⚡ Work Calculator
Calculate the work done by a force using the physics formula W = F × d × cos(θ). Enter force, displacement, and the angle between them to find the work in joules. Supports multiple force and distance units, and provides a step-by-step breakdown.
What is Work in Physics?
In physics, work is defined as the transfer of energy that occurs when a force is applied to an object and the object moves in the direction of the force. The standard formula for work is:
W = F × d × cos(θ)
Where:
W = Work (Joules)
F = Magnitude of force (Newtons)
d = Distance (meters)
θ = Angle between force and displacement
Work is measured in joules (J) in the SI system. One joule is defined as the work done by a force of one newton moving an object one meter. If the force is perpendicular to the displacement (θ = 90°), no work is done. If the force acts in the same direction as the displacement (θ = 0°), maximum work is done.
Understanding the Angle
The angle θ is the angle between the force vector and the displacement vector. Only the component of force that acts in the direction of displacement does work. The component of force perpendicular to displacement does no work (since cos 90° = 0).
Common Work Examples
- Lifting an object: Force of gravity acts downward, displacement upward — angle 180°, work done against gravity is negative (W = F × d × cos180° = −F×d).
- Pushing a box across the floor: Force parallel to displacement — angle 0°, positive work.
- Carrying a suitcase while walking: Force from your hand is vertical (to hold it up), displacement is horizontal — angle 90°, no work done by the lifting force.
Units of Work
Work can be expressed in various units depending on the system:
- SI: Joule (J) = N·m = kg·m²/s²
- CGS: Erg = 10⁻⁷ J
- Imperial/US: Foot-pound (ft·lb)
- Other: Calorie (cal), kilowatt-hour (kWh)
How the Calculator Works
- Convert Units: Force and distance are converted to SI units (N and m) for calculation.
- Compute Work: Apply the formula W = F × d × cos(θ) using the angle in radians.
- Convert Output: The result is converted to the selected output work unit.
- Display Breakdown: Step-by-step calculation with intermediate values is shown.
Important Notes
This calculator assumes a constant force applied over the entire distance. In real-world scenarios, force may vary, requiring integration (work is the area under a force-distance curve). The calculator also assumes motion in a straight line (displacement vector).
❓ Work Calculator FAQ
What is the formula for work?
The formula for work is W = F × d × cos(θ), where F is force, d is distance, and θ is the angle between the force and displacement vectors.
What is the unit of work?
In the SI system, work is measured in joules (J). One joule is equal to one newton-meter (N·m).
When is work zero?
Work is zero when there is no displacement (d = 0), no force (F = 0), or when the force is perpendicular to displacement (θ = 90°).
What is the difference between work and energy?
Work is the transfer of energy. Energy is the capacity to do work. They have the same units (joules).
Can work be negative?
Yes. Work is negative when the force acts opposite to displacement (θ > 90°). For example, when you lift an object against gravity, gravity does negative work.
What is the angle in the work formula?
The angle θ is the angle between the force vector and the displacement vector. It ranges from 0° to 180°.
How do I convert between work units?
1 J = 0.001 kJ = 0.239 cal = 0.000239 kcal = 0.000278 Wh = 0.000000278 kWh = 0.7376 ft·lb.
What is the work done by gravity?
Work done by gravity on a falling object is positive (force and displacement same direction), while on a rising object it is negative (opposite directions).
Is work a vector or scalar?
Work is a scalar quantity. It has magnitude but no direction, though it can be positive or negative.
What is the relationship between work and power?
Power is the rate at which work is done: Power = Work / Time. Work is measured in joules, power in watts (J/s).