Daily DAX : Day 416 ATANH

Power BI DAX – ATANH Function

ATANH returns the inverse hyperbolic tangent of a number.

Syntax

ATANH(number)

Parameter	Description
number	A real number between -1 and 1 (inclusive: -1 ≤ number ≤ 1). The value must be in this range, otherwise the function returns an error.

Return Value

A decimal number representing the inverse hyperbolic tangent of the input.

Key Properties

• ATANH is the inverse of TANH: ATANH(TANH(x)) = x
• ATANH(-x) = -ATANH(x) → it is an odd function
• Domain: -1 ≤ number ≤ 1
• Range: All real numbers (-∞ to +∞)

Common Use Cases in Power BI / Analysis Services

ATANH is relatively rare in typical business reports, but very useful in specific advanced scenarios:

1. Financial modeling – when working with Fisher transformations of correlation coefficients (common in portfolio analysis).
2. Statistical analysis – transforming correlation coefficients to make them normally distributed for hypothesis testing.
3. Scientific & engineering calculations – any model involving hyperbolic functions (e.g., catenary curves, certain physics formulas).
4. Data normalization / scaling – mapping bounded values (-1 to 1) to an unbounded scale.

Example 1: Fisher Transformation of a Correlation

Convert a Pearson correlation coefficient (r) to a z-score:

FisherZ = 0.5 * LN( (1 + [Correlation]) / (1 - [Correlation]) )
        = ATANH([Correlation])   // Equivalent and simpler!
        

Example 2: Simple Calculated Column

Hyperbolic Inverse = ATANH([Value])   // Where [Value] is between -1 and 1
        

Example 3: Handling Errors Gracefully

Safe ATANH = 
IF(
    ABS([Value]) <= 1,
    ATANH([Value]),
    BLANK()   // or some default value
)
        

Summary: Use ATANH whenever you need to reverse a hyperbolic tangent operation or perform a Fisher transformation on correlation coefficients. It’s a niche but powerful function in advanced analytical models inside Power BI.