Work, Energy & Power Calculator

Calculate work done, kinetic energy, potential energy, and power in one tool.

⚡ Work, Energy & Power - Overview

Work in physics is done when a force causes an object to move in the direction of the force. Simply pushing on a wall without it moving does no work in the physics sense, no matter how hard you push. Work is measured in Joules (J), the SI unit of energy.

Energy is the capacity to do work. The two most fundamental forms of mechanical energy are kinetic energy (energy due to motion) and potential energy (energy due to position in a gravitational field). Both are measured in Joules. The law of conservation of energy states that energy cannot be created or destroyed - it only converts between forms.

Power is the rate at which work is done or energy is transferred. Two machines can do the same amount of work but the faster one has more power. Power is measured in Watts (W), where 1 W = 1 J/s. Understanding these three concepts is foundational to classical mechanics and engineering.

📐 Formulas

Work: W = F × d × cos(θ)

Kinetic Energy: KE = ½ × m × v²

Potential Energy: PE = m × g × h

Power: P = E / t

F = Force (Newtons, N)

d = Displacement (metres, m)

θ = Angle between force and displacement (degrees)

m = Mass (kilograms, kg)

v = Velocity (metres per second, m/s)

g = Gravitational acceleration (9.81 m/s² on Earth)

h = Height above reference point (metres, m)

E = Energy / Work done (Joules, J)

t = Time (seconds, s)

📖 How to Use This Calculator

Steps

Select the mode - Work, Kinetic Energy, Potential Energy, or Power - using the tabs.

Enter the required values for the selected mode. Units are shown next to each field.

Click Calculate to see the result in Joules or Watts, plus related quantities.

💡 Example Calculations

Example 1 - Work Done (F = 200 N, d = 15 m, θ = 30°)

W = F × d × cos(30°) = 200 × 15 × 0.866

W = 2,598 J

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Example 2 - Kinetic Energy (car: m = 1200 kg, v = 25 m/s)

KE = 0.5 × 1200 × 25² = 0.5 × 1200 × 625

KE = 375,000 J = 375 kJ

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Example 3 - Potential Energy (m = 5 kg, h = 10 m)

PE = 5 × 9.81 × 10 = 490.5 J

PE = 490.5 J

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❓ Frequently Asked Questions

What happens when the angle is 90° in the work formula?+

When θ = 90°, cos(90°) = 0, so W = 0. No work is done. This is why carrying a heavy bag horizontally (force = downward, displacement = horizontal) does zero work in the physics sense - the force and motion are perpendicular. Only the component of force in the direction of motion does work.

What is the work-energy theorem?+

The work-energy theorem states that net work done on an object equals its change in kinetic energy: W = delta KE = 0.5mv2 squared - 0.5mv1 squared. If a 2 kg object accelerates from 3 m/s to 7 m/s, net work = 0.5 x 2 x (49 - 9) = 40 J. This connects force and distance to changes in motion.

How is power different from energy?+

Energy is the capacity to do work (measured in joules). Power is the rate of doing work: P = W/t (measured in watts). A 100 W bulb and a 1000 W heater both use energy, but the heater uses it 10x faster. An athlete and a machine might both lift the same weight (same work/energy), but the machine does it faster (more power).

What is conservative vs non-conservative work?+

Conservative forces (gravity, spring) do work that is path-independent - the work to lift an object 10 m vertically equals the work along any curved 10 m path. Non-conservative forces (friction, drag) dissipate energy as heat and are path-dependent. Mechanical energy is conserved only when all forces are conservative.

How do you calculate the efficiency of a machine?+

Efficiency = (useful work output / total work input) x 100%. A motor that inputs 500 W but delivers 400 W of mechanical output runs at 80% efficiency. The remaining 100 W becomes heat. No real machine reaches 100% efficiency. Use power output / power input for continuous processes.

What is the difference between energy and power?+

Energy is the total capacity to do work, measured in Joules. Power is the rate at which energy is transferred or work is done, measured in Watts (Joules per second). A strong engine and a weak engine might do the same total work, but the strong engine does it faster - meaning it has more power. Think of energy as a bucket of water and power as how fast you pour it out.

How do I convert Joules to kilowatt-hours (kWh)?+

1 kWh = 3,600,000 J = 3.6 MJ. To convert Joules to kWh, divide by 3,600,000. For example, 7,200,000 J = 2 kWh. Your electricity bill uses kWh as the unit of energy consumed. A 100 W appliance running for 10 hours uses 1 kWh of energy.

