⬡ 正多边形面积计算器（边长，含周长）Area of a Regular Polygon Calculator (Side Length, with Perimeter)
正 n 边形面积 A = (n s²) / (4 tan(π/n))，并给出周长 n s。边数 3-1000 的整数，边长大于 0。本地处理。Regular n-gon area A = (n s²) / (4 tan(π/n)), plus perimeter n s. Sides: whole number 3-1000; side length greater than 0. Processed locally.
使用说明与常见问题How-to & FAQ
「正多边形面积计算器（边长，含周长）」是什么？What is the Area of a Regular Polygon Calculator (Side Length, with Perimeter) tool?
正 n 边形面积 A = (n s²) / (4 tan(π/n))，并给出周长 n s。边数 3-1000 的整数，边长大于 0。本地处理。Regular n-gon area A = (n s²) / (4 tan(π/n)), plus perimeter n s. Sides: whole number 3-1000; side length greater than 0. Processed locally.
如何使用「正多边形面积计算器（边长，含周长）」？How do I use the Area of a Regular Polygon Calculator (Side Length, with Perimeter) tool?
在「正多边形面积计算器（边长，含周长）」中，填写「边数」、「边长」等参数，结果会随输入实时计算并显示在下方。In the Area of a Regular Polygon Calculator (Side Length, with Perimeter): Fill in "Sides", "Side length"; results are recalculated instantly as you type.
外接圆半径怎么算？How do I get the circumradius?
本页用边长。外接圆半径 R = s / (2 sin(π/n))，内切圆半径 r = s / (2 tan(π/n))。This page uses side length. Circumradius R = s / (2 sin(π/n)); inradius r = s / (2 tan(π/n)).
正三角形和正方形？Equilateral triangle and square?
边数填 3 或 4 即可。正方形边长 5：面积 25；正六边形边长 4：面积 ≈ 41.57。Enter 3 or 4 sides. A square of side 5 has area 25; a regular hexagon of side 4 has area ≈ 41.57.
能举个计算实例吗？Can you show a worked example?
例如在「正多边形面积计算器（边长，含周长）」中填 边数 = 6，边长 = 4，结果区显示：面积：41.569219；周长：24For example, entering Sides = 6, Side length = 4 in the Area of a Regular Polygon Calculator (Side Length, with Perimeter) gives: Area: 41.569219; Perimeter: 24
哪些输入会被检查？Which inputs are validated?
「正多边形面积计算器（边长，含周长）」会检查这些输入——「边数」：必须填写，须为不小于 3且不大于 1,000的整数；「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 Area of a Regular Polygon Calculator (Side Length, with Perimeter) checks its inputs — "Sides": required, must be at least 3 and at most 1,000 (a whole number); "Side length": 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?
「正多边形面积计算器（边长，含周长）」的设置：「边数」默认 6；「边长」默认 4。每次生成结果都按当前设置处理。Settings in the Area of a Regular Polygon Calculator (Side Length, with Perimeter) — "Sides" default 6; "Side length" default 4. The result always uses the current settings.
计算精度如何？How precise are the results?
「正多边形面积计算器（边长，含周长）」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 Area of a Regular Polygon Calculator (Side Length, with Perimeter) uses double-precision floating point (about 15–16 significant digits); very large or very small values may lose precision.
「正多边形面积计算器（边长，含周长）」免费吗？需要注册吗？Is the Area of a Regular Polygon Calculator (Side Length, with Perimeter) free? Do I need an account?
「正多边形面积计算器（边长，含周长）」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 Area of a Regular Polygon Calculator (Side Length, with Perimeter) is completely free with no sign-up or install and works on phones and desktops; what you enter is processed only in your browser.