **function is one of the math functions of Excel.

It Returns the** inverse hyperbolic tangent** of a number.

We can find this function in **Math & trig** category of insert function Tab.

## How to use **ATANH **function in excel

- Click on
**an empty cell**(like F5 )

2. Click on **fx icon** (or press** shift+F3**)

3. In the** insert function tab** you will see all functions

4. Select **math and trig** category

5. Select **ATANH **function

6. Then select **ok**

7. In the function arguments Tab you will see ** ATANH **function

8. Number Is any real number **between -1 and 1** excluding -1 and 1

9. You will see **results **in the formula result section

## Examples of **ATANH** function in Excel

- To find the hyperbolic arctangent of a number in cell A1, use the formula =ATANH(A1).
- To calculate the inverse hyperbolic tangent of the sum of two numbers in cells A1 and B1, use the formula =ATANH(A1+B1).
- To calculate the inverse hyperbolic tangent of the difference between two numbers in cells A1 and B1, use the formula =ATANH(A1-B1).
- To calculate the inverse hyperbolic tangent of the product of two numbers in cells A1 and B1, use the formula =ATANH(A1*B1).
- To calculate the inverse hyperbolic tangent of the quotient of two numbers in cells A1 and B1, use the formula =ATANH(A1/B1).
- To calculate the inverse hyperbolic tangent of the square root of a number in cell A1, use the formula =ATANH(SQRT(A1)).
- To calculate the inverse hyperbolic tangent of the absolute value of a number in cell A1, use the formula =ATANH(ABS(A1)).
- To calculate the inverse hyperbolic tangent of the minimum value between two numbers in cells A1 and B1, use the formula =ATANH(MIN(A1,B1)).
- To calculate the inverse hyperbolic tangent of the maximum value between two numbers in cells A1 and B1, use the formula =ATANH(MAX(A1,B1)).
- To calculate the inverse hyperbolic tangent of the average of three numbers in cells A1, B1, and C1, use the formula =ATANH((A1+B1+C1)/3).

**Example 1:**

**How to use ATANH function in excel**

You can see examples of ATANH function below:

**atanh**(-0.5) ----->>>>answer is -0.549
**atanh**(-0.2) ----->>>>answer is -0.202
**atanh**(0) ----->>>>answer is 0
**atanh**(0.2) ----->>>>answer is 0.202
**atanh**(0.5) ----->>>>answer is 0.549

## ATANH Function in Excel: What It Is and How It Works

The ATANH function in Excel returns the inverse hyperbolic tangent of a given number. The inverse hyperbolic tangent of a number is the value whose hyperbolic tangent is equal to that number. In other words, if x = tanh(y), then y = atanh(x). The ATANH function takes only one argument, which must be between -1 and 1.

For example, if you want to find the hyperbolic tangent of 0.5, you can use the TANH function in Excel: `=TANH(0.5)`

. This will return 0.462117157. If you then want to find the inverse hyperbolic tangent of 0.462117157, you can use the ATANH function: `=ATANH(0.462117157)`

. This will return 0.549306144, which is the value whose hyperbolic tangent is equal to 0.462117157.

## Understanding the Syntax of the ATANH Function in Excel

The syntax of the ATANH function in Excel is as follows:

`=ATANH(number)`

The only argument for the ATANH function is the number for which you want to find the inverse hyperbolic tangent. This argument must be between -1 and 1.

For example, if you want to find the inverse hyperbolic tangent of 0.3, you can use the following formula: `=ATANH(0.3)`

. This will return 0.309519604, which is the value whose hyperbolic tangent is equal to 0.3.

## What Values Can be Used as Arguments for the ATANH Function in Excel?

The ATANH function in Excel takes only one argument, which is the number for which you want to find the inverse hyperbolic tangent. This argument must be between -1 and 1.

For example, if you want to find the inverse hyperbolic tangent of 0.7, you can use the following formula: `=ATANH(0.7)`

. This will return 0.867300527, which is the value whose hyperbolic tangent is equal to 0.7.

If the argument for the ATANH function is outside the range of -1 to 1, the function will return a #NUM! error.

## Range of Output for the ATANH Function in Excel

The output of the ATANH function in Excel can range from negative infinity to positive infinity. However, the argument for the function must be between -1 and 1.

For example, if you want to find the inverse hyperbolic tangent of 0.9, you can use the following formula: `=ATANH(0.9)`

. This will return 1.47221949, which is the value whose hyperbolic tangent is equal to 0.9.

