In physics, power is defined as the rate at which work is performed or energy is transferred from one form to another. While work measures the total energy expended to accomplish a task, power measures how quickly that task is completed. Two machines may do the same amount of work, but the one that finishes faster is more powerful.

The Fundamental Formula: P = W / t

The most widely used power equation states that power equals work divided by time. If a 70-kilogram person climbs a 10-meter ladder in 20 seconds, the work done against gravity is approximately 6,860 Joules (mass × gravity × height), and the average power output is 6,860 J ÷ 20 s = 343 Watts. The same climb in 10 seconds doubles the power to 686 Watts, even though the total work remains identical.

Mechanical Power: P = F × v

When an object moves at constant velocity against a constant opposing force, mechanical power can be expressed as force multiplied by velocity. This form is especially useful for vehicles, conveyor belts, and turbines. A truck maintaining 25 m/s on a highway while overcoming 3,000 N of drag requires P = 3,000 × 25 = 75,000 W, or 75 kW, of continuous engine output.

Electrical Power: P = I × V

In electrical circuits, power equals current (I, in Amperes) multiplied by voltage (V, in Volts). A household outlet delivering 120 V to a device drawing 10 A supplies 1,200 W of electrical power. This formula is the backbone of all electrical engineering calculations, from sizing circuit breakers to designing power grids. Ohm’s Law variants give equivalent forms: P = I²R and P = V²/R.

Horsepower and Unit Conversions

The Watt (W) is the SI unit of power, where 1 W = 1 J/s. Larger quantities use kilowatts (1 kW = 1,000 W) or megawatts (1 MW = 1,000,000 W). The imperial unit horsepower (hp) was devised by James Watt to compare steam engines to draft horses: 1 mechanical hp = 745.7 W. A typical family sedan produces about 150 hp (roughly 112 kW), while a modern electric vehicle may deliver over 300 hp (224 kW) of peak motor output.

Efficiency and Real-World Power

No machine converts energy with 100% efficiency. An incandescent light bulb rated at 60 W converts only about 5% of its electrical input into visible light; the remaining 95% becomes heat. Efficiency is calculated as (useful power output ÷ total power input) × 100%. LED bulbs achieve roughly 40–50% efficiency, producing the same brightness at 8–10 W. Understanding efficiency is essential when comparing appliances, engines, and renewable energy systems, because it determines how much input energy is wasted.