diff --git a/CONTRIBUTING.md b/CONTRIBUTING.md
index 262462e..fd92d0a 100644
--- a/CONTRIBUTING.md
+++ b/CONTRIBUTING.md
@@ -8,25 +8,25 @@ Thank you for considering contributing to FatPy, a Python package for fatigue li
 
 Get started contributing to FatPy in a few simple steps:
 
-1. **Fork the Repository**  
+1. **Fork the Repository**
 Create a personal copy on GitHub.
-2. **Clone Your Fork**  
+2. **Clone Your Fork**
 
 ```bash
 git clone https://github.com/your-username/FatPy.git  # Clone your fork
 ```
 
-3. **Create a Branch**  
+3. **Create a Branch**
 
 ```bash
 git checkout -b my-feature-branch  # Create a new branch for your feature
 ```
 
-4. **Implement the Feature**  
+4. **Implement the Feature**
 Write code to pass your tests.
-5. **Write Tests for Your Feature**  
+5. **Write Tests for Your Feature**
 Define expected behavior first.
-6. **Submit a Pull Request**  
+6. **Submit a Pull Request**
 Share your changes for review.
 
 ## :hammer_and_wrench: Development Setup
@@ -63,7 +63,7 @@ FatPy emphasizes comprehensive testing to ensure code reliability and quality. A
 ### Testing Guidelines
 
 - **Write comprehensive tests** - Cover all functionality with unit and integration tests
-- **Test edge cases** - Include boundary conditions and error scenarios  
+- **Test edge cases** - Include boundary conditions and error scenarios
 - **Maintain test coverage** - Aim for high coverage to ensure reliability
 - **Keep tests updated** - Update tests when modifying existing functionality
 - **Use clear test names** - Write descriptive test names and docstrings
@@ -92,7 +92,7 @@ FatPy aims for high code quality utilizing these tools:
 - **MyPy**  - Static type checking for reliability.
 - **Pre-commit** - Automated checks before commits.
 
-Follow our coding standards for contributions, see **[Code Style Guide :arrow_right:](https://faberorg.github.io/FatPy/development/code_style/)**  
+Follow our coding standards for contributions, see **[Code Style Guide :arrow_right:](https://faberorg.github.io/FatPy/development/code_style/)**
 
 ### Running Code Quality Checks
 
@@ -117,11 +117,11 @@ pre-commit run --all-files
 
 Keep FatPy’s documentation clear and up-to-date with these guidelines:
 
-- **API Changes**  
+- **API Changes**
 Update documentation for any API modifications.
-- **Docstrings**  
+- **Docstrings**
 Add docstrings following Google style to all new code.
-- **Examples**  
+- **Examples**
 Include examples and mathematical formulas where helpful to aid users.
 
 Learn best practices and guidelines for documentation, see **[Documentation Guide :arrow_right:](https://faberorg.github.io/FatPy/development/documentation/)**
@@ -140,15 +140,15 @@ mkdocs serve
 
 Submit a high-quality pull request with these steps:
 
-1. **Run Tests and Checks**  
+1. **Run Tests and Checks**
    Ensure tests pass and code quality checks succeed.
-2. **Update Documentation**  
+2. **Update Documentation**
    Reflect changes in relevant docs.
-3. **Link Issues**  
+3. **Link Issues**
    Reference related GitHub issues.
-4. **Follow guidelines**  
+4. **Follow guidelines**
    Make sure your code follows the project's style guidelines.
-5. **Await Review**  
+5. **Await Review**
    Respond to feedback from maintainers.
 
 ## :book: Code of Conduct
@@ -161,11 +161,11 @@ Understand our expectations for collaboration, see **[Code of Conduct :arrow_rig
 
 Join discussion, create an issue or reach out to maintainers:
 
-- :speech_balloon:  **[GitHub Discussions :arrow_right:](https://github.com/faberorg/FatPy/discussions)**  
+- :speech_balloon:  **[GitHub Discussions :arrow_right:](https://github.com/faberorg/FatPy/discussions)**
     Join for community support.
-- :beetle: **[Report an Issue :arrow_right:](https://github.com/faberorg/fatpy/issues)**  
+- :beetle: **[Report an Issue :arrow_right:](https://github.com/faberorg/fatpy/issues)**
     Create an issue on our GitHub repository for bugs or questions.
-- :envelope: **[Contact our Team :arrow_right:](https://faberorg.github.io/FatPy/contact/)**  
+- :envelope: **[Contact our Team :arrow_right:](https://faberorg.github.io/FatPy/contact/)**
     Visit our contact page.
 
