Catenoid Calculator
Free online catenoid 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：悬链面在线计算器
原理：把悬链线 x = a·cosh(z/a) 绕 z 轴旋转，得到的旋转曲面称为悬链面，它是连接两个圆环之间面积最小的极小曲面（Meusnier 1776 年证明）。
步骤：输入 a 与半高 b，由 u = b/a 直接代入闭式 S = 2πa²(sinh u·cosh u + u) 与 V = πa³(sinh u·cosh u + u)。
示例：a = 1、b = 1 时 S = 17.677303320067、V = 8.838651660034、边缘半径 cosh 1 = 1.543080634815。
注意事项：悬链面只在 b/a 小于约 0.6392 时才是两环间的最小面积曲面；b/a 更大时边界环之间会出现更省面积的膜（Goldschmidt 不连续解）。
参考值：S(1,1) = 17.677303320067；cosh(1) = 1.543080634815；sinh(1)·cosh(1) = 1.813430203923。
How to use the Catenoid 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 Catenoid 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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