➡️ 合力计算器（分量或大小+方向，二维/三维）Resultant Force Calculator (Components or Magnitude and Angle, 2D or 3D)

使用说明与常见问题How-to & FAQ

「合力计算器（分量或大小+方向，二维/三维）」是什么？What is the Resultant Force Calculator (Components or Magnitude and Angle, 2D or 3D) tool?

把多个力合成为一个合力。可按分量输入 Fx、Fy（可选 Fz），也可按“大小 + 方向角”输入（角度从 +x 轴逆时针量）。给出合力分量、大小、方向角，以及让物体平衡所需的平衡力；输入质量可求加速度 a = F/m。本地处理。Combines several forces into one resultant. Enter components Fx, Fy (and optionally Fz), or magnitudes with direction angles measured anticlockwise from the +x axis. Gives the resultant components, magnitude and direction, the equilibrant force that would balance them, and the acceleration a = F/m if you enter a mass. Processed locally.

如何使用「合力计算器（分量或大小+方向，二维/三维）」？How do I use the Resultant Force Calculator (Components or Magnitude and Angle, 2D or 3D) tool?

在「合力计算器（分量或大小+方向，二维/三维）」中，填写「输入方式」、「Fx 列表」、「Fy 列表」、「Fz 列表（可选，三维）」、「力的大小列表 N」等参数，结果会随输入实时计算并显示在下方。In the Resultant Force Calculator (Components or Magnitude and Angle, 2D or 3D): Fill in "Input", "Fx list", "Fy list", "Fz list (optional, 3D)", "Force magnitudes N"; results are recalculated instantly as you type.

合力怎么算？How is the resultant force found?

把每个力分解成 x、y（和 z）分量后分别相加：Rx = ΣFx，Ry = ΣFy。合力大小 |R| = √(Rx² + Ry²)，方向 θ = atan2(Ry, Rx)。Resolve each force into x and y (and z) components and add them: Rx = ΣFx and Ry = ΣFy. The magnitude is |R| = √(Rx² + Ry²) and the direction is θ = atan2(Ry, Rx).

已知大小和角度怎么分解？How do I resolve a force given its size and angle?

Fx = F·cos θ，Fy = F·sin θ，θ 从 +x 轴逆时针量起。例如 10 N 在 0° 和 5 N 在 90°，合力约 11.18 N，方向约 26.57°。Fx = F·cos θ and Fy = F·sin θ, with θ measured anticlockwise from +x. 10 N at 0° and 5 N at 90° give about 11.18 N at about 26.57°.

平衡力是什么？What is the equilibrant?

与合力大小相等、方向相反的力。加上它后所有力之和为 0，物体处于平衡状态。A force equal in size and opposite in direction to the resultant. Adding it makes the net force zero, so the object is in equilibrium.

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

例如在「合力计算器（分量或大小+方向，二维/三维）」中填 输入方式 = 分量 Fx，Fx 列表 = 3 0，Fy 列表 = 4 0，结果区显示：Rx：3；Ry：4；|R|：5；方向角（自 +x 轴逆时针）：53.1301°；平衡力：(-3, -4)，大小 5For example, entering Input = Fy / Fz / Components Fx / Fy…, Fx list = 3 0, Fy list = 4 0 in the Resultant Force Calculator (Components or Magnitude and Angle, 2D or 3D) gives: Rx: 3; Ry: 4; |R|: 5; Direction (anticlockwise from +x): 53.1301°; Equilibrant: (-3, -4), magnitude 5

哪些输入会被检查？Which inputs are validated?

「合力计算器（分量或大小+方向，二维/三维）」会检查这些输入——「质量 kg（可选）」：须大于 0（留空则不计算加速度）；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 Resultant Force Calculator (Components or Magnitude and Angle, 2D or 3D) checks its inputs — "Mass kg (optional)": must be greater than 0 (leave blank to skip the acceleration); 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?

「合力计算器（分量或大小+方向，二维/三维）」的设置：「输入方式」可选 分量 Fx、大小与方向角（默认 分量 Fx）；「Fx 列表」默认 3 0 -1；「Fy 列表」默认 4 2 0；「Fz 列表（可选，三维）」可留空；「力的大小列表 N」默认 10 5；「方向角列表 °」默认 0 90；「质量 kg（可选）」可留空。每次生成结果都按当前设置处理。Settings in the Resultant Force Calculator (Components or Magnitude and Angle, 2D or 3D) — "Input": Fy / Fz / Components Fx / Fy / Fz, Magnitude and angle (default Fy / Fz / Components Fx / Fy / Fz); "Fx list" default 3 0 -1; "Fy list" default 4 2 0; "Fz list (optional, 3D)" optional; "Force magnitudes N" default 10 5; "Direction angles °" default 0 90; "Mass kg (optional)" optional. The result always uses the current settings.

计算结果可以用于作业或工程吗？Can I use the results for homework or engineering?

「合力计算器（分量或大小+方向，二维/三维）」使用教科书标准公式（公式写在说明和常见问题中），适合学习和估算核对；涉及安全的工程设计请以规范和实测为准。The Resultant Force Calculator (Components or Magnitude and Angle, 2D or 3D) uses standard textbook formulas (given in the description and FAQ), which is good for learning and checking estimates; for safety-critical engineering follow codes and measured values.

「合力计算器（分量或大小+方向，二维/三维）」免费吗？需要注册吗？Is the Resultant Force Calculator (Components or Magnitude and Angle, 2D or 3D) free? Do I need an account?

「合力计算器（分量或大小+方向，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 Resultant Force Calculator (Components or Magnitude and Angle, 2D or 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.