 Thank you for contributing to FatPy!
diff --git a/docs/contact.md b/docs/contact.md
index c1165bd..b783000 100644
--- a/docs/contact.md
+++ b/docs/contact.md
@@ -28,13 +28,13 @@ Check out these resources:
 
 Use GitHub as a main way to collaborate, discuss and improve the FatPy package.
 
-- **Explore the Repository**:  
+- **Explore the Repository**:
 Visit our [:fontawesome-brands-github: GitHub repository](https://github.com/faberorg/fatpy) to access the source code.
 
-- **Contribute**:  
+- **Contribute**:
 Follow our [:fontawesome-solid-handshake: Contribution Guidelines](development/contributing.md) to help improve FatPy.
 
-- **Collaborate**:  
+- **Collaborate**:
 Join our [:fontawesome-solid-comment-dots: Discussions](https://github.com/faberorg/fatpy/discussions) or [:fontawesome-solid-bug: Report issues](https://github.com/faberorg/fatpy/issues).
 
 ---
@@ -48,6 +48,6 @@ You can also contact our team directly! Here is a list of active members:
 
 ---
 
-Thank you for reaching out and contributing your ideas!  
-Your feedback and suggestions help us grow and improve.  
+Thank you for reaching out and contributing your ideas!
+Your feedback and suggestions help us grow and improve.
 We appreciate your involvement in the FatPy and FABER communities!
diff --git a/docs/development/ci_cd.md b/docs/development/ci_cd.md
index 3b5d045..a5c58fa 100644
--- a/docs/development/ci_cd.md
+++ b/docs/development/ci_cd.md
@@ -120,7 +120,7 @@ Status badges are displayed in the README.md:
       - Check Python version differences
       - Check dependency versions
       - Review test logs for environment-specific issues
-  
+
 === "**Type Errors**"
 
     - **Issue**: Mypy reports type errors
diff --git a/docs/development/documentation.md b/docs/development/documentation.md
index eece616..b783cd1 100644
--- a/docs/development/documentation.md
+++ b/docs/development/documentation.md
@@ -108,15 +108,15 @@ Follow these guidelines to create clear and effective documentation for FatPy.
 
 ### **General Guidelines**
 
-- **Clear Language**  
+- **Clear Language**
   Use concise, straightforward wording.
-- **Examples**  
+- **Examples**
   Include practical code or use-case examples, where possible.
-- **Related Links**  
+- **Related Links**
   Reference related documentation.
-- **Headers**  
+- **Headers**
   Organize content with clear section headings.
-- **Mathematical Formulas**  
+- **Mathematical Formulas**
   Use LaTeX for mathematical notation where appropriate.
 
 ---
@@ -174,15 +174,15 @@ Consistent naming is crucial for code readability and maintainability. Follow th
     - **`fat`**: fatigue (e.g., `fat_limit` for fatigue limit)
     - **`frac`**: fracture (e.g., `frac_toughness` for fracture toughness)
 
-    Common names and material parameters:  
-    - `first_principal_stress`, `second_principal_stress` and `third_principal_stress`  
-    - `elastic_modulus`, `shear_modulus` and `poisson_ratio`  
-    - `ultimate_tensile_strength` and `yield_strength`  
+    Common names and material parameters:
+    - `first_principal_stress`, `second_principal_stress` and `third_principal_stress`
+    - `elastic_modulus`, `shear_modulus` and `poisson_ratio`
+    - `ultimate_tensile_strength` and `yield_strength`
 
     !!! warning "Clarity First"
         If an abbreviation makes the code harder to understand for someone new to the specific module or fatigue in general, prefer the full name. Document any project-specific abbreviations clearly.
 
-Learn more about the naming conventions form our discussion page:  
+Learn more about the naming conventions form our discussion page:
 
 [:simple-github::fontawesome-solid-comment-dots: Naming Conventions for FatPy Functions & Parameters #18](https://github.com/faberorg/FatPy/discussions/18)
 
@@ -209,7 +209,7 @@ Use LaTeX for mathematical formulas. This allows for clear rendering of equation
     Hooke's Law can be expressed as $\sigma = E \cdot \epsilon$.
     ```
 
-    **Rendered output:**  
+    **Rendered output:**
     Hooke's Law can be expressed as $\sigma = E \cdot \epsilon$.
 
