Work & Energy Calculator
Calculate work done, kinetic energy, potential energy, and power.
Calculation Type
0° = force parallel to motion
What Is the Work & Energy Calculator?
The Work & Energy Calculator covers five calculation modes: Work (W = F·d·cos θ), Kinetic Energy (KE = ½mv²), Potential Energy (PE = mgh), Power (P = W/t), and the Work-Energy Theorem (W_net = ΔKE). Results are shown in Joules with automatic conversion to 8 energy units (kJ, MJ, cal, kcal, Wh, kWh, BTU, eV), smart unit selection, and step-by-step workings. Power results include watts, kilowatts, and horsepower.
Formula
W = F · d · cos(θ)KE = ½mv²PE = mghP = W / tW_net = ΔKE = ½mv² − ½mv₀²How to Use
- ›Select the calculation mode from the row of buttons at the top.
- ›Enter the required values, only the relevant inputs for the selected mode appear.
- ›For Work mode, use the angle slider to set the direction of force relative to displacement.
- ›Click Calculate (or press Enter) to see the result with all unit conversions.
- ›Use Reset to clear inputs and start a new calculation.
Example Calculation
Example 1, Pushing a box (Work)
A 50 N force pushes a box 10 m at 30° to displacement.
Example 2, Car kinetic energy
A 1,200 kg car at 100 km/h (27.78 m/s):
Example 3, Electric motor power
A motor does 3,600 J of work in 2 seconds:
Understanding Work & Energy
Work, Energy, and Power, Core Concepts
Work, energy, and power form the triad of classical mechanics that connects forces to motion and time. Work is the transfer of energy when a force displaces an object. Energy is the capacity to perform work, existing in many forms, kinetic, potential, thermal, chemical, nuclear. Power is how fast energy transfers. All three are scalar quantities measured in SI units derived from the joule.
- ›Work = 1 J when 1 N of force moves an object 1 m in the direction of the force.
- ›Kinetic energy scales with velocity squared, doubling speed quadruples KE.
- ›Gravitational PE depends on height above a reference; the reference choice is arbitrary.
- ›Conservation of energy: total mechanical energy (KE + PE) is conserved in the absence of friction.
Energy Unit Conversion Reference
| Unit | = Joules | Abbreviation | Common context |
|---|---|---|---|
| 1 Joule | 1 | J | SI base unit; kinetic energy of 2 kg at 1 m/s |
| 1 Kilojoule | 1,000 | kJ | Food energy, heating |
| 1 Megajoule | 1,000,000 | MJ | Vehicle fuel, explosives |
| 1 Calorie (small) | 4.184 | cal | Chemistry lab calorimetry |
| 1 Kilocalorie | 4,184 | kcal | Food Calorie (written Cal) |
| 1 Watt-hour | 3,600 | Wh | Small battery capacity |
| 1 Kilowatt-hour | 3,600,000 | kWh | Household electricity billing |
| 1 BTU | 1,055.06 | BTU | HVAC, US energy industry |
| 1 Electronvolt | 1.602 × 10⁻¹⁹ | eV | Atomic/particle physics |
| 1 Horsepower-hour | 2,684,520 | hp·h | Motor/engine output |
Power Output Reference
| Source | Power (W) | Power (hp) | Context |
|---|---|---|---|
| Human (resting) | 80 | 0.107 | Basal metabolic rate |
| Human (cycling, peak) | 400–500 | 0.54–0.67 | Tour de France sprints |
| Horse (sustained) | 745.7 | 1.0 | Definition of 1 horsepower |
| Car engine (typical) | 100,000–200,000 | 134–268 | Family sedan |
| Commercial aircraft | 40,000,000 | 53,600 | Per engine, takeoff thrust |
| Large wind turbine | 3,000,000 | 4,023 | Peak rated output |
| Nuclear power plant | 1,000,000,000 | 1,341,000 | Per reactor, ~1 GW |
The Work-Energy Theorem in Practice
- ›Braking distance, All kinetic energy must be removed as heat. At 100 km/h, a 1,500 kg car has 578 kJ of KE; brake pads must absorb all of it.
- ›Roller coasters, PE at the top converts to KE at the bottom; KE − friction losses = final speed.
- ›Projectile motion, Vertical KE converts to PE at peak height; horizontal KE is unchanged (no work done against gravity horizontally).
- ›Structural engineering, Impact loads are quantified in joules; energy absorbers (crumple zones, crash cushions) are rated by the energy they can absorb.
Frequently Asked Questions
What is the Work-Energy Theorem?
The Work-Energy Theorem states that the net work done on an object equals its change in kinetic energy: W_net = ΔKE = ½mv² − ½mv₀². This theorem links force-based calculations (work) to motion-based calculations (kinetic energy), making it the central bridge between Newton's second law and energy methods in mechanics.
Why does work depend on cos(θ)?
Work is defined as the dot product of force and displacement vectors: W = F · d = Fd·cos(θ). Only the component of force parallel to displacement does work. At θ = 0° (force parallel to motion): W = Fd. At θ = 90° (force perpendicular): W = 0. At θ = 180° (opposing motion): W = −Fd (negative work, removing energy).
What is the difference between energy and power?
Energy (Joules) is the capacity to do work, it is a state quantity. Power (Watts) is the rate at which energy is transferred or converted, it is a rate quantity: P = W/t = ΔE/t. A 100W bulb consumes 100 J every second. A 1000W motor running for 1 hour uses 3,600,000 J = 3.6 MJ = 1 kWh.
What is gravitational potential energy?
Gravitational PE = mgh, where m is mass (kg), g is gravitational acceleration (9.81 m/s² on Earth), and h is height above a reference point. This represents stored energy that converts to kinetic energy when an object falls. A 70 kg person climbing 10 m of stairs gains PE = 70 × 9.81 × 10 = 6,867 J ≈ 1.64 kcal.
How do I convert between energy units?
- ›1 kJ = 1,000 J = 0.239 kcal = 0.278 Wh = 0.948 BTU
- ›1 kcal = 4,184 J (food calorie, written as Cal)
- ›1 kWh = 3,600,000 J = 3.6 MJ = 860 kcal
- ›1 BTU = 1,055 J = 0.293 Wh
- ›1 eV = 1.602 × 10⁻¹⁹ J (atomic/particle physics)