Work Calculator – Instantly Calculate Mechanical Work in Physics

Theory & Formulas

In physics, work is the energy transferred to or from an object via the application of force along a displacement. It's a scalar quantity, meaning it has magnitude but no direction.

• The standard unit of work is the Joule (J), which is equivalent to one Newton-meter (N·m).
• Work can be positive (if the force has a component in the direction of displacement, energy is added to the object/system) or negative (if the force has a component opposite to the direction of displacement, energy is removed).

Common formulas for calculating work include:

• Work done by a constant force:
  • When force is in the direction of displacement: W = F × d
  • When there's an angle θ between force and displacement: W = F × d × cos(θ)
    (Where F is force, d is displacement, and θ is the angle between the force and displacement vectors.)
• Work-Energy Theorem: The net work done on an object is equal to its change in kinetic energy (ΔKE).

  W_net = ΔKE = KE_final - KE_initial

  Where Kinetic Energy (KE) is given by: KE = ½mv² (m is mass, v is velocity).

• Work and Potential Energy: Work can also result in a change in potential energy (PE). For example, the work done by an external force against gravity to lift an object is stored as gravitational potential energy.

  W_{against gravity} = ΔPE_gravity = mg(h_final - h_initial) = mgΔh

  (Where m is mass, g is acceleration due to gravity, h is height.)