 === "Block Syntax"
@@ -218,7 +218,7 @@ Use LaTeX for mathematical formulas. This allows for clear rendering of equation
     **How to write it:**
     ``` latex title="Block syntax"
     % This line is empty
-    $$ 
+    $$
     \sigma_{eq} = \sqrt{3J_2} = \sqrt{\frac{3}{2}s_{ij}s_{ij}}
     $$
     % This line is empty
@@ -231,7 +231,7 @@ Use LaTeX for mathematical formulas. This allows for clear rendering of equation
     $$
 
 === "Display Complex Expression"
-    For more complex expressions, like summations, matrices, or a sequence of aligned equations.  
+    For more complex expressions, like summations, matrices, or a sequence of aligned equations.
 
     This example shows Miner's rule for damage accumulation:
 
@@ -289,7 +289,7 @@ API documentation is automatically generated from docstrings using mkdocstrings.
 1. All public functions, classes, and modules must have Google-style docstrings.
 2. Type hints should be used for all function parameters and return values.
 3. Examples should be included in docstrings where appropriate.
-4. Mathematical formulas should use LaTeX syntax within docstrings, e.g.:  
+4. Mathematical formulas should use LaTeX syntax within docstrings, e.g.:
     `$$ \sigma = \sqrt{x^2} $$`
 
 View the generated API documentation: **[:fontawesome-solid-book-open: API Reference](../api/index.md)**
@@ -298,11 +298,11 @@ View the generated API documentation: **[:fontawesome-solid-book-open: API Refer
 
 To add new documentation pages, follow these steps:
 
-- **Create File**  
+- **Create File**
   Add a new Markdown file in the appropriate directory (e.g., `docs/`).
-- **Update Navigation**  
+- **Update Navigation**
   Include the file in `mkdocs.yml` under the `nav` section.
-- **Format Content**  
+- **Format Content**
   Use headers, code blocks, and consistent Markdown formatting.
 
 ??? note "Documentation Deployment"
diff --git a/docs/development/index.md b/docs/development/index.md
index 0ec87d3..4cff1fc 100644
--- a/docs/development/index.md
+++ b/docs/development/index.md
@@ -15,24 +15,24 @@ This section provides comprehensive resources to help you contribute to FatPy, a
 
 New to FatPy? Start with these resources to set up your environment and understand how to contribute effectively:
 
-- :fontawesome-solid-download: **[Installation Guide](install.md)**  
+- :fontawesome-solid-download: **[Installation Guide](install.md)**
   Set up your development environment for FatPy.
-- :fontawesome-solid-handshake: **[Contributing Guide](contributing.md)**  
+- :fontawesome-solid-handshake: **[Contributing Guide](contributing.md)**
   Learn how to contribute code, documentation, or ideas to the project.
-- :fontawesome-solid-book: **[Code of Conduct](code_of_conduct.md)**  
+- :fontawesome-solid-book: **[Code of Conduct](code_of_conduct.md)**
   Understand our community standards for respectful collaboration.
 
 ## :fontawesome-solid-code: Development Resources
 
 Deepen your understanding of FatPy development with these resources:
 
-- :fontawesome-solid-code: **[Code Style](code_style.md)**  
+- :fontawesome-solid-code: **[Code Style](code_style.md)**
   Follow our coding standards for consistent, high-quality code.
-- :fontawesome-solid-file-pen: **[Documentation](documentation.md)**  
+- :fontawesome-solid-file-pen: **[Documentation](documentation.md)**
   Learn best practices for writing and maintaining FatPy documentation.
-- :fontawesome-solid-vial: **[Testing](testing.md)**  
+- :fontawesome-solid-vial: **[Testing](testing.md)**
   Understand how to write and run tests to ensure code reliability.
-- :material-cogs: **[CI/CD Process](ci_cd.md)**  
+- :material-cogs: **[CI/CD Process](ci_cd.md)**
   Explore our continuous integration and deployment workflow.
 
