Trabalho F·d (vetorial)
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
Formula
W = F·d
About this calculator
The Work F·d (vector) calculator computes the work done by a constant force along a straight-line displacement, using the dot product between the force and displacement vectors. Work is a scalar quantity that measures the energy transferred by the force during motion.
The formula used is W = F · d, where F and d are vectors. The dot product is calculated as the sum of the products of corresponding components: W = Fx * dx + Fy * dy + Fz * dz. The result is given in joules (J) in the International System, considering force in newtons and displacement in meters.
This calculator is useful for physics and engineering students solving mechanical work problems, especially when the force is not parallel to the displacement. It is also applicable in everyday situations, such as pushing an object in a direction that does not align with the applied force.
Caution: the dot product depends on the angle between the vectors. If the angle is greater than 90 degrees, the work is negative, indicating that the force opposes the motion. Ensure you enter the correct vector components, respecting signs and units.
Frequently asked questions
What does negative work mean?
Negative work occurs when the angle between force and displacement is greater than 90 degrees, meaning the force opposes motion. For example, friction does negative work.
Can I use this calculator for variable forces?
No, this calculator is only for constant forces. For variable forces, integration is required.
What units should I use?
Use newtons (N) for force and meters (m) for displacement. Work will be calculated in joules (J).
What if displacement is zero?
If displacement is zero, work is zero, regardless of the applied force.
What if I only have the magnitude of force and the angle?
You can decompose the force into components using the angle. The calculator expects Cartesian components of the vectors.