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Select a mode and enter your values to calculate force, work, or power. Results will appear here.
Calculate force (F = m·a), work (W = F·d·cos θ), and power (P = W/t). Analyze inclined planes with friction and compute work from variable forces.
Force (N) = mass × acceleration — any push or pull that changes motion.
Work (J) = force × distance × cos(angle) — energy transferred when moving an object.
Power (W) = work ÷ time — how fast work is done.
For example, pushing a 10 kg box with 2 m/s² acceleration requires 20 N of force. Moving that box 5 meters horizontally does 100 J of work (20 N × 5 m × cos(0°)). If done in 2 seconds, your power output is 50 W.
Example: Lifting a Box
Lifting a 20 kg box to a 1.5 m high shelf against gravity (9.8 m/s²):
Select a mode and enter your values to calculate force, work, or power. Results will appear here.
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.
Understanding these principles allows you to design motors, optimize athletic performance, calculate engine output, and predict energy requirements for mechanical systems.
This calculator provides multiple modes to solve different physics problems involving force, work, and power. Follow these steps:
Pro Tip: When the force varies across distance (e.g., spring compression, variable drag, or non-uniform applied forces), use Variable Force Integration mode for accurate work calculations. Constant force assumptions can lead to significant errors in these scenarios.
Remember: Always verify that units are consistent before calculating. Mixing SI and Imperial units without proper conversion will produce incorrect results. The calculator handles conversions automatically when you select a unit system.
The calculator presents results with detailed explanations and unit conversions. Here's how to interpret each output:
| Quantity | Symbol | Unit (SI) | Description |
|---|---|---|---|
| Force | F | N (newton) | Push or pull on an object. 1 N accelerates 1 kg at 1 m/s². Causes changes in motion (acceleration or deceleration). |
| Work | W | J (joule) | Energy transferred by force over distance. 1 J = 1 N·m. Only force component parallel to motion does work. W = 0 if force is perpendicular to motion. |
| Power | P | W (watt) | Rate of doing work (energy per time). 1 W = 1 J/s. Higher power = faster energy transfer. 1 hp = 745.7 W (common in automotive contexts). |
| Angle | θ | degrees or rad | Direction of force relative to motion. θ = 0° means force and motion aligned (maximum work). θ = 90° means perpendicular (zero work). W = Fd cos(θ). |
| Friction Coefficient | μ | — | Dimensionless resistance between surfaces. Typical values: ice ~0.05, wood on wood ~0.4, rubber on concrete ~0.7. Friction force F_f = μN. |
| Normal Force | N | N (newton) | Reaction force perpendicular to surface. On horizontal surface: N = mg. On incline: N = mg cos(α). Determines friction magnitude. |
| Required Force | Freq | N (newton) | Net force needed to move mass on incline. F_req = mg sin(α) + μmg cos(α). Includes both gravitational and frictional resistance. |
| Work (Variable Force) | Wtotal | J (joule) | Total energy via numerical integration when force varies with displacement. W ≈ Σ[(Fi + Fi+1)/2 × Δx]. More accurate than assuming constant force. |
Outputs Display:
• Constant Force Assumption: Basic calculations assume force remains constant throughout the motion. Variable forces (such as springs, air resistance, or changing applied force) require integration methods or numerical approaches not fully modeled in simple work calculations.
• Rigid Body Approximation: Objects are treated as perfectly rigid with no deformation. Real materials compress, stretch, and absorb energy during force application, which affects the actual work done and power transmitted.
• Idealized Friction Model: Friction calculations use constant coefficients (Coulomb friction model). Real friction depends on velocity, surface conditions, temperature, and contact area variations that can cause significant deviations from calculated values.
• No Energy Losses to Heat or Sound: Power efficiency calculations may not account for all real-world losses including heat generation, vibration, sound energy, and material fatigue that reduce the useful work output in practical systems.
Important Note: This calculator is strictly for educational and informational purposes only. It demonstrates fundamental force, work, and power principles for learning. Engineering applications requiring motor sizing, structural analysis, or machine design need comprehensive analysis accounting for dynamic loads and efficiency factors.
The formulas and principles used in this calculator are based on established physics principles from authoritative sources:
Note: This calculator implements standard physics formulas for educational purposes. For engineering applications requiring high precision, consult professional engineering references and standards.
Common questions about force, work, power, angles, friction, and variable force integration.
Force is a push or pull measured in newtons (N), defined by F = m × a where m is mass and a is acceleration. Force causes objects to change their state of motion but doesn't necessarily involve energy transfer. Work is energy transferred when a force moves an object over a distance, calculated as W = F × d × cos(θ), measured in joules (J). Work requires both force and displacement—if an object doesn't move, no work is done regardless of force applied (e.g., pushing against a wall). Power is the rate of doing work, measured in watts (W) or horsepower (hp), calculated as P = W/t (work per unit time) or P = F × v (force times velocity). Power indicates how quickly energy is transferred—a 100 W motor does the same work as a 1000 W motor, just 10 times slower. In summary: Force is the cause, work is the energy transferred, and power is how fast that transfer happens.