 ??? tip "Additional resources"
@@ -45,32 +45,32 @@ Get a detailed overview of FatPy’s modules and functions, visit **[API Referen
 
 Follow our development workflow:
 
-1. **Set Up Your Environment**  
+1. **Set Up Your Environment**
    :fontawesome-solid-download: [Installation Guide](install.md)
-2. **Create a Feature Branch**  
+2. **Create a Feature Branch**
 
     ```bash
     git checkout -b feature-name
     ```
 
-3. **Implement the Feature**  
+3. **Implement the Feature**
     Follow the [Code Style Guide](code_style.md).
-4. **Write and Run Tests**  
+4. **Write and Run Tests**
     :fontawesome-solid-vial: [Testing Guide](testing.md)
-5. **Document your Changes**  
+5. **Document your Changes**
     Use [Documentation](documentation.md) resources!
-6. **Submit a pull request**  
+6. **Submit a pull request**
     :fontawesome-solid-handshake: [Contributing Guide](contributing.md)
 
 ## :material-help-box-outline: Getting Help
 
 Need assistance with FatPy development? Reach out through these channels:
 
-- :simple-github:  **[GitHub Discussions](https://github.com/faberorg/FatPy/discussions)**  
+- :simple-github:  **[GitHub Discussions](https://github.com/faberorg/FatPy/discussions)**
     Join for community support.
-- :fontawesome-solid-bug: **[Report an Issue](https://github.com/faberorg/fatpy/issues)**  
+- :fontawesome-solid-bug: **[Report an Issue](https://github.com/faberorg/fatpy/issues)**
     Create an issue on our GitHub repository for bugs or questions.
-- :fontawesome-solid-envelope: **[Contact our Team](../contact.md)**  
+- :fontawesome-solid-envelope: **[Contact our Team](../contact.md)**
     Visit our contact page.
 
 Thank you for contributing to FatPy!
diff --git a/docs/development/install.md b/docs/development/install.md
index a09eb22..346b811 100644
--- a/docs/development/install.md
+++ b/docs/development/install.md
@@ -65,7 +65,7 @@ The easiest way to install FatPy is from PyPI:
         To install package and add dependency to your project .toml file use:
 
         ```bash
-        uv add fatpy # Install from PyPI and add dependency 
+        uv add fatpy # Install from PyPI and add dependency
         ```
 
 This installs the latest stable release with all dependencies.
diff --git a/docs/development/testing.md b/docs/development/testing.md
index 3f8f4b7..009efb8 100644
--- a/docs/development/testing.md
+++ b/docs/development/testing.md
@@ -10,17 +10,17 @@ This guide outlines the testing approach and best practices for the FatPy projec
 
 FatPy emphasizes comprehensive testing to ensure code reliability and quality:
 
-1. **Write comprehensive tests**  
+1. **Write comprehensive tests**
     Cover all functionality with appropriate unit and integration tests
-2. **Test edge cases**  
+2. **Test edge cases**
     Include boundary conditions and error scenarios
-3. **Maintain test coverage**  
+3. **Maintain test coverage**
     Aim for high test coverage to ensure code reliability
-4. **Verify functionality**  
+4. **Verify functionality**
     Ensure all tests pass before submitting changes
-5. **Keep tests updated**  
+5. **Keep tests updated**
     Update tests when modifying existing functionality
-6. **Document test cases**  
+6. **Document test cases**
     Use clear test names and docstrings to explain test purpose
 
 ## :simple-pytest: Testing Framework
diff --git a/docs/index.md b/docs/index.md
index f0ae914..9218e7d 100644
--- a/docs/index.md
+++ b/docs/index.md
@@ -17,26 +17,26 @@ material science.
 
 #### Core Modules
 
-- **Stress-Life**  
+- **Stress-Life**
     Stress-based fatigue assessment methods for estimating fatigue damage with corrections for various effects (stress concentration, size, surface quality, etc.)
-- **Strain-Life**  
+- **Strain-Life**
     Fatigue analysis using strain amplitude and cycles to failure relationships (ε-N approaches) such as Coffin-Manson and Basquin laws, suited for low-cycle and transitional fatigue regimes
-- **Energy-Life**  
+- **Energy-Life**
     Fatigue analysis methods based on the relationship between strain energy density and number of cycles to failure
-- **Damage Cumulation**  
+- **Damage Cumulation**
     Various fatigue damage accumulation rules for variable amplitude loading, including linear models (Palmgren-Miner) and advanced non-linear approaches accounting for load sequence effects
-- **Decompositions**  
+- **Decompositions**
     Methods for breaking down complex load signals into cycles, containing both uniaxial and multiaxial procedures
-- **Plane-Based Methods**  
+- **Plane-Based Methods**
     Methods for processing stress tensor paths on material planes, providing infrastructure for critical-plane and integral prediction approaches
 
