# ATANH Function in Excel

### 🌟 Part 1: Introduction

#### Definition

The ATANH function in Microsoft Excel returns the inverse hyperbolic tangent of a number.

#### Purpose

The primary purpose of the ATANH function is to compute the value whose hyperbolic tangent is a given number. In other words, if you apply the ATANH function to the result of the TANH function, you’ll return the original number: ATANH(TANH(number)) equals number.

#### Syntax & Arguments

syntax
`ATANH(number)`
• number: This is a required argument. It represents any number between -1 and 1, excluding the values -1 and 1.

#### Return Value

The function returns the inverse hyperbolic tangent of the provided number.

#### Remarks

The number provided as an argument must lie between -1 and 1 but cannot be -1 or 1.

### 🌟 Part 2: Examples

🔍 Example 1

• Purpose: Calculate the inverse hyperbolic tangent for a business’s growth rate.
• Data & Formulas:
ABC
1Growth RateFormulaResult
20.45=ATANH(A2)0.480472
30.55=ATANH(A3)0.587787
40.65=ATANH(A4)0.732668
• Explanation: This example calculates the inverse hyperbolic tangent of a business’s growth rate. It can be used to analyze and compare growth rates in a hyperbolic context, which might be helpful in specific financial or economic models.

🔍 Example 2

• Purpose: Analyzing the efficiency of a new marketing strategy.
• Data & Formulas:
ABC
1Marketing EfficiencyFormulaResult
20.25=ATANH(A2)0.2554128
30.35=ATANH(A3)0.3670238
40.40=ATANH(A4)0.4236489
• Explanation: This example calculates the inverse hyperbolic tangent of a company’s marketing efficiency after implementing a new strategy. The results can be used to gauge the strategy’s effectiveness in a hyperbolic context.

🔍 Example 3

• Purpose: Evaluating the response rate of a customer feedback survey.
• Data & Formulas:
ABC
1Response RateFormulaResult
20.60=ATANH(A2)0.6931472
30.70=ATANH(A3)0.8673005
40.75=ATANH(A4)0.9729551
• Explanation: By calculating the inverse hyperbolic tangent of the response rate, businesses can analyze the effectiveness of their customer feedback mechanisms in a unique mathematical context.

🔍 Example 4

• Purpose: Assessing the impact of a training program on employee productivity.
• Data & Formulas:
ABC
1Productivity IncreaseFormulaResult
20.15=ATANH(A2)0.1511823
30.20=ATANH(A3)0.2027326
40.30=ATANH(A4)0.3095196
• Explanation: This example evaluates the impact of a new training program on employee productivity. The ATANH function provides a unique perspective on the relative increase in productivity.

🔍 Example 5

• Data & Formulas:
ABC
1Conversion RateFormulaResult
20.10=ATANH(A2)0.1003353
30.12=ATANH(A3)0.1205812
40.14=ATANH(A4)0.1413296
• Explanation: This example calculates the inverse hyperbolic tangent of the conversion rates from an online ad campaign. It provides a unique mathematical perspective on the campaign’s effectiveness.

🔍 Example 6: Using ATANH with IF

• Purpose: Determine if the inverse hyperbolic tangent of a number is more significant than a threshold.
• Data & Formulas:
ABC
1ValueFormulaResult
20.45=IF(ATANH(A2)>0.4, “Above”, “Below”)Above
30.35=IF(ATANH(A3)>0.4, “Above”, “Below”)Below
40.55=IF(ATANH(A4)>0.4, “Above”, “Below”)Above
• Explanation: This example uses the ATANH function nested within an IF function to determine if the inverse hyperbolic tangent of a number is above or below a specified threshold. It can be helpful in scenarios where certain operations or decisions are contingent upon a value surpassing a limit.

🔍 Example 7: Using ATANH with SUM

• Purpose: Sum the inverse hyperbolic tangents of multiple values.
• Data & Formulas:
ABC
1ValueFormulaResult
20.25=ATANH(A2)0.2554128
30.30=ATANH(A3)0.3095196
4=SUM(B2:B3)0.5649324
• Explanation: Using the ATANH function in conjunction with the SUM function, we can aggregate the inverse hyperbolic tangents of multiple values. This can be useful in scenarios where cumulative measurements are required, such as statistical analyses.

🔍 Example 8: Using ATANH with VLOOKUP

• Purpose: Find the inverse hyperbolic tangent of a specific value from a table.
• Data & Formulas:
ABCDE
1IDValueFormulaResult
21010.40
31020.50
41030.60
5102=ATANH(VLOOKUP(B5, A2:B4, 2, FALSE))0.5493061
• Explanation: This example demonstrates how to use the ATANH function with the VLOOKUP function to find the inverse hyperbolic tangent of a specific value from a table. It’s beneficial when you have a large dataset and need to quickly retrieve and compute a value.

🔍 Example 9: Using ATANH with AVERAGE

• Purpose: Calculate the average inverse hyperbolic tangent from multiple values.
• Data & Formulas:
ABC
1ValueFormulaResult
20.20=ATANH(A2)0.2027326
30.30=ATANH(A3)0.3095196
4=AVERAGE(B2:B3)0.2561261
• Explanation: This example calculates the average inverse hyperbolic tangent from multiple values. It’s helpful in scenarios requiring an average measurement, such as market research analyses.

🔍 Example 10: Using ATANH with MAX

• Purpose: Determine the maximum inverse hyperbolic tangent from a set of values.
• Data & Formulas:
ABC
1ValueFormulaResult
20.10=ATANH(A2)0.1003353
30.15=ATANH(A3)0.1511823
4=MAX(B2:B3)0.1511823
• Explanation: Using the ATANH function with the MAX function, this example determines the maximum inverse hyperbolic tangent from a set of values. This can be beneficial in scenarios where peak values are of interest.

🔍 Example 11: Using ATANH with MIN

• Purpose: Determine the minimum inverse hyperbolic tangent from a set of values.
• Data & Formulas:
ABC
1ValueFormulaResult
20.05=ATANH(A2)0.0501674
30.10=ATANH(A3)0.1003353
4=MIN(B2:B3)0.0501674
• Explanation: This example determines the minimum inverse hyperbolic tangent from a set of values using the ATANH function nested with the MIN function. It’s helpful in scenarios where the most negligible value is of interest.

🔍 Example 12: Using ATANH with ROUND

• Purpose: Round the result of the ATANH function to a specified number of decimal places.
• Data & Formulas:
ABC
1ValueFormulaResult
20.12=ROUND(ATANH(A2), 2)0.12
30.14=ROUND(ATANH(A3), 2)0.14
40.16=ROUND(ATANH(A4), 2)0.16
• Explanation: This example rounds the result of the ATANH function to two decimal places using the ROUND function. It’s beneficial in scenarios where precision is essential, but too many decimal places can be cumbersome.

### 🌟 Part 3: Tips and Tricks

1. Ensure the number you input into the ATANH function is between -1 and 1 but not equal to these values.
2. The ATANH function can benefit advanced mathematical models, especially those involving hyperbolic functions.
3. Always cross-check the results, especially when using the function for critical business decisions.