The Force • Work • Power Calculator helps you analyze how physical effort translates into mechanical energy and rate of performance. It applies classic physics laws that describe motion, energy transfer, and system efficiency—essential for engineering, sports science, automotive design, and physics education.
Core Formulas
- Force (F): F = m × a, where m is mass (kg or lbm) and a is acceleration (m/s² or ft/s²). Force is the push or pull that causes an object to change its velocity. Measured in newtons (N) in SI units or pounds-force (lbf) in Imperial units. Newton's Second Law: 1 N = 1 kg·m/s².
- Work (W): W = F × d × cos(θ), where F is force, d is displacement (distance moved), and θ is the angle between the force vector and the direction of motion. Work represents energy transferred when a force moves an object. Only the component of force parallel to motion contributes to work. Measured in joules (J) in SI or foot-pounds (ft·lbf) in Imperial units. 1 J = 1 N·m.
- Power (P): P = W/t (work per unit time) or P = F × v (force times velocity), where t is time and v is velocity. Power is the rate of doing work—how quickly energy is transferred or converted. Measured in watts (W) where 1 W = 1 J/s, or horsepower (hp) where 1 hp ≈ 745.7 W. Higher power means faster energy transfer.
Related Concepts
- Inclined Plane with Friction: Calculates the force required to move a mass along a slope, accounting for both gravitational resistance (component of weight parallel to incline) and frictional resistance (μ × normal force). The normal force N = mg cos(α) is perpendicular to the surface, and friction force F_friction = μN opposes motion. Net required force = mg sin(α) + μmg cos(α), where α is the incline angle.
- Variable Force Integration: When force varies with displacement (e.g., spring force F = kx, or non-uniform applied forces), work cannot be calculated with simple multiplication. Instead, use numerical integration: W = ∫F(x)dx over the displacement range. The calculator uses trapezoidal or Simpson's rule to approximate the area under the force vs. displacement curve.
- Unit Conversion: Supports both SI (metric) and Imperial (US customary) systems. Automatically converts between N ↔ lbf (1 lbf ≈ 4.448 N), J ↔ ft·lbf (1 J ≈ 0.7376 ft·lbf), and W ↔ hp (1 hp = 745.7 W). Ensures consistency across mass (kg ↔ lbm), distance (m ↔ ft), and time (s) units.
Understanding these principles allows you to design motors, optimize athletic performance, calculate engine output, and predict energy requirements for mechanical systems.