 #### Supporting Modules
 
-- **Material Laws**  
+- **Material Laws**
     Functions dealing with various material constitutive laws and behavior models
-- **Structural Mechanics**  
+- **Structural Mechanics**
     Stress analysis and transformation utilities
-- **Utils**  
+- **Utils**
     General utilities for mesh handling, signal processing, and data manipulation
 
 ## :fontawesome-solid-download: Installation
@@ -60,7 +60,7 @@ material science.
         To install package and add dependency to your project .toml file use:
 
         ```bash
-        uv add fatpy # Install from PyPI and add dependency 
+        uv add fatpy # Install from PyPI and add dependency
         ```
 
 For detailed installation options, see the [Installation Guide :octicons-arrow-right-24:](development/install.md)
@@ -99,13 +99,13 @@ interested in coding, testing, documentation, or providing feedback, your partic
 
 ### Getting Involved
 
-- **Explore the Repository**:  
+- **Explore the Repository**:
 Visit our [:fontawesome-brands-github: GitHub repository](https://github.com/faberorg/fatpy) to access the source code.
 
-- **Contribute**:  
+- **Contribute**:
 Follow our [:fontawesome-solid-handshake: Contribution Guidelines](development/contributing.md) to help improve FatPy.
 
-- **Collaborate**:  
+- **Collaborate**:
 Join our [:fontawesome-solid-comment-dots: Discussions](https://github.com/faberorg/fatpy/discussions) or [:fontawesome-solid-bug: Report issues](https://github.com/faberorg/fatpy/issues).
 
 By participating, you'll be part of a collaborative effort to advance the field of material fatigue analysis.
diff --git a/docs/overrides/main.html b/docs/overrides/main.html
index 9b8b639..d059509 100644
--- a/docs/overrides/main.html
+++ b/docs/overrides/main.html
@@ -5,4 +5,4 @@
   <meta name="google-site-verification" content="KZitDe_Rc9dWnFEa9hNgxXUbtJvIeOv2w4GZSStHE0A" />
 
   {{ super() }}
-{% endblock %}
\ No newline at end of file
+{% endblock %}
diff --git a/docs/stylesheets/extra.css b/docs/stylesheets/extra.css
index b8b362d..d5c6092 100644
--- a/docs/stylesheets/extra.css
+++ b/docs/stylesheets/extra.css
@@ -17,11 +17,11 @@
 --fatpy-heading2-color: var(--md-primary-fg-color--light);
 
 /* Defined custom colors for admonitions in light mode */
---custom-note-color: #98b8d8; 
---custom-abstract-color: #6490bc; 
---custom-info-color: #296595; 
---custom-tip-color: #034670; 
---custom-example-color: #6a5acd; 
+--custom-note-color: #98b8d8;
+--custom-abstract-color: #6490bc;
+--custom-info-color: #296595;
+--custom-tip-color: #034670;
+--custom-example-color: #6a5acd;
 --custom-api-color: #98b8d8;  /* Used for API doc section headers */
 
 /* Define custom icons for admonitions - set to existing standard icons */
@@ -139,7 +139,7 @@ h2.doc-heading {
 /* Modified admonition styles for Abstract */
 .md-typeset .admonition.abstract,
 .md-typeset details.abstract {
-  border-color: var(--custom-abstract-color); 
+  border-color: var(--custom-abstract-color);
 }
 
 .md-typeset .abstract > .admonition-title,
@@ -149,20 +149,20 @@ h2.doc-heading {
 
 .md-typeset .abstract > .admonition-title::before,
 .md-typeset .abstract > summary::before {
-  background-color: var(--custom-abstract-color); 
+  background-color: var(--custom-abstract-color);
   /* -webkit-mask-image: var(--md-admonition-icon--custom-abstract);
           mask-image: var(--md-admonition-icon--custom-abstract); */
 }
 
 .md-typeset .abstract > .admonition-title::after,
 .md-typeset .abstract > summary::after {
-  background-color: var(--custom-abstract-color); 
+  background-color: var(--custom-abstract-color);
 }
 
 /* Modified admonition styles for Note */
 .md-typeset .admonition.note,
 .md-typeset details.note {
-  border-color: var(--custom-note-color); 
+  border-color: var(--custom-note-color);
 }
 
