Calculate mechanical work done by a force on an object. Enter the force (in Newtons), displacement (in meters), and the angle between the force and direction of motion — and get back the work done in Joules. Perfect for physics students and engineers solving problems in classical mechanics.
Work Done
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Work Done (Kilojoules)
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Work Done (kWh)
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Work Done (Calories)
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Effective Force Component
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Mechanical work is calculated using the formula 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 (theta) is the angle between the force vector and the direction of motion. When force and displacement are parallel (θ = 0°), the formula simplifies to W = F × d.
The SI unit of work is the Joule (J), named after physicist James Prescott Joule. One Joule equals the work done when a force of 1 Newton moves an object 1 meter in the direction of the force. Work is also commonly expressed in kilojoules (kJ), kilowatt-hours (kWh), or calories in different contexts.
When the angle between the force and displacement is 90°, cos(90°) = 0, so the work done is zero. This means that if you push on an object perpendicular to its motion — like a centripetal force keeping something moving in a circle — no work is actually done on the object in the direction of travel.
Yes, work can be negative. When the angle between force and displacement is greater than 90° (up to 180°), the cosine of that angle is negative, resulting in negative work. This typically occurs when a force opposes the motion — for example, friction does negative work on a sliding object because the friction force acts opposite to the direction of motion.
Work measures the total energy transferred by a force over a displacement (measured in Joules), while power measures the rate at which that work is done (measured in Watts = Joules per second). Two scenarios can involve the same amount of work but very different power levels if they take different amounts of time.
1 pound-force (lbf) equals approximately 4.44822 Newtons. 1 kilonewton (kN) equals 1,000 Newtons. 1 dyne equals 0.00001 Newtons. This calculator automatically converts your selected force and displacement units to SI units (Newtons and meters) before computing work in Joules.
The effective force component is the portion of the applied force that acts in the direction of displacement — calculated as F × cos(θ). Only this component contributes to doing work on the object. The perpendicular component (F × sin(θ)) does not contribute to work along the direction of motion.
While the work calculator is rooted in physics, it has many practical applications: engineers use it to determine energy requirements for machinery, construction workers assess lifting loads, biomechanics researchers analyze human movement, and students use it to solve textbook problems. Any scenario involving a force moving an object through a distance can be analyzed with this tool.