Work Calculator (Physics)

Calculate physical work, power, and gravitational potential energy with clear formulas, units, and step‑by‑step explanations.

Work from Force and Displacement

Compute work done when a constant force acts over a displacement at a given angle.

0° = same direction, 90° = no work.

What is work in physics?

In physics, work measures how much energy is transferred when a force causes an object to move. If you push, pull, or lift something and it moves in the direction of the force, you are doing work on it.

General formula for work:

\( W = \vec{F} \cdot \vec{s} = F \, s \cos\theta \)

  • \( W \) = work (joules, J)
  • \( F \) = magnitude of the force (newtons, N)
  • \( s \) = displacement (meters, m)
  • \( \theta \) = angle between force and displacement

Only the component of the force in the direction of motion does work. If the force is perpendicular to the motion (for example, centripetal force in uniform circular motion), the work done is zero.

Power and energy relationships

Average power:

\( P = \dfrac{W}{t} \)

  • \( P \) = power (watts, W)
  • \( W \) = work or energy (joules, J)
  • \( t \) = time (seconds, s)

Gravitational potential energy (near Earth’s surface):

\( E_\text{p} = m g h \)

  • \( E_\text{p} \) = gravitational potential energy (J)
  • \( m \) = mass (kg)
  • \( g \) = gravitational acceleration (m/s²)
  • \( h \) = height relative to reference level (m)

Example: Work done lifting a box

Suppose you lift a 10 kg box straight up by 1.5 m on Earth (\( g \approx 9.81 \,\text{m/s}^2 \)).

  1. Compute the weight (force): \( F = m g = 10 \times 9.81 = 98.1 \,\text{N} \).
  2. Displacement is \( s = 1.5 \,\text{m} \), angle \( \theta = 0^\circ \) (force and motion are both upward).
  3. Work: \( W = F s \cos\theta = 98.1 \times 1.5 \times \cos 0^\circ \approx 147.15 \,\text{J} \).

The gravitational potential energy of the box has increased by the same amount, \( \Delta E_\text{p} = 147.15 \,\text{J} \).

Common unit conversions used by this calculator

  • 1 kN = 1000 N
  • 1 lbf ≈ 4.44822 N
  • 1 ft = 0.3048 m
  • 1 Wh = 3600 J
  • 1 kWh = 3 600 000 J

Frequently asked questions

Is work a scalar or a vector?

Work is a scalar quantity. It can be positive (energy transferred to an object) or negative (energy taken from an object), but it has no direction.

When is work equal to zero?

Work is zero if:

  • There is no displacement (the object does not move), or
  • The force is perpendicular to the displacement (\( \theta = 90^\circ \)), or
  • No net force acts on the object along the direction of motion.

How is work related to kinetic energy?

The work–energy theorem states that the net work done on an object equals its change in kinetic energy: \( W_\text{net} = \Delta K = K_\text{final} - K_\text{initial} \).