 .md-typeset .note > .admonition-title,
@@ -172,18 +172,18 @@ h2.doc-heading {
 
 .md-typeset .note > .admonition-title::before,
 .md-typeset .note > summary::before {
-  background-color: var(--custom-note-color); 
+  background-color: var(--custom-note-color);
 }
 
 .md-typeset .note > .admonition-title::after,
 .md-typeset .note > summary::after {
-  background-color: var(--custom-note-color); 
+  background-color: var(--custom-note-color);
 }
 
 /* Modified admonition styles for Info */
 .md-typeset .admonition.info,
 .md-typeset details.info {
-  border-color: var(--custom-info-color); 
+  border-color: var(--custom-info-color);
 }
 
 .md-typeset .info > .admonition-title,
@@ -193,18 +193,18 @@ h2.doc-heading {
 
 .md-typeset .info > .admonition-title::before,
 .md-typeset .info > summary::before {
-  background-color: var(--custom-info-color); 
+  background-color: var(--custom-info-color);
 }
 
 .md-typeset .info > .admonition-title::after,
 .md-typeset .info > summary::after {
-  background-color: var(--custom-info-color); 
+  background-color: var(--custom-info-color);
 }
 
 /* Modified admonition styles for Tip */
 .md-typeset .admonition.tip,
 .md-typeset details.tip {
-  border-color: var(--custom-tip-color); 
+  border-color: var(--custom-tip-color);
 }
 
 .md-typeset .tip > .admonition-title,
@@ -214,18 +214,18 @@ h2.doc-heading {
 
 .md-typeset .tip > .admonition-title::before,
 .md-typeset .tip > summary::before {
-  background-color: var(--custom-tip-color); 
+  background-color: var(--custom-tip-color);
 }
 
 .md-typeset .tip > .admonition-title::after,
 .md-typeset .tip > summary::after {
-  background-color: var(--custom-tip-color); 
+  background-color: var(--custom-tip-color);
 }
 
 /* Modified admonition styles for Example */
 .md-typeset .admonition.example,
 .md-typeset details.example {
-  border-color: var(--custom-example-color); 
+  border-color: var(--custom-example-color);
 }
 
 .md-typeset .example > .admonition-title,
@@ -235,12 +235,12 @@ h2.doc-heading {
 
 .md-typeset .example > .admonition-title::before,
 .md-typeset .example > summary::before {
-  background-color: var(--custom-example-color); 
+  background-color: var(--custom-example-color);
 }
 
 .md-typeset .example > .admonition-title::after,
 .md-typeset .example > summary::after {
-  background-color: var(--custom-example-color); 
+  background-color: var(--custom-example-color);
 }
 