Only the component of force that acts in the direction of motion contributes to work. The formula W = F × d × cos(θ) includes the cosine factor to account for this directional alignment. When force is applied at an angle θ to the direction of motion, we decompose the force into two components: F_parallel = F cos(θ) (in the direction of motion) and F_perpendicular = F sin(θ) (perpendicular to motion). Only F_parallel does work because work involves moving an object in the direction of force. Examples: (1) θ = 0° (force aligned with motion): cos(0°) = 1, so W = Fd (maximum work). (2) θ = 90° (force perpendicular to motion): cos(90°) = 0, so W = 0 (no work, like normal force when sliding horizontally). (3) θ = 180° (force opposite to motion): cos(180°) = -1, so W = -Fd (negative work, removing energy from the system, like friction). This principle explains why pulling a wagon at an angle is less efficient than pulling horizontally—only part of your force contributes to forward motion.
Horsepower (hp) and watts (W) both measure power but use different unit systems. The conversion factor is: 1 horsepower = 745.7 watts (approximately). To convert: hp × 745.7 = watts, or watts ÷ 745.7 = hp. Examples: (1) A 200 hp car engine produces 200 × 745.7 ≈ 149,140 W ≈ 149 kW. (2) A 2000 W (2 kW) electric motor is equivalent to 2000 ÷ 745.7 ≈ 2.68 hp. Historical note: Horsepower was defined by James Watt in the 18th century as the power output of a typical draft horse—approximately 33,000 foot-pounds per minute. Today, mechanical horsepower (hp_I) = 745.7 W, while metric horsepower (PS, CV, or hp_M) ≈ 735.5 W, and electrical horsepower ≈ 746 W. Always verify which horsepower definition is being used in automotive or industrial contexts. In physics and engineering, watts are preferred because they integrate naturally with SI units (1 W = 1 J/s = 1 N·m/s).
An inclined plane is a flat surface tilted at an angle α to the horizontal, used to lift or move objects with reduced force compared to vertical lifting. It's one of the six classical simple machines. The gravitational force on an object (weight W = mg) can be decomposed into two components: (1) W_parallel = mg sin(α), acting down the slope, and (2) W_perpendicular = mg cos(α), pressing into the surface (creating normal force N = mg cos(α)). Without friction, the force required to push an object up the incline is F = mg sin(α). With friction, an additional resistance F_friction = μN = μmg cos(α) opposes motion, where μ is the friction coefficient. The total required force becomes F_total = mg sin(α) + μmg cos(α) = mg(sin α + μ cos α). Friction increases the effort needed but provides stability—preventing objects from sliding down unintentionally. Trade-off: Inclined planes reduce force requirements (compared to lifting vertically) but increase the distance traveled. Work done remains approximately the same: W_vertical = mgh (lifting straight up) vs. W_incline = F_total × d ≈ mgh + friction losses. Applications: ramps, roads in mountains, screws, wedges.
Use variable force integration when the applied force changes with displacement (position), making simple multiplication W = F × d inaccurate. This occurs in several scenarios: (1) Springs and elastic systems: Force increases linearly with compression/extension (Hooke's Law: F = kx). Work done compressing a spring: W = ∫₀ˣ kx dx = ½kx². Simple F × d would overestimate. (2) Gravity over large distances: Gravitational force F = GMm/r² decreases with distance r from a massive object. For satellite launches, integration accounts for changing force. (3) Variable friction or drag: Friction changing with surface conditions, or air resistance increasing with velocity (F_drag ∝ v²). (4) Non-uniform applied forces: Manually pushing an object with varying effort, or engine force that changes during acceleration. (5) Experimental data: When you have measured force vs. position data points and need to find total work. The calculator uses numerical integration (trapezoidal rule): W ≈ Σ[(F_i + F_(i+1))/2 × (x_(i+1) - x_i)], summing the area under the force-displacement curve. This provides accurate results when force isn't constant—essential for realistic engineering calculations, spring systems, and experimental analysis.
Learn more about force, work, and power from these authoritative physics resources:
Comprehensive physics education on work, energy, and power
Educational resource on force, motion, and Newton's laws
Georgia State University physics reference on work and energy
Official SI unit definitions from the National Institute of Standards and Technology
Disclaimer: This calculator provides educational estimates based on classical mechanics principles. For professional engineering applications, consult qualified engineers and refer to relevant industry standards.
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