Energy units: joules, watts, capacity factor, LCOE

Two distinct quantities anchor every energy conversation.

Energy is the capacity to do work. The SI unit is the joule (J), equivalent to lifting 1 kg by about 10 cm. A 100 W lightbulb running for one second uses 100 J. Energy is conserved: it can be transformed (chemical to thermal to electrical to mechanical) but not created or destroyed. Common multiples: kilojoule (kJ, $10^3$), megajoule (MJ, $10^6$), gigajoule (GJ, $10^9$).

Power is the rate of energy flow. The SI unit is the watt (W), defined as 1 joule per second. A 100 W appliance moves 100 J of energy every second it operates. Common multiples: kilowatt (kW, $10^3$), megawatt (MW, $10^6$), gigawatt (GW, $10^9$).

The distinction matters because the two quantities answer different questions. 'How big is this power plant?' is a power question (gigawatts). 'How much energy did it produce last year?' is an energy question (terawatt-hours).

A standard unit that combines both: the kilowatt-hour (kWh) is energy equal to 1 kW of power for 1 hour, or 3.6 megajoules. Household electricity bills are denominated in kWh. Annual generation of a power plant is quoted in TWh (terawatt-hours, $10^{12}$ Wh).

Confusing the two — saying 'gigawatt' when meaning 'gigawatt-hour' — is the most common mistake in energy reporting. Always read the unit, not just the number.

Different energy sources pack different amounts of energy into the same mass or volume. Energy density is the energy per unit mass (specific energy, J/kg) or per unit volume (volumetric energy density, J/m³).

Typical specific energies, by source:

The span across the table is more than nine orders of magnitude. Three structural consequences follow.

• Transportation is constrained by mass and volume. Aviation, long-distance trucking, and shipping prefer fuels with high specific energy because moving heavy fuel is expensive in fuel itself. This is why batteries face structural difficulty in long-range aviation and shipping while doing well in passenger cars.
• Nuclear is fundamentally different. Fission and fusion fuels are seven to eight orders of magnitude denser than chemical fuels. A nuclear plant consumes tons of fuel per year while a coal plant consumes millions of tons. The implications for fuel logistics, waste volume, and proliferation security follow directly from this number.
• Hydrogen's contradictory profile. Hydrogen has the highest specific energy by mass of any chemical fuel but among the worst by volume. The engineering problem of hydrogen as a fuel is storing it at sufficient density. Compressed gas, liquefaction, and chemical carriers (ammonia, methanol) all try to address this.

A power plant's capacity factor is the ratio of its actual annual energy output to the energy it would produce running at full nameplate power all year.

$\text{capacity factor} = \frac{\text{actual annual energy output}}{\text{nameplate power} \times \text{hours in year}}.$

Typical capacity factors by source (global averages):

Capacity factor depends on:

• Resource availability. Solar produces only when the sun shines; wind only when the wind blows.
• Demand alignment. Plants used only at peak demand cycle on and off, lowering capacity factor by design.
• Maintenance and outages. Even baseload plants are offline for refueling and maintenance.
• Curtailment. When supply exceeds local demand and transmission is constrained, output is reduced administratively.

The central practical point: nameplate capacity does not equal energy delivered. A 1 GW wind farm with 30% capacity factor produces 1 GW × 0.30 × 8760 hours = 2,628 GWh per year. A 1 GW nuclear plant with 90% capacity factor produces 7,884 GWh per year — three times as much energy from the same nameplate. Comparing nameplate alone overstates intermittent sources' output and undersells dispatchable sources'.

Levelized cost of energy (LCOE) is the average cost per unit of energy that a plant must charge over its lifetime to break even, given its capital cost, operating cost, fuel cost, and expected output. It is usually quoted in $/MWh or$/kWh.

$\text{LCOE} = \frac{\sum_t \frac{I_t + O_t + F_t}{(1+r)^t}}{\sum_t \frac{E_t}{(1+r)^t}}$

where $I_t$ is investment, $O_t$ is O&M, $F_t$ is fuel, $E_t$ is energy output in year $t$, and $r$ is the discount rate.

LCOE has become the default headline metric for comparing generation technologies. It is useful but easy to misuse.

What LCOE captures well. Average cost per unit of energy from a single plant in isolation, given assumptions about its operating profile.

What LCOE captures poorly.

• System integration costs. The cost of variable sources (wind, solar) understates their full system cost because they need backup, storage, or transmission to deliver power when local demand exists.
• Time-of-day value differences. A kWh delivered at peak demand is worth more than a kWh delivered at off-peak. LCOE averages this out.
• Capacity value. A plant that can reliably deliver power when demand is high (regardless of weather) has 'capacity value' beyond its average energy output. LCOE ignores this.
• Discount-rate sensitivity. Capital-intensive technologies (nuclear, hydro) are very sensitive to the discount rate; fuel-intensive ones (gas) are less so. LCOE comparisons at one discount rate can flip at another.

LCOE is a useful starting point but not a substitute for system-level analysis. The value of energy — distinct from its cost — depends on when, where, and reliably it is delivered. The next four lessons examine specific generation sources; the last lesson returns to the grid level where these distinctions reassert themselves.