 /* API Documentation styles */
@@ -261,7 +261,7 @@ div.doc-contents:not(.first) {
 .md-typeset .doc-contents .doc-function > h4,
 .md-typeset .doc-contents .doc-function > h5,
 .md-typeset .doc-contents .doc-function > h6 {
-  font-size: 1rem;                 
+  font-size: 1rem;
   font-weight: 600;
   color: var(--md-primary-fg-color--dark);
   margin-top: 0.6em;
diff --git a/src/fatpy/core/stress_life/damage_params/s_eqa_goodman.py b/src/fatpy/core/stress_life/damage_params/s_eqa_goodman.py
new file mode 100644
index 0000000..967141d
--- /dev/null
+++ b/src/fatpy/core/stress_life/damage_params/s_eqa_goodman.py
@@ -0,0 +1,115 @@
+"""Goodman mean-stress correction for uniaxial S–N life.
+
+This module exposes :func:`s_eqa_goodman`, which computes the Goodman
+equivalent stress amplitude and the corresponding cycles to failure:
+
+    sigma_aeq = sigma_a / (1 - sigma_m / sigma_UTS)
+    N         = 0.5 * (sigma_aeq / sigma_f) ** (1 / b)
+
+The implementation is vectorized (NumPy broadcasting) and unit-agnostic
+(provided all inputs use consistent units). It returns `(N, sigma_aeq)`,
+where `N` is rounded to the nearest integer and clipped to a minimum of 1.
+
+"""
+
+from __future__ import annotations
+
+from typing import Union
+import warnings
+
+import numpy as np
+from numpy.typing import ArrayLike, NDArray
+
+
+Number = Union[int, float]
+
+
+def s_eqa_goodman(
+    stress_amp: ArrayLike,
+    mean_stress: ArrayLike,
+    fat_strength_coef: ArrayLike | Number,
+    fat_strength_exp: ArrayLike | Number,
+    ult_stress: ArrayLike | Number,
+) -> tuple[NDArray[np.int64], NDArray[np.float64]]:
+    """Stress-life (S–N) prediction using the Goodman mean-stress correction.
+
+    Implements the Goodman mean-stress correction (Suresh, 1998):
+
+        σ_a,eq = σ_a / (1 - σ_m / σ_UTS)
+        N      = 0.5 * (σ_a,eq / σ_f) ** (1 / b)
+
+    where `b < 0` is the Basquin exponent.
+
+    Args:
+        stress_amp: σ_a. Stress amplitude(s). Must be > 0.
+        mean_stress: σ_m. Mean stress(es).
+        fat_strength_coef: σ_f. Basquin fatigue strength coefficient(s). Must be > 0.
+        fat_strength_exp: b. Basquin fatigue strength exponent(s). Must be < 0.
+        ult_stress: σ_UTS. Ultimate tensile strength(s). Must be > 0.
+
+    Returns:
+        (N, sigma_aeq):
+            N: integer ndarray of predicted cycles to failure (rounded to nearest int,
+               clipped to a minimum of 1).
+            sigma_aeq: float ndarray of equivalent stress amplitude(s) per Goodman.
+
+    Raises:
+        ValueError: If inputs violate constraints (e.g., b >= 0, σ_f <= 0, σ_UTS <= 0,
+            σ_a <= 0) or if any (σ_m / σ_UTS) >= 1, which would make the Goodman
+            denominator non-positive.
+
+    Notes:
+        * Vectorized: all arguments broadcast via NumPy rules.
+        * If σ_a,eq > σ_f anywhere (which would give N < 1), a warning is issued.
+          In that case, N is clipped to a minimum of 1.
+        * Units must be consistent throughout (e.g., MPa or Pa).
+    """
+    # Convert to arrays (float64) for safe broadcasting / math
+    sa = np.asarray(stress_amp, dtype=np.float64)
+    sm = np.asarray(mean_stress, dtype=np.float64)
+    sf = np.asarray(fat_strength_coef, dtype=np.float64)
+    b = np.asarray(fat_strength_exp, dtype=np.float64)
+    uts = np.asarray(ult_stress, dtype=np.float64)
+
+    # Basic validation (constraints)
+    if np.any(sa <= 0):
+        raise ValueError("stress_amp (σ_a) must be > 0.")
+    if np.any(sf <= 0):
+        raise ValueError("fat_strength_coef (σ_f) must be > 0.")
+    if np.any(uts <= 0):
+        raise ValueError("ult_stress (σ_UTS) must be > 0.")
+    if np.any(b >= 0):
+        raise ValueError("fat_strength_exp (b) must be < 0 for Basquin.")
+
+    # Goodman denominator
+    denom = 1.0 - (sm / uts)
+    if np.any(denom <= 0.0):
+        raise ValueError(
+            "Invalid mean stress: (σ_m / σ_UTS) must be < 1. "
+            "Goodman denominator became non-positive."
+        )
+
+    # Equivalent stress amplitude
+    sigma_aeq = sa / denom
+
+    # Warn if σ_a,eq exceeds σ_f (implies N < 1)
+    if np.any(sigma_aeq > sf):
+        warnings.warn(
+            "Equivalent stress amplitude exceeds σ_f; "
+            "predicted life would be < 1 cycle. Clipping N to a minimum of 1.",
