Work Calculator

Mechanical work describes energy transferred by a force while its point of application moves. For a constant force and straight displacement, the scalar work is W = Fd cos(θ). Here F is force magnitude in newtons, d is displacement magnitude in metres, and θ is the angle between the force and displacement vectors. Multiplying newtons by metres produces joules, the SI unit of both work and energy. The cosine factor selects the component of force acting along the direction of motion. At zero degrees, force and displacement point together, cosine is one, and all of the force performs positive work. At 90 degrees, the force is perpendicular to motion and performs zero work. A familiar example is uniform circular motion: the inward centripetal force is perpendicular to instantaneous motion, so it changes direction but not speed. At angles greater than 90 degrees and less than 270 degrees, cosine is negative and the force removes mechanical energy from the object. Negative work does not mean that no physical interaction occurred. It means the force component opposes displacement. Friction on a sliding object commonly performs negative work, while an applied pulling force may perform positive work. The net work from all forces equals the change in kinetic energy, a relationship known as the work-energy theorem. Calculating each force separately and summing its signed work can therefore predict how an object's speed changes. This calculator assumes a constant force, constant angle, and a single straight displacement. If force varies with position, work is the integral of the force component along the path. Springs, changing fluid resistance, and variable engine thrust need that more general treatment. A curved path may also require dividing motion into small segments when the force direction changes relative to displacement. Use magnitudes in newtons and metres, and specify the included angle in degrees. The result gives work in joules and also reports the force component parallel to motion. Distinguish displacement from total path length: only the displacement occurring while the stated force and angle apply belongs in this formula. The calculator is useful for mechanics exercises and estimates, but complex systems may also involve rotational work, deformation, heat, and losses.