Not all joules are equally useful. A joule of high-temperature heat can do more work than a joule of low-temperature heat. The concept of exergy captures this.

Exergy is the maximum work extractable from a given amount of energy as it equilibrates with the environment. A joule of energy at 1000 K has more exergy than a joule of energy at 300 K (room temperature), because the temperature difference with the environment is what drives a heat engine.

The practical consequence: heat engines (steam turbines, gas turbines, internal combustion) are bounded by the Carnot efficiency depending on operating temperatures:

$\eta_{\text{Carnot}} = 1 - \frac{T_{\text{cold}}}{T_{\text{hot}}}$

where temperatures are in kelvin. A steam plant operating at $T_{\text{hot}} = 800$ K and $T_{\text{cold}} = 300$ K has a theoretical efficiency of $1 - 300/800 = 62.5\%$. Real-world steam plants reach roughly half of this Carnot bound (35–45% efficiency).

Why this matters in practice:

• All thermal power plants (coal, gas, oil, nuclear, concentrated solar, fusion if it gets there) are heat engines. Their efficiency is fundamentally bounded by Carnot.
• Direct conversion (photovoltaic, wind turbines, hydropower) is not heat-engine-limited. Their efficiency bound is different physics — Shockley-Queisser for PV, Betz limit (59.3%) for wind turbines, hydraulic losses for hydro.
• High-grade vs low-grade heat. Burning a fuel for high-temperature heat (steel, glass, cement manufacturing) and then 'wasting' the lower-temperature exhaust is structurally different from generating electricity from the same fuel and then using electric resistance heating at low temperatures. Exergy accounting catches inefficiencies that energy accounting alone misses.

A grab bag of magnitudes worth memorizing for reading energy claims.

• Global primary energy demand: ~620 EJ/year (exajoules; $10^{18}$ J), or ~170 PWh/year, equivalent to about 19 TW of average power.
• Global electricity demand: ~30 PWh/year, equivalent to about 3.4 TW of average electric power. Electricity is roughly 20% of primary energy demand.
• US electricity demand: ~4 PWh/year (about 13% of global), at about 460 GW of average power, with peaks closer to 800 GW.
• Solar irradiance: ~1000 W/m² on a clear day at midday; ~200 W/m² annual average at a sunny location after capacity factor. A 20% efficient PV panel produces ~200 W/m² peak, ~40 W/m² annual average.
• Wind power density: depends sharply on wind speed. A 7 m/s annual mean delivers about 350 W/m² of rotor swept area (annual average), so a 100 m diameter rotor (~7,850 m² swept area) delivers about 2.7 GWh/year — capacity factor ~30%.
• A typical US home: ~12 MWh/year electricity, ~1.4 kW average; peak draw ~5–10 kW. (Highly variable by region.)
• A US passenger car: ~13,000 km/year × ~0.7 kWh/km (gasoline-equivalent for ICE) = ~9 MWh/year. EV equivalent: ~0.2 kWh/km × 13,000 km = ~2.6 MWh/year.
• An aluminum smelter: ~15 MWh per tonne of aluminum. A large smelter draws several hundred MW continuously.
• A data center campus: 50–500 MW typical; modern AI-training clusters reach gigawatt scale.

These numbers are not memorized for their own sake. They give you a sanity check on any claim: when a press release says 'this project will produce enough electricity for 100,000 homes,' you can multiply 12 MWh/year × 100,000 = 1.2 TWh/year and check whether that matches the project's nameplate × capacity factor.

A few practical reading rules from this lesson.

• Always check the unit. Watts and watt-hours differ by a time unit. Joules and joules per second differ by the same. Many press claims mix them up; many reports use one when they should use the other.
• Always check the capacity factor. Nameplate capacity is the headline; energy delivered is what matters. A 1 GW solar farm and a 1 GW nuclear plant produce different amounts of energy in a year.
• Always check the LCOE assumptions. Discount rate, lifetime, capacity factor, fuel-cost trajectory. Two analyses of the same technology with different assumptions can produce very different LCOEs without either being wrong.
• Distinguish primary energy from final energy from useful work. Burning fuel for heat is different from generating electricity is different from doing mechanical work. Conversion losses are real and substantial.
• Check the system, not just the source. A generation source's value depends on when it produces relative to demand, where transmission can deliver it, and what else is on the system. The next lessons examine specific sources; the final lesson returns to the system.

Three structural points that carry through the cursus.

• Energy and power are different. Confusing the two is the most common source of misreading in energy debates. Read the unit; check the time integration.
• Energy density spans nine orders of magnitude. From batteries to fossil fuels to nuclear, the differences are not marginal. Many engineering and policy choices follow directly from where on this scale a source sits.
• System-level metrics beat plant-level metrics for grid decisions. Capacity factor, LCOE, and system integration cost together describe what a plant contributes to a grid. No single number captures the full picture.

The next lesson moves from these units to specific sources, starting with the largest current source of global primary energy: combustion of fossil fuels and the thermal cycles that convert their heat to electricity and mechanical work.