Work and Energy Calculator
Work in physics is defined as the energy transferred to an object by a force acting along a displacement. The general formula is W = F * d * cos(theta), where F is the applied force in newtons, d is the displacement in metres, and theta is the angle between the direction of the force and the direction of motion. When the force and motion are in the same direction (theta = 0), the formula simplifies to W = F * d. When theta = 90 degrees, no work is done even though a force is applied (for example, a person carrying a heavy box horizontally does no work against gravity). The unit of work is the joule (J), identical to the unit of energy. The work-energy theorem provides a second approach: the net work done on an object equals the change in its kinetic energy, W = 0.5 * m * v² - 0.5 * m * u², where u is initial velocity and v is final velocity. This calculator supports both approaches. Mode 1 uses force, distance, and angle. Mode 2 uses mass, initial velocity, and final velocity.
Work done: -- J
How work is calculated
Work measures the energy transferred to an object by a force acting through a displacement. Only the component of force parallel to the motion contributes; the perpendicular component does no work.
Mode 1: Force, distance, and angle
W = F × d × cos(θ)
where W = work (J), F = force (N), d = displacement (m), θ = angle between force and motion
Mode 2: Work-energy theorem
W = ΔKE = 0.5 × m × v² − 0.5 × m × u²
where m = mass (kg), v = final velocity (m/s), u = initial velocity (m/s)
Worked example (Mode 1)
Force 50 N, distance 10 m, angle 0 degrees:
- cos(0) = 1.00
- W = 50 × 10 × 1 = 500.00 J
Worked example (Mode 2)
Mass 5 kg, initial velocity 0 m/s, final velocity 10 m/s:
- KE_i = 0.5 × 5 × 0² = 0.00 J
- KE_f = 0.5 × 5 × 10² = 250.00 J
- W = 250 − 0 = 250.00 J
Work and energy calculator: frequently asked questions
What is work in physics?
In physics, work (W) is defined as the energy transferred to or from an object by a force acting over a displacement. The formula is W = F * d * cos(theta), where F is the magnitude of the force (N), d is the displacement (m), and theta is the angle between the force direction and the direction of motion. Work is measured in joules (J).
Why does the angle matter in the work formula?
Only the component of force parallel to the displacement does work. The cosine term extracts this component. When theta = 0 degrees (force and motion in the same direction), cos(0) = 1 and W = F * d, the maximum. When theta = 90 degrees (force perpendicular to motion, like a centripetal force), cos(90) = 0 and no work is done. When theta = 180 degrees (force opposes motion), cos(180) = -1 and the work is negative (energy is removed from the object).
What is the work-energy theorem?
The work-energy theorem states that the net work done on an object equals the change in its kinetic energy: W = KE_final - KE_initial = 0.5 * m * v² - 0.5 * m * u². Here v is final velocity and u is initial velocity. This provides a powerful shortcut: instead of tracking forces through time, you can compute the energy change directly from initial and final speeds.
What is a joule?
The joule (J) is the SI unit of energy, work, and heat. It is defined as the work done when a force of one newton moves an object one metre in the direction of the force: 1 J = 1 N m = 1 kg m² s⁻². It is named after physicist James Prescott Joule. One watt-second is also equal to one joule.
Can work be negative?
Yes. When the angle between the applied force and the displacement is greater than 90 degrees, the cosine is negative and the work done by that force is negative. This means the force removes kinetic energy from the object (for example, friction always does negative work on a moving object). The net work can also be negative if opposing forces exceed driving forces.
Official sources
- NIST SP 330 (2019) "The International System of Units (SI)": NIST SP 330 PDF.
- NIST SI Unit definitions: nist.gov SI units.
Reviewed by the CalculatorHub team, edited by James Graham, 14 June 2026. See our methodology. General information only.