What is g on other planets?+

Gravitational acceleration g varies by planet. On Earth: 9.81 m/s². On the Moon: 1.62 m/s². On Mars: 3.72 m/s². On Jupiter: 24.79 m/s². On the Sun: 274 m/s². The Potential Energy calculator lets you enter any value of g - just replace 9.81 with the planet's value to calculate PE on other celestial bodies.

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 = delta_KE = 0.5mv^2 - 0.5mu^2. If a 2 kg object accelerates from 3 m/s to 7 m/s, the net work done is 0.5 x 2 x (7^2 - 3^2) = 0.5 x 2 x 40 = 40 J. This theorem connects the force-displacement concept of work to the mass-velocity concept of kinetic energy.

What is the difference between work and energy?+

Energy is the capacity to do work (measured in Joules). Work is the process of transferring energy via force over a distance (also Joules). When you push a box 5 m with 20 N of force, you do 100 J of work, transferring 100 J of kinetic energy to the box. Energy exists in many forms (kinetic, potential, thermal, chemical); work converts energy from one form to another or transfers it between objects.

Why is the formula for work W = F x d x cos(theta)?+

Only the component of force in the direction of displacement does work. If you push at an angle theta to the horizontal and the object moves horizontally, only Fcos(theta) contributes to displacement. At 90 degrees, cos(90) = 0, so a purely perpendicular force does no work (e.g., carrying a box horizontally while gravity acts downward does no work against gravity). At 180 degrees, work is negative (friction opposing motion).

How is power related to force and velocity?+

P = W/t = F x d/t = F x v. An engine that exerts 500 N at 20 m/s produces 10,000 W (10 kW). This is why car power is often given in horsepower: 1 HP = 746 W. At highway speed (30 m/s), a car overcoming 300 N of aerodynamic drag uses P = 300 x 30 = 9,000 W (9 kW) just to maintain speed, separate from any acceleration power.

🔗 Related Calculators

What is the difference between work and energy?

Energy is the capacity to do work, measured in joules. Work is the transfer of energy when a force causes displacement. Work = Force x Displacement x cos(theta), where theta is the angle between force and displacement. When work is done on an object, its energy changes. The work-energy theorem states: net work done on an object = change in kinetic energy. Energy and work are both measured in joules, but energy is a state property while work is a process (transfer).

What is the unit of power and how is it calculated?

Power is the rate at which work is done or energy is transferred, measured in Watts (W). 1 Watt = 1 Joule per second. Formula: P = W / t (power = work divided by time). Also: P = F x v (power = force x velocity). Horsepower (hp) is an older unit: 1 hp = 746 watts. Example: lifting a 50 kg box 2 metres in 4 seconds: work = mgh = 50 x 9.8 x 2 = 980 J. Power = 980 / 4 = 245 W.

What is the law of conservation of energy?

The law of conservation of energy states that energy cannot be created or destroyed - only converted from one form to another. Total energy in a closed system remains constant. In mechanics: potential energy converts to kinetic energy as an object falls (PE + KE = constant, ignoring friction). In electrical circuits: electrical energy converts to heat, light, or mechanical energy. The total always balances - the universe cannot gain or lose energy.

How is kinetic energy different from potential energy?

Kinetic energy (KE) is the energy of motion: KE = (1/2) x m x v^2. It depends on mass and velocity. Potential energy (PE) is stored energy due to position or configuration. Gravitational PE = m x g x h (depends on mass, gravity, and height). Elastic PE = (1/2) x k x x^2 (depends on spring constant and compression). As an object falls from height h: PE converts to KE. At the ground: KE = mgh = initial PE (ignoring air resistance).

What is the work-energy theorem?

How is power different from energy?

What is conservative vs non-conservative work?

How do you calculate the efficiency of a machine?

📌 Quick Tips

💡1 Joule = 1 Newton × 1 metre = 1 kg·m²/s². It is the SI unit of energy.

💡1 Watt = 1 Joule per second. A 60 W bulb uses 60 J every second.

💡Potential energy depends on height above a reference point - always specify what you are measuring from.

💡Results are rounded to a practical number of decimal places for everyday use.

💡Use this calculator as a starting point, then consult a professional for high-stakes decisions.