⬠ 不规则多边形面积（坐标法）Irregular Polygon Area Calculator
按顺序输入各顶点坐标（每行一个"x y"），用鞋带公式计算面积和周长。本地处理。Enter the vertices in order (one "x y" per line); the shoelace formula gives the area and perimeter. Processed locally.
使用说明与常见问题How-to & FAQ
「不规则多边形面积（坐标法）」是什么？What is the Irregular Polygon Area Calculator tool?
按顺序输入各顶点坐标（每行一个"x y"），用鞋带公式计算面积和周长。本地处理。Enter the vertices in order (one "x y" per line); the shoelace formula gives the area and perimeter. Processed locally.
如何使用「不规则多边形面积（坐标法）」？How do I use the Irregular Polygon Area Calculator tool?
在文本框中按顺序填写多边形的各个顶点，每行一个「x y」，即可用鞋带公式得到面积和周长。结果会随输入实时更新。List the polygon's vertices in order in the box, one "x y" per line, to get the area (shoelace formula) and the perimeter. The result updates as you type.
边交叉？Crossing edges?
鞋带公式要求多边形不自相交，否则结果不是真实面积。The shoelace formula needs a non-self-intersecting polygon.
计算精度如何？How precise are the results?
「不规则多边形面积（坐标法）」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 Irregular Polygon Area Calculator uses double-precision floating point (about 15–16 significant digits); very large or very small values may lose precision.
「不规则多边形面积（坐标法）」免费吗？需要注册吗？Is the Irregular Polygon Area Calculator free? Do I need an account?
「不规则多边形面积（坐标法）」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 Irregular Polygon 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.