Energy, power and the units that measure them: Energy versus power

3.1 Power is the rate; energy is the amount

Power is energy divided by time. Its unit is the watt (W), one joule per second. A 10 W LED bulb converts ten joules of electricity every second. Run it for an hour and it has used 36,000 joules, which is 10 watt-hours or 0.01 kWh.

The kilowatt-hour makes the link explicit: it is a power (one kilowatt) multiplied by a time (one hour). So energy = power x time, and power = energy / time. An air conditioner rated at 1.5 kW that runs for eight hours on a hot Chennai night uses 12 kWh. A 2,000 kilocalorie diet spread over 24 hours is an average power of about 97 W, which is why a resting adult is often compared with an old 100 W light bulb.

A water analogy helps. Energy is like the volume of water in a tank, measured in litres. Power is like the flow through a pipe, measured in litres per second. A large tank can be emptied slowly through a thin pipe or quickly through a fat one. In the same way, a battery's energy (kWh) tells you how much it holds, while its power (kW) tells you how fast it can deliver. A grid battery described as 100 MW / 400 MWh can deliver 100 MW for four hours.

Most confusions come from dropping the time. Saying a plant "produces 500 MW" describes its rate at a moment. Saying it "produced 3 TWh last year" describes an amount. Both are needed: the grid needs enough power at the evening peak, and the economy needs enough energy over the year. A source that is excellent at one need not be good at the other.

• Smil, Energy: A Beginner's Guide (2006) · via Smil Mastery Course, M1 'Energy versus power'

3.2 Capacity is not generation: the capacity factor

Power plants are sold and counted by their installed capacity, the maximum power they can produce. But no plant runs at full output all year. The capacity factor is the ratio of what a plant actually produces in a year to what it would produce if it ran flat out for all 8,760 hours.

A 1 GW plant at full output for a year would produce 8.76 TWh. A nuclear plant with a 90% capacity factor delivers about 7.9 TWh. India's coal fleet, held back by low demand at night and increasingly by solar at midday, ran at a plant load factor of about 69% in 2024-25. Onshore wind typically achieves 25 to 35%, depending on site and turbine. Solar photovoltaics manage roughly 10 to 25% depending on latitude and cloud: towards the top of that range in sunny places such as Rajasthan and Gujarat, towards the bottom in cloudy northern Europe, because panels produce nothing at night and little in heavy cloud.

This is why comparisons by capacity mislead. If a country installs 100 GW of solar at a 20% capacity factor, its average output is about 20 GW. Its contribution to annual energy is therefore similar to 25 GW of nuclear, not 100 GW. That does not make solar a poor investment; its cost per unit of energy is now very low. It means you must always convert capacity into energy before comparing.

The low capacity factor also explains why a grid with a lot of solar needs other resources for the evening, and why storage is measured in hours. Capacity tells you the size of the tap; the capacity factor tells you how often it is open.

Smil adds a further twist: power density, the rate of energy flow per square metre of land. A city consumes tens of watts per square metre of its area, while a solar farm averages only about 5 to 10 W per square metre over a year. That spatial version of the energy-power distinction returns in later modules.

• Smil, Energy: A Beginner's Guide (2006) · via Smil Mastery Course, M1 'Energy versus power'
• Smil, Power Density: A Key to Understanding Energy Sources and Uses (2015) · via Smil Mastery Course, M1 'Energy versus power'
• Business Today, 'Coal plants' PLF to fall to 55% by FY32: Report' (reporting Ember analysis), 29 October 2025 · Indian coal plant load factor 69% in FY 2024-25. https://www.businesstoday.in/latest/economy/story/coal-plants-plf-to-fall-to-55-by-fy32-report-499990-2025-10-29

3.3 From a human body to a power station: the scales of power

Power figures span an enormous range, and placing devices on a single ladder gives a feel for what each technology can do. A resting adult runs at about 80 to 100 W. Hard physical labour sustained over a working day yields only 50 to 100 W of useful mechanical work, which is why pre-industrial societies needed so many people and animals to farm and build. A good working horse delivers 500 to 800 W, about ten labourers.

Machines changed the scale. A small motorcycle engine in India produces about 7 kW. A family car engine gives around 100 kW, the work of more than a thousand labourers in a box under the bonnet. A diesel locomotive delivers 3 to 5 MW. A large wind turbine is rated at 3 to 15 MW. A big jet engine at take-off produces tens of megawatts. A single large coal or nuclear generating unit runs at about 0.5 to 1.6 GW, and the biggest power stations combine several such units.

Comparing these with the per-person flows from Part 2 is revealing. The average Indian's share of national energy supply runs at about 850 W, the equivalent of eight or nine people working full time without rest. The average American's share, about 8,400 W, is like having over 80 such people. Smil uses comparisons like these to show how completely modern life depends on machines powered by fuels, and how much of that dependence is invisible to the people who benefit.

The ladder also shows why some substitutions are hard. Replacing a 100 kW car engine with human pedal power is absurd, but replacing it with a 100 kW electric motor is routine, because electric motors pack a lot of power into a small, light package.

• Smil, Energy: A Beginner's Guide (2006) · via Smil Mastery Course, M1 'Energy versus power'
• Smil, Power Density: A Key to Understanding Energy Sources and Uses (2015) · via Smil Mastery Course, M1 'Energy versus power'

See it in the table

Check your understanding

A 1.5 kW air conditioner runs for 6 hours. How much electricity does it use?

A country adds 50 GW of solar with a 20% capacity factor. Its average output is about...

A grid battery is rated 200 MW / 800 MWh. For how long can it deliver full power?