Imagine two cranes lifting identical steel beams to the top of a building. Crane A does it in 1 minute. Crane B does it in 5 minutes. Both cranes did the exact same amount of Work (force $\times$ distance). However, Crane A is clearly more powerful. Why? Because it did the same work in less time.
Power is the physical quantity that measures this "rate of doing work." It is crucial in engineering, engines, electricity, and sports performance.
The Formula
P = W / t
P (Power)Watts (W)
W (Work)Joules (J)
t (Time)Seconds (s)
The Watt (W)
One Watt is equal to one Joule of energy transferred per second ($1\text{W} = 1\text{J / s}$). A typical LED lightbulb uses about 10 Watts.
Horsepower (hp)
An older unit still common for engines and motors. Historically defined as the power of a working horse. $1\text{hp} \approx 746\text{W}$.
Time Matters
Crucially, Power is inversely proportional to Time. doing a task twice as fast requires twice the power.
Frequently Asked Questions
Q. What is the scientific definition of Power?
In physics, Power is defined as the rate at which work is done or energy is transferred. While Work tells you how much energy was transferred, Power tells you how fast it happened. The SI unit of power is the Watt (W), which equals one Joule per second.
Q. What is the formula for Power?
The average power ($P$) is calculated by dividing the Work done ($W$) by the Time interval ($t$) it took to do that work: $P = W / t$. Alternatively, if a constant force acts on an object moving at a constant velocity, Power can be calculated as Force times Velocity ($P = F \times v$).
Q. What is 1 Horsepower equal to?
One mechanical Horsepower (hp) is approximately equal to 745.7 Watts. This unit was coined by James Watt to compare steam engines to the power of draft horses. In electrical contexts, 1 hp is sometimes approximated as 746 Watts.
Q. How does Power relate to Energy?
Power is simply Energy divided by Time ($P = E/t$). Therefore, Energy is Power multiplied by Time ($E = P \times t$). This explains why electricity bills are measured in Kilowatt-hours (kWh), which is a unit of Energy, not Power (Power $\times$ Time).
Q. If I run up the stairs instead of walking, do I use more power?
Yes! The Work done (lifting your body mass against gravity to the same height) is exactly the same whether you walk or run. However, running takes less **Time** ($t$). Since $P = W/t$, a smaller $t$ results in a larger **Power** ($P$).
Q. What is the difference between kW and kWh?
A kW (Kilowatt) is a unit of **Power** (rate of energy use), like the speed of a car. A kWh (Kilowatt-hour) is a unit of **Energy** (total amount used), like the distance traveled. A 1 kW heater running for 1 hour consumes 1 kWh of energy.
Q. Can Power be negative?
Yes, Power can be instantaneous negative power. This happens when the force component is opposite to the velocity vector (just like negative work). For example, when you catch a fast ball and bring it to rest, your hand does negative work, and thus negative power is exerted on the ball.
Q. What is Electrical Power?
In electrical circuits, Power is the rate at which electrical energy is converted into other forms (like heat or light). It is calculated as Voltage ($V$) times Current ($I$): $P = V \times I$. The unit is still Watts.
Q. Who was James Watt?
James Watt (1736–1819) was a Scottish inventor whose improvements to the steam engine were fundamental to the Industrial Revolution. The unit of power, the Watt, was named in his honor.
Q. Is human power output limited?
Yes. An average healthy human can sustain about 75-100 Watts of power for a long period (like walking or cycling). Elite cyclists can sustain 300-400 Watts for an hour. In very short bursts (sprinting), humans can output over 1000 Watts (more than 1 hp)!