🔷 正十二边形面积计算器Regular Dodecagon Area Calculator
正十二边形面积 A = 3 s² (2+√3)，并给出周长 12s。边长须大于 0。本地处理。Regular dodecagon area A = 3 s² (2+√3), plus perimeter 12s. Side length must be greater than 0. Processed locally.
使用说明与常见问题How-to & FAQ
「正十二边形面积计算器」是什么？What is the Regular Dodecagon Area Calculator tool?
正十二边形面积 A = 3 s² (2+√3)，并给出周长 12s。边长须大于 0。本地处理。Regular dodecagon area A = 3 s² (2+√3), plus perimeter 12s. Side length must be greater than 0. Processed locally.
如何使用「正十二边形面积计算器」？How do I use the Regular Dodecagon Area Calculator tool?
在「正十二边形面积计算器」中，填写「边长」等参数，结果会随输入实时计算并显示在下方。In the Regular Dodecagon Area Calculator: Fill in "Side"; results are recalculated instantly as you type.
外接圆半径怎么求？How do I get the circumradius?
正十二边形 R = s / (2 sin(π/12)) = s (√6+√2)/2。本页用边长面积公式。For a regular dodecagon R = s / (2 sin(π/12)) = s (√6+√2)/2. This page uses the side-area formula.
和正多边形通用公式的关系？How does this relate to the general regular-polygon formula?
通用式 A = n s² / (4 tan(π/n)) 在 n=12 时化简为 3s²(2+√3)。The general A = n s² / (4 tan(π/n)) simplifies to 3s²(2+√3) when n=12.
能举个计算实例吗？Can you show a worked example?
例如在「正十二边形面积计算器」中填 边长 = 2，结果区显示：面积：44.78461；周长：24For example, entering Side = 2 in the Regular Dodecagon Area Calculator gives: Area: 44.78461; Perimeter: 24
哪些输入会被检查？Which inputs are validated?
「正十二边形面积计算器」会检查这些输入——「边长」：必须填写，须大于 0且不大于 1,000,000,000,000,000；绝对值超过 10¹⁵ 的数也会被拒绝。不符合时结果区显示具体提示，不会给出数字。The Regular Dodecagon Area Calculator checks its inputs — "Side": required, must be more than 0 and at most 1,000,000,000,000,000; numbers above 10¹⁵ in absolute value are rejected too. When a value fails, the result area names the problem instead of showing a number.
有哪些选项可以调整？What options can I adjust?
「正十二边形面积计算器」的设置：「边长」默认 2。每次生成结果都按当前设置处理。Settings in the Regular Dodecagon Area Calculator — "Side" default 2. The result always uses the current settings.
计算精度如何？How precise are the results?
「正十二边形面积计算器」使用 JavaScript 双精度浮点数（约 15–16 位有效数字）；极大或极小的数值可能存在精度误差。The Regular Dodecagon Area Calculator uses double-precision floating point (about 15–16 significant digits); very large or very small values may lose precision.
「正十二边形面积计算器」免费吗？需要注册吗？Is the Regular Dodecagon Area Calculator free? Do I need an account?
「正十二边形面积计算器」完全免费，无需注册或安装，打开网页即可使用，手机和电脑都能用；输入的内容只在你的浏览器本地处理。The Regular Dodecagon Area Calculator is completely free with no sign-up or install and works on phones and desktops; what you enter is processed only in your browser.