Capacity factor: why is 1 MW not always 1 MW?

Run three 100 MW plants for a year and count what they make

Lesson 5 of Energy Systems, Step by Step: compare a year of output from nuclear, wind and solar plants of the same size, compute a capacity factor from 24 hourly outputs, meet the wind’s cube law and turn megawatts into megawatt-hours.
  • Foundations · L1
  • Lesson 5 of 14
  • 15 min
  • After lesson 1

The idea in one table: three plants of 100 MW, one year (2025 U.S. capacity factors)

Plant, 100 MW Energy in the year Capacity factor
Nuclear 798,000 MWh 91.1%
Wind 296,088 MWh 33.8%
Solar 210,240 MWh 24.0%
At full size every hour 876,000 MWh 100%

Count one day: the 100 MW solar farm on 3 September 2025

The day hour by hour, MW
Hour from MW Hour from MW
00:00 0 12:00 76
01:00 0 13:00 72
02:00 0 14:00 53
03:00 0 15:00 72
04:00 0 16:00 79
05:00 0 17:00 63
06:00 0 18:00 31
07:00 3 19:00 6
08:00 32 20:00 0
09:00 56 21:00 0
10:00 62 22:00 0
11:00 71 23:00 0

Energy made: the 24 outputs add up to 676 MWh. Capacity factor: 676 ÷ (100 × 24) = 28.2%. The night hours count too.

The power curve of an illustrative 3 MW wind turbine

  • Below 3 m/s (cut-in): no electricity.
  • 3 to 12 m/s (rated): output follows the cube of the wind speed; doubling a speed within this range gives eight times the output.
  • 12 to 25 m/s (cut-out): output holds at 3,000 kW.
  • Above 25 m/s: the turbine shuts down to protect itself.

With JavaScript on, you work through this step by step: a year of output, the solar day, the turbine's power curve and a quick calculation.

Real data. Capacity factors are the 2025 U.S. averages from EIA's Electric Power Monthly, Table 6.07.B (released 23 October 2026).

Real shapes, reshaped. Wind and solar keep the Southwest Power Pool's 2025 hour-by-hour pattern (EIA-930), reshaped month by month to those U.S. averages. So the solar day is illustrative, not one farm's meter.

Illustrative. The nuclear plant's refuelling outage and the 3 MW wind turbine.

Need a refresher? Toolbox K1 (MW held for 8,760 h is MWh) and K2 (capacity factor as a rate).

What you just did, as diagrams

Capacity factor
Energy made ÷ (size × hours): the share of the most a plant could make that it actually made.
Same MW, different MWh
In 2025, U.S. nuclear plants ran at 91.1% of their size on average, wind at 33.8% and solar at 24.0%.
Every hour counts
Nights and calm hours stay in the count, which is why solar's capacity factor is low.
The cube law
Between cut-in (3 m/s) and rated speed (12 m/s), twice the wind speed gives this turbine eight times the output.
Rated and cut-out speeds
From the rated speed to cut-out (25 m/s) the output holds at 3,000 kW; above cut-out the turbine shuts down.
Go deeper · AnalystCapacity factor depends on the period and the place

Every fleet’s capacity factor changes from month to month. U.S. averages in 2025 (EIA, Table 6.07.B):

Fleet Lowest month Highest month
Wind 23.1% (September) 43.1% (March)
Solar 13.1% (December) 31.9% (June and July)
Nuclear 81.0% (October) 99.2% (December)

Nuclear dips in spring and fall, the seasons when many reactors stop to refuel.

  • Availability is not capacity factor. A solar farm can be ready all night and still make nothing.
  • Curtailment lowers it. A wind farm turned down by the grid makes less than its weather allowed (lesson 0).
  • Sites differ. The U.S. averages hide windy plains and sunny deserts; Prairie Town’s shapes come from one region.

Lesson 7 uses capacity factor to spread a plant’s building cost over the MWh it makes.

Go deeper · ModelerThe power curve, from physics to measurements

Power in the wind. Through a rotor, the wind carries \(P_\text{wind} = \tfrac{1}{2}\rho A v^3\).

