Logarithmic Spiral Calculator
Free online logarithmic spiral calculator. Enter your values and get instant results with the formula, step-by-step working, a worked example and FAQs — everything runs locally in your browser on Calcton, no signup required.
中文版：对数螺线在线计算器
对数螺线 r = a·e^(bθ) 是自然界最偏爱的曲线：鹦鹉螺壳室、旋涡星系旋臂、飓风云图、鹰俯冲的路径都在按它生长。原因只有一个——自相似：曲线放大任意倍数后与自身旋转一定角度完全重合。
它的招牌性质是等角性：切线与径向的夹角 ψ = arctan(1/b) 处处相同，因此也叫等角螺线。鹰捕捉猎物时保持视线与飞行方向成固定角度，轨迹正是对数螺线；昆虫趋光飞行同理。伯努利对自己的发现如此着迷，遗嘱要求把这条线刻上墓碑。
参考值
a = 1、b = 0.2、θ = 2π：r = 3.5135856242857，s = 12.816822147319
ψ = arctan(5) = 1.37340076695，扇形面积 = 14.462456048292
How to use the Logarithmic Spiral Calculator
- Fill in the inputs with your own numbers — every field shows what it expects.
- The result updates instantly as you type; no "Calculate" click needed.
- Read the result card for the main figure, the step-by-step formula, and practical notes.
Frequently asked questions
Is the Logarithmic Spiral Calculator free?
Yes — all math calculators on Calcton are free, with no sign-up required. Your inputs are processed in your browser and never sent to a server.
Is there a Chinese version of this tool?
Yes. Use the Chinese version link above — it is the same calculator with the interface in Simplified Chinese.
References
Formulas and benchmarks used by this calculator follow these published sources.
KevinContent LeadCalcton Editorial Team · Last updated 2026-09-28
Kevin maintains Calcton's formula verification and content: every calculator cites the standard it implements, worked examples are recomputed programmatically, and health benchmarks follow WHO and international guidelines.
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