If the argument for the ATANH function is outside the range of -1 to 1, the function will return a #NUM! error.

## Calculating the Inverse Hyperbolic Tangent with the ATANH Function in Excel

The inverse hyperbolic tangent of a number can be calculated using the ATANH function in Excel. The syntax of the function is:

`=ATANH(number)`

Where “number” is the value whose inverse hyperbolic tangent needs to be calculated.

For example, if you want to calculate the inverse hyperbolic tangent of 0.5, you can use the following formula: `=ATANH(0.5)`

. This will return approximately 0.549306144, which is the angle whose hyperbolic tangent is equal to 0.5.

## Negative Numbers and the ATANH Function in Excel

The ATANH function in Excel can be used with negative numbers as well as positive numbers. The function returns the inverse hyperbolic tangent of the input number, regardless of its sign.

For example, if you want to calculate the inverse hyperbolic tangent of -0.7, you can use the following formula: `=ATANH(-0.7)`

. This will return approximately -0.867300527.

## Using Zero with the ATANH Function in Excel

The ATANH function in Excel can be used with zero as an input. When the input number is zero, the function returns zero.

For example, if you want to calculate the inverse hyperbolic tangent of 0, you can use the following formula: `=ATANH(0)`

. This will return 0.

## Non-Numeric Values and the ATANH Function in Excel

The ATANH function in Excel can only be used with numeric values. If you try to use the function with a non-numeric value, such as text or logical values, Excel will return a #VALUE! error.

For example, if you want to calculate the inverse hyperbolic tangent of the text string “hello”, you will get a #VALUE! error if you use the following formula: `=ATANH("hello")`

.

## Differences Between the ATANH and TANH Functions in Excel

The ATANH function in Excel calculates the inverse hyperbolic tangent of a number, while the TANH function calculates the hyperbolic tangent of a number. The two functions are related by the equation:

tanh(x) = sinh(x) / cosh(x)

atanh(x) = 0.5 * ln((1 + x) / (1 – x))

For example, if you want to calculate the hyperbolic tangent of 0.5, you can use the following formula: `=TANH(0.5)`

. This will return approximately 0.462117157. If you then want to find the inverse hyperbolic tangent of this value, you can use the following formula: `=ATANH(0.462117157)`

. This will return approximately 0.549306144.

## Converting Output from the ATANH Function to Degrees or Radians in Excel

The output of the ATANH function in Excel is a numeric value that represents the angle whose hyperbolic tangent is equal to the input value. To convert this output to degrees or radians, you can use the RADIANS or DEGREES function in Excel.

For example, if you want to calculate the inverse hyperbolic tangent of 0.5 and convert the output to degrees, you can use the following formula: `=DEGREES(ATANH(0.5))`

. This will return approximately 31.6891053 degrees. If you want to convert the output to radians instead, you can use the following formula: `=RADIANS(ATANH(0.5))`

. This will return approximately 0.552449964 radians.

## The Inverse of the ATANH Function in Excel

The inverse of the ATANH function in Excel is the hyperbolic tangent of a number. In other words, if x = atanh(y), then y = tanh(x). This relationship can be used to check the validity of the output of the ATANH function.

For example, if you want to calculate the inverse hyperbolic tangent of 0.7 and then find the hyperbolic tangent of the result, you can use the following formula: `=TANH(ATANH(0.7))`

. This will return approximately 0.7, which confirms that the output of the ATANH function is correct.

## Plotting the Graph of the ATANH Function in Excel

To plot the graph of the ATANH function in Excel, you can create a table with input values and corresponding output values. You can then use Excel’s charting tools to create a line chart.

For example, you can create a table with input values from -1 to 1 in increments of 0.1, like this:

Input | Output |
---|---|

-1 | -Infinity |

-0.9 | -1.47221949 |

-0.8 | -1.09861229 |

-0.7 | -0.867300527 |

-0.6 | -0.684136704 |

-0.5 | -0.549306144 |

-0.4 | -0.42364893 |

-0.3 | -0.295875854 |

-0.2 | -0.147558437 |

-0.1 | -0.049587065 |

0 | 0 |

0.1 | 0.049587065 |

0.2 | 0.147558437 |

0.3 | 0.295875854 |

0.4 | 0.42364893 |

0.5 | 0.549306144 |

0.6 | 0.684136704 |

0.7 | 0.867300527 |

0.8 | 1.09861229 |

0.9 | 1.47221949 |

1 | Infinity |

You can then select the table and create a line chart, with input values on the x-axis and output values on the y-axis, to visualize the graph of the ATANH function.

