Two cars can do identical work climbing a hill — but if one does it in half the time, it is twice as powerful. Power is not about how much work is done; it is about how quickly work is done. Power is the rate of energy transfer, and it is one of the most practically important quantities in all of physics — the number that determines whether your car can overtake on a motorway, whether a power station can supply a city, and whether your muscles can sustain a sprint.
Power is the rate at which work is done or energy is transferred. Formula: P = W/t, where W is work done (J) and t is time (s). The SI unit is the watt (W): 1 W = 1 J/s. A machine with power P does W = Pt joules of work in t seconds.
The Power Formula
where P is power (watts, W), W is work done (joules, J), and t is time (seconds, s).
For a constant force F applied over displacement d in time t, since W = Fd:
where v = d/t is the speed. This form — P = Fv — is extremely useful in mechanics: it gives the power output of an engine directly from the driving force and the speed of travel.
The Watt and Other Power Units
| Unit | Value | Context |
|---|---|---|
| Watt (W) | 1 J/s | SI unit; named after James Watt |
| Kilowatt (kW) | 1,000 W | Car engines, home appliances |
| Megawatt (MW) | 10⁶ W | Power stations, large industrial plants |
| Horsepower (hp) | 746 W | Car engine ratings; imperial unit |
| Kilowatt-hour (kWh) | 3.6 × 10⁶ J | Unit of energy (not power); used on electricity bills |
The kilowatt-hour is a unit of energy, not power: 1 kWh = 1 kW × 3600 s = 3.6 MJ. A 100 W light bulb running for 10 hours consumes 1 kWh of electrical energy. Electricity bills charge per kWh — a useful reminder that energy, not power, is what costs money.
Worked Examples
Example 1: Lifting a load
A crane lifts a 500 kg load by 8 m in 10 seconds. What is its power output?
Example 2: Car engine — P = Fv
A car travels at 30 m/s against a total resistive force (air drag + rolling friction) of 800 N. What engine power is needed to maintain constant speed?
At constant speed, the engine force equals the resistive force — all engine power goes into overcoming resistance (converting to heat and sound), not into increasing kinetic energy.
Example 3: Electrical power
A kettle element draws 8.7 A from a 230 V supply. What is its power, and how much energy does it use in 2 minutes?
Power and Efficiency
No real machine converts input power entirely to useful output — some is always lost, typically as heat. Efficiency is the ratio of useful output power to total input power:
A car engine converts chemical energy in fuel to kinetic energy with typical efficiency 25–35%. The rest (~65–75%) is wasted as heat in the exhaust and cooling system. An electric motor is typically 85–95% efficient. LED lights convert ~90–95% of electrical energy to light; incandescent bulbs only ~5% (the rest is heat — which is why they get so hot).
| Device | Typical efficiency |
|---|---|
| Electric motor | 85–95% |
| LED lamp | 90–95% (electrical → light) |
| Petrol car engine | 25–35% |
| Coal power station | 33–40% |
| Incandescent bulb | ~5% (electrical → light) |
Human Power Output
The average adult can sustain approximately 75–100 W of mechanical power output over several hours (e.g., cycling). Sprint power can reach 500–1,500 W for a few seconds in trained athletes. The world record for a 1-hour cycling time trial corresponds to a sustained average power of around 440 W — roughly 0.6 horsepower. Elite rowers sustain ~400–500 W over 6 minutes for 2,000 m races.
James Watt defined one horsepower (746 W) by estimating the power output of a working mill horse — roughly 10× what a human worker could sustain. This gave customers a standard way to compare steam engines: a 10-hp engine replaced 10 horses.
Power in Electrical Circuits
For electrical systems, power is related to voltage and current by:
where I is current (A), V is voltage (V), and R is resistance (Ω). These three forms follow from combining P = IV with Ohm's Law (V = IR). The form P = I²R shows why transmission lines carry electricity at high voltages: for a given power P = IV, higher V means lower I, and power lost in the cable resistance R_line is P_loss = I²R_line — dramatically reduced by reducing current.
Frequently Asked Questions
What is power in physics?
Power is the rate at which work is done or energy is transferred. Formula: P = W/t = energy/time. The SI unit is the watt (W), where 1 W = 1 J/s. Power measures how quickly a process transfers energy — the same work done faster requires more power.
What is the formula for power?
P = W/t (work divided by time). For a constant force F at speed v: P = Fv. For electrical circuits: P = IV = I²R = V²/R. All give power in watts (W).
What is the difference between power and energy?
Energy (J) is the total amount of work done or heat transferred. Power (W) is the rate at which energy is transferred per second. A 100 W bulb and a 50 W bulb both use electrical energy, but the 100 W bulb uses it twice as fast. Energy = Power × Time (W = Pt).
What is a watt?
The watt (W) is the SI unit of power, named after James Watt. 1 W = 1 joule per second = 1 J/s. Common multiples: kilowatt (kW) = 1,000 W; megawatt (MW) = 10⁶ W. 1 horsepower = 746 W.
What is efficiency in physics?
Efficiency = useful output power / total input power × 100%. No real machine is 100% efficient — some energy is always lost, typically as heat. Electric motors (~90%) are much more efficient than petrol engines (~30%). The second law of thermodynamics places fundamental limits on efficiency for heat engines.
What is the difference between watts and kilowatt-hours?
Watts measure power (rate of energy use). Kilowatt-hours measure energy (total amount used). 1 kWh = 1,000 W × 3,600 s = 3.6 million joules. A 2 kW kettle running for 30 minutes uses 1 kWh of energy. Electricity bills charge in kWh because that measures total energy consumed, not the rate.
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Written by
Dr. James CarterPhysicist and educator with 15+ years teaching classical mechanics and thermodynamics at the university level. Former MIT OpenCourseWare contributor.
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