+            RuntimeWarning,
+            stacklevel=2,
+        )
+
+    # Basquin inversion: N = 0.5 * (σ_a,eq / σ_f) ** (1 / b)
+    with np.errstate(divide="raise", invalid="raise"):
+        N_float = 0.5 * (sigma_aeq / sf) ** (1.0 / b)
+
+    # Enforce a minimum of 1 cycle to avoid N < 1.0
+    N_float = np.maximum(N_float, 1.0)
+
+    # Integer cycles as in your original function
+    N = np.rint(N_float).astype(np.int64)
+
+    # Return both N and σ_a,eq
+    return N, sigma_aeq
diff --git a/tests/stress_life/test_s_eqa_goodman.py b/tests/stress_life/test_s_eqa_goodman.py
new file mode 100644
index 0000000..51e81fe
--- /dev/null
+++ b/tests/stress_life/test_s_eqa_goodman.py
@@ -0,0 +1,123 @@
+# tests/stress_life/test_s_eqa_goodman.py
+import numpy as np
+import pytest
+
+# Import the function (not the module); alias to avoid name shadowing
+from fatpy.core.stress_life.damage_params.s_eqa_goodman import (
+    s_eqa_goodman as goodman_fn,
+)
+
+
+def test_returns_tuple_and_dtypes() -> None:
+    N, sigma_aeq = goodman_fn(
+        stress_amp=150.0,
+        mean_stress=25.0,
+        fat_strength_coef=400.0,
+        fat_strength_exp=-0.1,
+        ult_stress=700.0,
+    )
+    # Accept NumPy scalars or arrays:
+    N_arr = np.asarray(N)
+    sig_arr = np.asarray(sigma_aeq)
+
+    assert N_arr.dtype == np.int64
+    assert sig_arr.dtype == np.float64
+
+    # For scalar inputs, function returns 0-D; this documents the behavior.
+    assert N_arr.ndim == 0
+    assert sig_arr.ndim == 0
+
+
+def test_example_numeric_values() -> None:
+    """Concrete example to check both outputs."""
+    sa = 180.0
+    sm = 100.0
+    sf = 475.4
+    b = -0.078
+    uts = 700.0
+
+    N, sigma_aeq = goodman_fn(
+        stress_amp=sa,
+        mean_stress=sm,
+        fat_strength_coef=sf,
+        fat_strength_exp=b,
+        ult_stress=uts,
+    )
+
+    # sigma_aeq = 180 / (1 - 100/700) = 210
+    assert np.isclose(float(sigma_aeq), 210.0, rtol=0.0, atol=1e-12)
+    # N ≈ 17709 after rounding
+    assert int(N) == 17709
+
+
+def test_vectorization_and_broadcast() -> None:
+    sa = np.array([150.0, 180.0, 210.0])
+    sm = np.array([0.0, 50.0, 100.0])
+
+    N, sigma_aeq = goodman_fn(
+        stress_amp=sa,
+        mean_stress=sm,
+        fat_strength_coef=475.4,
+        fat_strength_exp=-0.078,
+        ult_stress=700.0,
+    )
+
+    assert N.shape == (3,)
+    assert sigma_aeq.shape == (3,)
+    # More severe loading should not increase life
+    assert N[0] >= N[1] >= N[2]
+    # sigma_aeq increases with mean stress under Goodman
+    assert sigma_aeq[0] <= sigma_aeq[1] <= sigma_aeq[2]
+
+
+def test_warns_and_clips_minimum_one_cycle() -> None:
+    """If σ_a,eq > σ_f, warn and clip N to at least 1."""
+    with pytest.warns(RuntimeWarning, match="exceeds σ_f"):
+        N, sigma_aeq = goodman_fn(
+            stress_amp=300.0,
+            mean_stress=0.0,
+            fat_strength_coef=200.0,  # small σ_f -> σ_a,eq > σ_f
+            fat_strength_exp=-0.08,
+            ult_stress=700.0,
+        )
+    assert int(N) >= 1
+    assert float(sigma_aeq) > 200.0
+
+
+def test_invalid_denominator_raises() -> None:
+    """Denominator must be positive: (σ_m / σ_UTS) < 1."""
+    with pytest.raises(ValueError, match="denominator became non-positive"):
+        _ = goodman_fn(
+            stress_amp=100.0,
+            mean_stress=700.0,  # equals UTS -> denom = 0
+            fat_strength_coef=400.0,
+            fat_strength_exp=-0.1,
+            ult_stress=700.0,
+        )
+
+
+def test_invalid_inputs_raise() -> None:
+    with pytest.raises(ValueError):
+        _ = goodman_fn(
+            stress_amp=0.0,  # must be > 0
+            mean_stress=0.0,
+            fat_strength_coef=400.0,
+            fat_strength_exp=-0.1,
+            ult_stress=700.0,
+        )
+    with pytest.raises(ValueError):
+        _ = goodman_fn(
+            stress_amp=100.0,
+            mean_stress=0.0,
+            fat_strength_coef=-1.0,  # must be > 0
+            fat_strength_exp=-0.1,
+            ult_stress=700.0,
+        )
+    with pytest.raises(ValueError):
+        _ = goodman_fn(
+            stress_amp=100.0,
+            mean_stress=0.0,
+            fat_strength_coef=400.0,
+            fat_strength_exp=0.0,  # b must be < 0
+            ult_stress=700.0,
+        )