## Statistical Analysis and the ATANH Function in Excel

The ATANH function in Excel can be used in statistical analysis to transform data that follows a logistic distribution. The inverse hyperbolic tangent transformation can be used to stabilize the variance of the data, which makes it more suitable for certain statistical tests.

For example, if you have a set of data that follows a logistic distribution, you can transform it using the ATANH function in Excel, like this: `=ATANH(data)`

. This will return a new set of data that has been transformed using the inverse hyperbolic tangent function.

## Relationship between the ATANH Function and Logarithmic Functions in Excel

There is a relationship between the ATANH function and logarithmic functions in Excel. The inverse hyperbolic tangent of a number can be expressed as the following natural logarithm:

atanh(x) = 0.5 * ln((1 + x) / (1 – x))

This equation shows that the inverse hyperbolic tangent of a number can be expressed as a ratio of natural logarithms.

For example, if you want to calculate the inverse hyperbolic tangent of 0.8, you can use the following formula: `=0.5*LN((1+0.8)/(1-0.8))`

. This will return approximately 1.09861229, which is the same value as `=ATANH(0.8)`

.

## Exploring the Relationship between the ATANH Function and Trigonometric Functions in Excel

There is a relationship between the ATANH function and trigonometric functions in Excel. The inverse hyperbolic tangent of a number can be expressed in terms of the inverse tangent of a complex number.

atanh(x) = 1/2 * ln((1+x)/(1-x)) = 1/2 * arctan(i*x)

This equation shows that the inverse hyperbolic tangent of a number can be expressed as half of the arctangent of a complex number.

For example, if you want to calculate the inverse hyperbolic tangent of 0.6, you can use the following formula: `=1/2*ATAN(IMAGINARY(0.6)/REAL(0.6))`

. This will return approximately 0.684136704, which is the same value as `=ATANH(0.6)`

.

## Complex Analysis and the ATANH Function in Excel

The ATANH function in Excel can be used in complex analysis to express the inverse hyperbolic tangent of a complex number. The inverse hyperbolic tangent of a complex number can be expressed in terms of logarithmic functions.

For example, if you want to calculate the inverse hyperbolic tangent of a complex number, such as 1 + 2i, you can use the following formula: `=0.5*LOG((1+2i)/(1-2i))`

. This will return approximately 1.107148718 – 0.463647608i, which is the value whose hyperbolic tangent is equal to 1 + 2i.

## Combining the ATANH Function in Excel with Other Excel Functions

The ATANH function in Excel can be combined with other Excel functions to perform more complex calculations. For example, you can use the ATANH function in conjunction with the SUM function to calculate the sum of the inverse hyperbolic tangents of a set of numbers.

For example, if you have a set of numbers in cells A1:A5 and you want to calculate the sum of their inverse hyperbolic tangents, you can use the following formula: `=SUM(ATANH(A1:A5))`

. This will return the sum of the inverse hyperbolic tangents of the numbers in cells A1:A5.

## Troubleshooting Errors Related to the ATANH Function in Excel

If you encounter errors related to the ATANH function in Excel, there are several things you can do to troubleshoot the problem. One common error is the #NUM! error, which occurs when the input value to the ATANH function is outside the range of -1 to 1.

For example, if you try to calculate the inverse hyperbolic tangent of a number greater than 1 or less than -1 using the ATANH function, you will get a #NUM! error. To fix this error, make sure that the input value to the ATANH function is within the range of -1 to 1.

Another error is the #VALUE! error, which occurs when the input to the ATANH function is not a numeric value. To fix this error, make sure that the input value to the ATANH function is a numeric value.

## More Information about the ATANH Function in Excel

The ATANH function in Excel is part of the mathematical functions group of functions. It calculates the inverse hyperbolic tangent of a number. The ATANH function takes one argument, which is the input value whose inverse hyperbolic tangent needs to be calculated. The function returns a numeric value that represents the angle whose hyperbolic tangent is equal to the input value.

The syntax of the ATANH function is:

`=ATANH(number)`

Where “number” is the value whose inverse hyperbolic tangent needs to be calculated.

For more information about the ATANH function in Excel, refer to the Excel Help documentation or other Excel references.

- ATAN function
- EXP function
- TAN function
- TANH function