⚖️ 质心计算器（一维、二维、三维）Center of Mass Calculator (1D, 2D, 3D)

使用说明与常见问题How-to & FAQ

「质心计算器（一维、二维、三维）」是什么？What is the Center of Mass Calculator (1D, 2D, 3D) tool?

按 x̄ = Σmᵢxᵢ ÷ Σmᵢ 计算一组质点的质心，支持一维、二维和三维坐标，位置可以为负。每行一个质点：质量后跟坐标。本地处理。Center of mass of point masses, x̄ = Σmᵢxᵢ ÷ Σmᵢ, in 1D, 2D or 3D; positions may be negative. One point per line: the mass followed by its coordinates. Processed locally.

如何使用「质心计算器（一维、二维、三维）」？How do I use the Center of Mass Calculator (1D, 2D, 3D) tool?

在「质心计算器（一维、二维、三维）」中，填写「维度」等参数，结果会随输入实时计算并显示在下方。In the Center of Mass Calculator (1D, 2D, 3D): Fill in "Dimensions"; results are recalculated instantly as you type.

怎么输入？How do I enter the points?

每行一个质点：先写质量，再写坐标，用空格或逗号分隔。一维写“质量 x”，二维写“质量 x y”，三维写“质量 x y z”。例如二维的 2 0 0、3 4 0、5 0 3 三个质点，质心是 (1.2, 1.5)。One point per line: the mass first, then its coordinates, separated by spaces or commas. In 1D write mass x, in 2D mass x y, in 3D mass x y z. For example, the 2D points 2 0 0, 3 4 0 and 5 0 3 have their center of mass at (1.2, 1.5).

坐标和质量可以为负吗？Can coordinates or masses be negative?

坐标可以为负（相对于任意原点）；质量必须大于 0，否则页面会指出是哪一行。Coordinates can be negative (relative to any origin); every mass must be more than 0, and the page names the line otherwise.

公式是什么？What is the formula?

每个坐标分别计算：x̄ = Σmᵢxᵢ ÷ Σmᵢ，ȳ、z̄ 同理。总质量为 0 时质心没有定义。Each coordinate separately: x̄ = Σmᵢxᵢ ÷ Σmᵢ, and likewise ȳ and z̄. The center of mass is undefined when the total mass is 0.

能举个计算实例吗？Can you show a worked example?

例如在「质心计算器（一维、二维、三维）」中填 维度 = 一维（m x），质点（每行：质量 坐标…） = 1 0（换行）1 2，结果区显示：质心：(1)；x̄：1；总质量：2（2 个质点）For example, entering Dimensions = 1D (m x), Points (each line: mass coordinates…) = 1 0 (new line) 1 2 in the Center of Mass Calculator (1D, 2D, 3D) gives: Center of mass: (1); x̄: 1; Total mass: 2 (2 points)

有哪些选项可以调整？What options can I adjust?

「质心计算器（一维、二维、三维）」的设置：「维度」可选 一维（m x）、二维（m x y）、三维（m x y z）（默认 二维（m x y））。每次生成结果都按当前设置处理。Settings in the Center of Mass Calculator (1D, 2D, 3D) — "Dimensions": 1D (m x), 2D (m x y), 3D (m x y z) (default 2D (m x y)). The result always uses the current settings.

计算精度如何？How precise are the results?

「质心计算器（一维、二维、三维）」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 Center of Mass Calculator (1D, 2D, 3D) uses double-precision floating point (about 15–16 significant digits); very large or very small values may lose precision.

「质心计算器（一维、二维、三维）」免费吗？需要注册吗？Is the Center of Mass Calculator (1D, 2D, 3D) free? Do I need an account?

「质心计算器（一维、二维、三维）」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 Center of Mass Calculator (1D, 2D, 3D) is completely free with no sign-up or install and works on phones and desktops; what you enter is processed only in your browser.