What is Work in physics, and can it be negative?

In physics, Work (W) is done when an external force (F) acts on an object causing a displacement (d) along the line of action. It is defined as W = F × d × cos(θ). Work can be positive (force acts in direction of motion), zero (force is perpendicular to motion, like gravity acting on a satellite in circular orbit), or negative (force opposes motion, such as friction or brake pads decelerating a vehicle).

What is the difference between Kinetic Energy and Potential Energy?

Kinetic Energy (KE = ½mv²) is the energy an object possesses due to its motion, dependent on mass and the square of velocity. Potential Energy (PE = mgh) is stored energy an object possesses due to its position in a gravitational field or elevated height relative to a zero reference level.

What is the Work-Energy Theorem?

The Work-Energy Theorem states that the net work done by all forces acting on an object equals the change in its kinetic energy: W_net = ΔKE = ½mv_final² - ½mv_initial². Positive work accelerates an object and increases its kinetic energy, while negative work decelerates it.

What is Power and how is it related to Work?

Power (P) is the rate at which work is done or energy is transferred per unit time: P = W / t. One Watt (W) equals one Joule per second (1 J/s). One mechanical Horsepower (HP) equals approximately 745.7 Watts.

How many Watts are in one Horsepower (HP)?

In standard imperial/mechanical engineering, 1 Horsepower (HP) is defined as exactly 550 ft·lbf/s, which converts to approximately 745.699872 Watts (~0.746 kW). In metric systems, 1 metric horsepower (PS / cv) is defined as approximately 735.49875 Watts.

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Work, Energy & Power Calculator

Calculate Work Done (W = F·d·cos θ), Kinetic Energy (KE = ½mv²), Gravitational Potential Energy (PE = mgh), and Mechanical/Electrical Power (P = W/t) with multi-unit conversion and step-by-step derivations.

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Joules
Watts
Horsepower
Calories

Work, Energy & Power Calculator

Calculate Work Done (W = F·d·cos θ), Kinetic Energy (KE = ½mv²), Potential Energy (PE = mgh), and Power (P = W/t) in real time with multi-unit conversion and step-by-step formula derivations.

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Select calculation mode:Work • Kinetic • Potential • Power

Physics Benchmarks:

Applied Force (F)

Magnitude of force pushing or pulling.

Displacement (d)

Distance moved along the direction of action.

Angle θ (Degrees)

Angle between force and displacement (0° = parallel).

Calculated Work DoneW = F · d · cos(θ)

2,000 J

= 2 kJ= 0.5556 Wh

Step:W = F × d × cos(θ) = 200 N × 10 m × cos(0°)

Includes units & derivation

Force (SI)200 NPrimary value

Displacement (SI)10 mSecondary metric

cos(θ)1Physics parameter

Energy in calories478.0115 calAlternative unit

Understanding Work, Energy, and Power

In classical mechanics, Work, Energy, and Power form the cornerstone of dynamics and thermodynamics. Work is the measure of energy transfer that occurs when an object is moved over a distance by an external force: W = F · d · cos(θ). According to the Work-Energy Theorem, the net work done on an object directly equals the change in its kinetic energy: W_net = ΔKE = ½mv₂² - ½mv₁².

Work Done (W)

Measured in Joules (J)

Energy transferred by force over distance. 1 Joule = 1 Newton-meter (1 N·m).

Kinetic Energy (KE)

Formula: ½mv²

Energy possessed due to velocity. Doubling velocity quadruples kinetic energy.

Potential Energy (PE)

Formula: mgh

Energy stored by position or elevation in a uniform gravitational field.

Power (P)

Measured in Watts (W)

Rate of doing work per second (1 W = 1 J/s). 1 HP ≈ 745.7 Watts.

How to use this Calculator?

Compute mechanical and electrical energy variables in five straightforward steps:

1
Select your calculation mode:
Choose between Work Done (W), Kinetic Energy (KE), Potential Energy (PE), or Power (P) from the mode selector tabs.
2
Enter your known values:
Type your values into the corresponding input fields, or load one of the quick physics presets like Lifting 10kg Box 2m or 1 HP Motor over 1 Hour.
3
Pick your preferred units:
Select Newtons, pounds-force, kilograms, pounds, meters, feet, km/h, mph, seconds, or hours using the unit selectors.
4
Review the live step-by-step substitution:
The calculator provides real-time answers with the exact mathematical derivation, auxiliary metric conversions (kJ, Wh, kcal, HP), and momentum or impact speed.
5
Copy or Reset:
Click "Copy Result" to copy the answer to your clipboard with toast feedback, or click "Reset" to clear all values.

Formula Reference Table

Summary of foundational equations for Work, Kinetic Energy, Potential Energy, and Power:

Quantity	Standard Formula	SI Unit & Symbol	Alternative Common Units
Work Done (W)	W = F · d · cos(θ)	Joule (J = N·m)	kJ, ft·lbf, erg
Kinetic Energy (KE)	KE = ½mv² = p² / 2m	Joule (J = kg·m²/s²)	kJ, cal, kcal, Wh, eV
Potential Energy (PE)	PE = mgh	Joule (J = N·m)	kJ, Wh, kWh
Power (P)	P = W / t = F · v	Watt (W = J/s)	kW, MW, Horsepower (HP), BTU/h

Frequently Asked Questions

Common questions on work, kinetic & potential energy, horsepower, and power dissipation.

Kinetic energy (KE = ½mv²) is the energy of an object in motion, determined by its mass and velocity. Potential energy (PE = mgh) is stored energy dependent upon an object's position or elevation in a force field (like gravity). In an isolated system without friction, mechanical energy is conserved: potential energy converts into kinetic energy as an object falls (PE + KE = constant).

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Quantity

Standard Formula

SI Unit & Symbol

Alternative Common Units

Work Done (W)

W = F · d · cos(θ)

Joule (J = N·m)

kJ, ft·lbf, erg

Kinetic Energy (KE)

KE = ½mv² = p² / 2m

Joule (J = kg·m²/s²)

kJ, cal, kcal, Wh, eV

Potential Energy (PE)

PE = mgh

Joule (J = N·m)

kJ, Wh, kWh

Power (P)

P = W / t = F · v

Watt (W = J/s)

kW, MW, Horsepower (HP), BTU/h

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Work, Energy & Power Calculator

Work, Energy & Power Calculator

Understanding Work, Energy, and Power

How to use this Calculator?

Formula Reference Table

Frequently Asked Questions

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Frequently Asked Questions