Fermat Spiral Calculator
Free online fermat 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：费马螺线在线计算器
原理：费马螺线 r² = a²θ（r = ±a√θ），极径扫掠面积 A = ½∫a²θ dθ = a²θ²/4，第 k 圈环面积为 π²a²(2k−1)——相邻环面积成等差数列。
步骤：输入 a 与 θ，读取极径、坐标与扫掠面积；双臂曲线取 r = ±a√θ 两条对称分支。
示例：a = 1、θ = 2π 时单臂扫掠 9.869604401089（= π²）、双臂合计 19.739208802179；r(π/2) = 1.253314137316。
注意事项：与阿基米德螺线（r 线性）不同，费马螺线 r 随 √θ 增长更慢，环与环更密集；负极角分支在直角坐标系中与正分支关于原点对称。
参考值：A₁ = 9.869604401089；第二环 = 29.608813203268；r(π/2) = 1.253314137316。
How to use the Fermat 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 Fermat 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 2026-10-01
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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