Disclaimer

General Disclaimer

The information and tools provided by GoldenSpiral (“https://www.fibonnaci.com”) are for general educational purposes only. Everything here is offered in good faith, but we make no representation or warranty of any kind, express or implied, as to the accuracy, adequacy, validity, reliability, or completeness of any information or result on the site.

Any use of the information or tools is entirely at your own risk. It is your responsibility to ensure the results meet your specific requirements and to verify them before acting.

An Educational Aid, Not Professional or Academic Advice

GoldenSpiral’s calculators — the Fibonacci calculator, the golden ratio calculator, the modular scale generator, the golden spiral & phyllotaxis calculator, the Lucas number calculator, and the golden ratio grid— are designed to help you understand and apply standard, published mathematical formulas: Binet’s formula, the golden-ratio proportion, Vogel’s phyllotaxis model, and simple geometric division. They do not constitute professional engineering, architectural, or design advice, and they are not a substitute for coursework, a qualified instructor, or peer-reviewed academic sources if you need citable or certified results. Blog and learn-section commentary about historical or biological claims involving the golden ratio reflects the current, generally accepted state of scholarship as we understand it, and is not a substitute for consulting primary academic sources on any specific claim you intend to rely on.

Results Are Rounded, Formula-Based Estimates

The tools apply standard formulas — Binet’s closed-form expression for Fibonacci and Lucas numbers, straightforward proportional division for golden-ratio splits, Vogel’s model for phyllotaxis coordinates — and round their output for readability. The Fibonacci and Lucas calculators are capped at n=70, the largest term a double-precision Binet calculation can return as an exact integer; results beyond that range are out of scope for this tool. Displayed spiral, scale, and grid figures are rounded to a small number of decimal places, which is appropriate for design and reference use but may not be sufficient precision for engineering or manufacturing work.

Why a Result May Look Off

A calculator can return an error or an unexpected answer when:

• A term index is out of range: the Fibonacci and Lucas calculators only accept whole numbers from 0 to 70.
• An input isn’t a positive number where one is required: lengths, base sizes, seed counts, and frame dimensions must all be positive.
• A step range or ratio is invalid: the modular scale generator requires a starting step no greater than the ending step, and a positive ratio.

No Warranty

GoldenSpiral expressly disclaims all warranties, whether express, implied, statutory, or otherwise, including implied warranties of merchantability, fitness for a particular purpose, and non-infringement. We do not warrant that our tools, calculations, or information are error-free or complete, or that the website will be available without interruption.

Limitation of Liability

To the maximum extent permitted by law, GoldenSpiral shall not be liable for any direct, indirect, incidental, special, consequential, or exemplary damages arising out of or related to your use of our tools and services.

External Links & Advertising

The site may link to third-party websites, displays advertisements from networks including Google AdSense, and includes Amazon affiliate links on some pages as described in our Affiliate Disclosure. We do not investigate, monitor, or endorse third-party content, and the presence of a link or ad is not an endorsement of any product or service.

Changes to This Disclaimer

We may modify this disclaimer at any time. Changes are posted here with an updated revision date, and your continued use of the site indicates acceptance of the changes.

Contact Us

If you have questions about this Disclaimer, please visit our Contact page or email us at support@fibonnaci.com.