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🏋️ 功的计算器（物理）Work Calculator (Physics)
按 W = F·d·cos θ 计算力对物体做的功，可求功、力或位移中的任意一个，并由做功时间算出平均功率；结果同时给出焦耳、千焦、千瓦时和卡路里。Calculate mechanical work W = F·d·cos θ — or solve for the force or distance — and the average power from the time taken, with results in joules, kilojoules, kilowatt-hours and calories.
使用说明与常见问题How-to & FAQ
「功的计算器（物理）」是什么？What is the Work Calculator (Physics) tool?
按 W = F·d·cos θ 计算力对物体做的功，可求功、力或位移中的任意一个，并由做功时间算出平均功率；结果同时给出焦耳、千焦、千瓦时和卡路里。Calculate mechanical work W = F·d·cos θ — or solve for the force or distance — and the average power from the time taken, with results in joules, kilojoules, kilowatt-hours and calories.
如何使用「功的计算器（物理）」？How do I use the Work Calculator (Physics) tool?
在「功的计算器（物理）」中，填写「求解」、「力 F（N）」、「位移 d（m）」、「功 W（J）」、「力与位移夹角 θ（度）」等参数，结果会随输入实时计算并显示在下方。In the Work Calculator (Physics): Fill in "Solve for", "Force F (N)", "Distance d (m)", "Work W (J)", "Angle θ between force and motion (degrees)"; results are recalculated instantly as you type.
功的公式？What is the work formula?
W = F × d × cos θ，F 为力（牛顿），d 为位移（米），θ 为力与运动方向的夹角。单位为焦耳（J = N·m）。W = F × d × cos θ, with force F in newtons, displacement d in metres and θ the angle between force and motion. The unit is the joule (J = N·m).
什么时候功为零或为负？When is work zero or negative?
力与运动方向垂直（θ = 90°）时不做功，例如水平移动时提着重物的竖直拉力；θ > 90° 时做负功，例如摩擦力。No work is done when the force is perpendicular to the motion (θ = 90°), like the upward pull on a bag carried level; above 90° the work is negative, like friction.
夹角可以填多少？What angle range is allowed?
θ 须在 0° 到 180° 之间：0° 表示力与运动同向，180° 表示完全相反。求力或位移时 θ 不能为 90°（不做功，无法反求），且功的正负须与夹角一致。θ must be from 0° to 180°: 0° means the force points along the motion, 180° directly against it. When solving for force or distance θ cannot be 90° (no work is done), and the sign of the work must match the angle.
计算结果可以用于作业或工程吗？Can I use the results for homework or engineering?
「功的计算器（物理）」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 Work Calculator (Physics) 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.
「功的计算器（物理）」免费吗？需要注册吗？Is the Work Calculator (Physics) free? Do I need an account?
「功的计算器（物理）」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 Work Calculator (Physics) is completely free with no sign-up or install and works on phones and desktops; what you enter is processed only in your browser.