Work Calculator
Calculate work done by a force using the physics formula W = F × d × cos(θ). Free online work calculator for mechanics, physics students, and engineers with charts, breakdowns, and shareable results.
About This Calculator
The Work Calculator helps you compute work done when a force moves an object over a displacement. Using the fundamental physics formula W = F × d × cos(θ), this tool is designed for physics students, engineers, and anyone studying mechanics. Simply enter the applied force in newtons, the displacement distance in meters, and the angle between the force and the direction of motion to get instant results.
The work equation W = F × d × cos(θ) comes from the definition of work in physics: the product of force and the component of displacement in the direction of the force. When the angle is 0°, the formula simplifies to W = F × d. The calculator also converts work to kilojoules (1 kJ = 1000 J) for convenience. Results include a step-by-step breakdown showing each input value and the computed work, plus an interactive chart for visual comparison.
About Work in Physics
Work in physics has a precise definition: it is the energy transferred to or from an object via a force acting over a displacement. Unlike everyday usage, physics work requires both a force and movement. If you push against a wall and it doesn't move, no physics work is done. The work-energy theorem states that the net work done on an object equals its change in kinetic energy, making work a fundamental concept in understanding motion and energy transfer across mechanics, thermodynamics, and electromagnetism.
Frequently Asked Questions
What is the formula for calculating work in physics?
The formula for work in physics is W = F × d × cos(θ), where W is work in joules, F is the applied force in newtons, d is the displacement in meters, and θ is the angle between the force and displacement vectors.
What are the SI units of work?
The SI unit of work is the joule (J). One joule equals one newton-meter (N·m). Work can also be expressed in kilojoules (kJ), where 1 kJ = 1000 J.
When is work done zero in physics?
Work done is zero when the applied force is zero, the displacement is zero, or the angle between the force and displacement is 90° (cos 90° = 0). For example, carrying a box horizontally while walking applies zero work in the physics sense because the force is vertical and displacement is horizontal.
How does the angle between force and displacement affect work?
The angle θ between the force and displacement vectors determines the effective component of force doing work. When θ = 0°, cos(θ) = 1 and all force contributes to work. As θ increases, less force contributes. At θ = 90°, work is zero. For angles above 90°, work becomes negative, meaning the force opposes motion.
What is the difference between work and power in physics?
Work is the energy transferred when a force moves an object over a distance, measured in joules. Power is the rate at which work is done, measured in watts (W). Power = Work / Time. A powerful machine does the same work in less time.
Can work be negative in physics?
Yes, work can be negative when the force opposes the direction of motion. This occurs when the angle θ is between 90° and 270°, where cos(θ) is negative. For example, friction does negative work on a sliding object because it acts opposite to the direction of motion.
How do you calculate work from force and distance without angle?
If the force is applied in the same direction as the displacement (θ = 0°), the formula simplifies to W = F × d. Simply multiply the force in newtons by the distance in meters to get work in joules. Set the angle to 0° in this calculator for this case.
How is work related to kinetic energy?
According to the work-energy theorem, the net work done on an object equals its change in kinetic energy: W_net = ΔKE = ½mv² - ½mv₀². This means doing work on an object increases its kinetic energy, which is a fundamental principle in mechanics.