⚡ Work Calculator
Calculate work done
0° for force parallel to displacement
How to Use This Calculator
Enter Force
Input the force applied in Newtons (N). This is the magnitude of the force doing the work. For example, lifting a 10 kg object requires about 98 N (10 kg × 9.81 m/s²), or pushing with 50 N of force.
Enter Distance
Enter the distance over which the force is applied in meters (m). This is the displacement in the direction of motion. For example, lifting an object 2 m high, or pushing a box 5 m across the floor.
Enter Angle (Optional)
Enter the angle between the force and displacement in degrees. The default is 0° (force parallel to displacement). For example, 0° for pushing directly forward, 90° for force perpendicular (no work), or 45° for force at an angle.
Calculate Work
Click the "Calculate Work" button to compute the work done. The calculator uses W = Fd cos(θ) to account for the angle between force and displacement. Work is measured in Joules (J).
About Work Calculator
The Work Calculator computes the work done when a force moves an object over a distance. Work is a fundamental concept in physics, defined as the product of force and displacement, with consideration for the angle between them. Work is measured in Joules (J) and represents the energy transferred when a force acts over a distance.
When to Use This Calculator
- Physics Problems: Solve work problems in physics homework and exams
- Engineering Calculations: Calculate work done in mechanical systems
- Energy Analysis: Determine energy requirements for moving objects
- Mechanical Design: Calculate work for lifting, pushing, or pulling operations
- Educational Purposes: Learn about work, energy, and the relationship between force and displacement
Why Use Our Calculator?
- ✅ Angle Consideration: Accounts for the angle between force and displacement
- ✅ Step-by-Step Formula: Shows the calculation process
- ✅ Accurate Calculations: Uses the standard physics formula
- ✅ Instant Results: Get answers immediately
- ✅ Free to Use: No registration or payment required
Understanding Work
Work in physics is defined as the product of force and displacement, but only the component of force in the direction of motion does work. The formula W = Fd cos(θ) accounts for this, where θ is the angle between force and displacement. When the force is parallel to displacement (θ = 0°), cos(0°) = 1, so work is maximum. When force is perpendicular (θ = 90°), cos(90°) = 0, so no work is done. Work is measured in Joules (J), where 1 J = 1 N·m. Positive work means energy is transferred to the object, while negative work means energy is removed.
Formula
W = F × d × cos(θ)
Where:
- W = Work (Joules)
- F = Force (Newtons)
- d = Displacement/Distance (meters)
- θ = Angle between force and displacement (degrees)
Example Calculation:
For a force of 100 N, distance of 10 m, and angle of 0°:
W = 100 × 10 × cos(0°)
W = 100 × 10 × 1
W = 1000 J
For the same force at 60°:
W = 100 × 10 × cos(60°) = 100 × 10 × 0.5 = 500 J
Important Note: Only the component of force in the direction of motion does work. When force is perpendicular to displacement (90°), no work is done. The cosine term accounts for this directional relationship.
Frequently Asked Questions
What is work in physics?
Work in physics is the energy transferred when a force acts on an object and causes it to move. It's calculated as W = Fd cos(θ), where only the component of force in the direction of motion does work. Work is measured in Joules (J), and 1 Joule = 1 Newton-meter. Work represents the energy transferred to or from an object.
Why is there a cosine term in the work formula?
The cosine term accounts for the angle between the force and the direction of motion. Only the component of force parallel to the displacement does work. If force is at an angle, you need the parallel component: F_parallel = F × cos(θ). When force is perpendicular to motion (90°), cos(90°) = 0, so no work is done—this makes sense because perpendicular forces don't move objects in that direction.
Can work be negative?
Yes, work can be negative. Negative work occurs when the force opposes the direction of motion (angle between 90° and 270°). For example, friction does negative work because it opposes motion. When you lift an object, gravity does negative work. Negative work means energy is removed from the object, while positive work means energy is added.
What's the difference between work and energy?
Work is the process of transferring energy, while energy is the capacity to do work. Work is the energy transferred when a force acts over a distance. For example, when you do work lifting an object, you transfer energy to it (as gravitational potential energy). Work and energy have the same units (Joules) because work is energy transfer.
When is no work done?
No work is done when: (1) there's no displacement (object doesn't move), (2) force is perpendicular to displacement (θ = 90° or 270°), (3) there's no force applied. For example, holding a heavy object stationary requires force but no work (no displacement). Pushing against a wall with no movement does no work. Carrying a backpack horizontally does no work against gravity (force is perpendicular to motion).