Why does work depend on angle?

The cos(θ) term captures only the component of force acting in the direction of motion. Pushing horizontally on a box (θ = 0°) does maximum work. Pushing at 30° does W = Fd cos(30°) ≈ 0.866 Fd. A force perpendicular to motion (θ = 90°), like gravity on a horizontally moving object, does zero work.

What is the difference between work, energy, and power?

Work (J) is the energy transferred by a force over a displacement. Energy (J) is the capacity to do work — it exists in kinetic, potential, thermal, and other forms. Power (W) is the rate at which work is done or energy is transferred: P = W/t. A 100 W light bulb uses 100 J of energy every second.

What is 1 horsepower in watts?

Mechanical horsepower (hp_mech) = 745.699 W ≈ 745.7 W. Metric horsepower (PS or hp_metric) = 735.499 W ≈ 735.5 W. These differ by about 1.4%. A car engine rated at 200 hp (mechanical) produces 200 × 745.7 = 149,140 W ≈ 149 kW.

How is power calculated from force and velocity?

Power equals force times velocity when force is applied in the direction of motion: P = F × v. This is the instantaneous power. For example, a car exerting 2000 N of traction force at 30 m/s produces P = 2000 × 30 = 60,000 W = 60 kW.

Can work be negative?

Yes. Work is negative when the force component opposes the motion (θ > 90°). For example, friction does negative work on a sliding object — it removes kinetic energy. Braking a car does negative work on the car, reducing its kinetic energy (converting it to heat in the brakes).

Is kWh a unit of energy or power?

kWh (kilowatt-hour) is a unit of energy, not power. 1 kWh = 1000 W × 3600 s = 3,600,000 J = 3.6 MJ. It is commonly used for electricity billing. A 1000 W (1 kW) appliance running for 1 hour consumes exactly 1 kWh of electrical energy.

Work, Energy & Power Calculator – W = Fd, P = W/t

Quick Presets

Solve For

Force F

Distance d

Angle θ (degrees)

°

Work W

Work inputs — same as Basic tab. Switch to Basic tab and use Solve For selector.

P = W/t | P = F × v — enter any two to find the third.

Work W

Time t

Force F (for P = Fv)

N

Velocity v (for P = Fv)

W_net = ½mv² − ½mu² | Enter m + u + v → W, or m + u + W → v

Mass m

Initial Velocity u

Final Velocity v

Net Work W_net (J)

Select what to solve for, enter known values.

What Is Work in Physics?

In physics, work is done when a force displaces an object in the direction of the force. Simply exerting a force without movement (like pushing a wall) does no work. Work transfers energy to or from an object.

The unit of work is the joule (J), where 1 J = 1 N × 1 m. One joule is roughly the work needed to lift a 100 g apple by 1 metre.

W = Fd cosθ

Work formula

P = W / t

Power from work and time

P = F · v

Power from force and velocity

Power: The Rate of Doing Work

Power measures how quickly work is done. Two people climbing the same stairs do the same work, but the faster climber produces more power. The SI unit is the watt (W), where 1 W = 1 J/s.

Unit	Equivalent
1 W	1 J/s
1 kW	1000 W
1 hp (mechanical)	745.7 W
1 hp (metric)	735.5 W
1 BTU/h	0.2931 W

The Work-Energy Theorem

The net work done on an object equals its change in kinetic energy:

W_net = ΔKE = ½mv² − ½mu²

This theorem is powerful because it connects force, distance, and velocity change without needing time. It explains why airbags work: increasing the stopping distance reduces the required force.

Units: Joules, Watts & Horsepower

Energy conversion constants:

1 cal = 4.184 J

1 kcal = 4184 J

1 kWh = 3,600,000 J

1 BTU = 1055.06 J

1 ft·lbf = 1.35582 J

1 hp = 745.7 W (mech)

Work Done Against Gravity

Lifting an object of mass m by height h against gravity requires work equal to the gained gravitational potential energy:

W_gravity = m × g × h = ΔPE

Note: gravity does positive work when the object moves downward (force and displacement in same direction) and negative work when moving upward.

Worked Examples

Example 1 — Lift Groceries

Given: F=50 N, d=1 m, θ=0°

W = 50 × 1 × cos(0°) = 50 × 1

W = 50 J

Example 2 — 60W Bulb for 1 hour

P=60 W, t=3600 s

W = P × t = 60 × 3600

W = 216,000 J = 216 kJ

Example 3 — Push at 30°

F=80 N, d=10 m, θ=30°

W = 80 × 10 × cos(30°)

= 800 × 0.866 = 692.8 J

Example 4 — Car Stops (Work-Energy)

m=1200 kg, u=25 m/s, v=0

W = ½×1200×(0−25²)

W = −375,000 J

Frequently Asked Questions

In physics, work is done when a force causes an object to move in the direction of the force. Mathematically, W = F × d × cos(θ), where F is the force, d is the displacement, and θ is the angle between them. Work is measured in joules (J), where 1 J = 1 N·m.

The cos(θ) term captures only the component of force acting in the direction of motion. Pushing horizontally (θ = 0°) does maximum work. Pushing at 30° does W = Fd cos(30°) ≈ 0.866 Fd. A force perpendicular to motion (θ = 90°) does zero work.

The work-energy theorem states that the net work done on an object equals the change in its kinetic energy: W_net = ΔKE = ½mv² − ½mu². It directly links force, distance, and speed changes, allowing you to find final velocity from known work input without needing time.

Work (J) is the energy transferred by a force over a displacement. Energy (J) is the capacity to do work — kinetic, potential, thermal, etc. Power (W) is the rate at which work is done: P = W/t. A 100 W bulb uses 100 J every second.

Mechanical horsepower = 745.699 W ≈ 745.7 W. Metric horsepower (PS) = 735.499 W. A car engine rated at 200 hp (mechanical) produces 200 × 745.7 = 149,140 W ≈ 149 kW.

Power equals force times velocity when the force is applied in the direction of motion: P = F × v. A car exerting 2000 N of traction at 30 m/s produces P = 2000 × 30 = 60,000 W = 60 kW.

Yes. Work is negative when the force component opposes the motion (θ > 90°). Friction does negative work on a sliding object, removing kinetic energy. Braking a car does negative work, reducing kinetic energy (converting it to heat).

kWh (kilowatt-hour) is a unit of energy, not power. 1 kWh = 1000 W × 3600 s = 3,600,000 J = 3.6 MJ. It is commonly used for electricity billing. A 1 kW appliance running for 1 hour consumes exactly 1 kWh.

Work, Energy & Power Calculator

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