Calculate coordinates and arc lengths for the logarithmic golden spiral.
Spiral Parameters
Logarithmic Growth Visualization
Spiral Geometry
6.8541
Radius at θ
Results for a golden spiral starting at given radius.
Total Arc Length19.9859
Growth Factor (b)0.306349
About this calculator
What is a Golden Spiral?
A golden spiral is a logarithmic spiral whose growth factor is φ, the golden ratio. It gets wider (or further from its origin) by a factor of φ for every quarter-turn it makes. It is a specific Case of the equiangular spiral.
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Pro Tips
The spiral is self-similar, meaning it looks the same at any scale.
In nature, it is seen in nautilus shells, sunflower seed patterns, and spiral galaxies.
The arc length can be calculated as the hypotenuse-like integral of the growth curve.
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Fun Facts
"Nautilus shells grow in a way that approximates a golden spiral to maintain buoyancy."
"The spiral never reaches its origin; it wraps infinitely many times around it."
"Approximation: You can draw a similar spiral using quarter-circles inside squares based on Fibonacci numbers."