Symbol Meaning The lesson’s turbine
\(\rho\) air density, kg/m³ 1.225 kg/m³, sea level
\(A\) area the blades sweep, m² 7,854 m², a 100 m rotor
\(v\) wind speed, m/s 12 m/s, its rated speed
\(P_\text{wind}\) power in the wind, kW 8,313 kW

What the turbine captures. It makes 3,000 kW at 12 m/s, so its power coefficient is \(C_p = 3{,}000 / 8{,}313 = 0.36\). No rotor can capture more than \(16/27 \approx 0.593\) of the wind’s power: the Betz limit.

The lesson’s clean power curve, output \(P\) in kW at wind speed \(v\) in m/s:

\[ P(v) = \begin{cases} 3000 \times (v/12)^3 \text{ kW} & 3 \le v < 12 \text{ m/s}\\ 3000 \text{ kW} & 12 \le v \le 25 \text{ m/s}\\ 0 & \text{otherwise.} \end{cases} \]

A measured curve. Real 10-minute averages scatter around a curve: gusts, air density and the turbine’s own controls move each one.

The chart shows a 1.5 MW research turbine that NREL tested in 2011, beside a clean curve built the same way for it: the cube law at its best \(C_p\), 0.52, capped at 1,500 kW.

Measured against clean, selected wind speeds (the full table appears with JavaScript on)
Wind speed, m/s Measured average, kW Spread (±1 SD), kW Clean curve, kW
3.97 59 28 93
5.99 304 52 319
8.00 742 74 759
10.03 1,200 75 1,497
11.98 1,400 127 1,500
13.97 1,482 47 1,500
15.98 1,497 17 1,500

From about 6 to 8 m/s the averages follow the cube law closely. Above that they bend over gradually: full power comes near 14 m/s, not at a sharp corner near 10 m/s.

Source: NREL, Power Performance Test Report for the U.S. Department of Energy 1.5-Megawatt Wind Turbine, Table 6 (2015; test from February to June 2011).

  • Research. Estimating a wind farm’s curve, with honest error bars, from few records is an active research topic (Li et al., 2023; open code: mfgpr-wind-power-curve).
  • Next. Modeler lesson M9 fits a curve to data; bridge B2 computes capacity factors in Python.
Go deeperWhat this lesson leaves out
  • The wind and solar shapes are whole regional fleets, smoother than any single farm.
  • Wind and solar are reshaped so that each month matches the U.S. average and the best hours reach full size.
  • The seasons are national; the hours are those of one region.
  • The nuclear plant's outage and the turbine are illustrative, not a real plant or model.
  • Air density changes with temperature and altitude, which shifts a real power curve.
  • The clean curve has no spread: a real turbine's output scatters around it (the measured curve above).

Check yourself

Myth or fact? “A 100 MW wind farm makes 100 MW most of the time.”

  • Myth
  • Fact
Answer

Myth. In 2025, U.S. wind farms made 33.8% of what they would have made at full size, and the cube law makes their output swing with every change in the wind.

Myth or fact? “A solar farm with a 24.0% capacity factor is broken three-quarters of the time.”

  • Myth
  • Fact
Answer

Myth. At night and under clouds it works as designed: the sun, not the machine, sets most of the gap.

Myth or fact? “Doubling the wind speed doubles a turbine's output.”

  • Myth
  • Fact
Answer

Myth. On this lesson's turbine it gives eight times the output (2 × 2 × 2), but only while both speeds lie between cut-in (3 m/s) and rated (12 m/s); then output holds at rated power until cut-out (25 m/s).

A 50 MW solar farm made 105,120 MWh in a year of 8,760 hours. What was its capacity factor?

  • 24.0%
  • 48.0%
  • 12.0%
  • 100%
Answer

24.0%: 105,120 ÷ (50 × 8,760) = 0.240. Leaving out the night hours would wrongly raise it: capacity factor counts every hour. Using 100 MW would halve it.

At the 2025 U.S. average of 91.1%, how much energy does 1 MW of nuclear make in a year?

  • 8,760 MWh
  • 7,980 MWh
  • 911 MWh
  • 91.1 MWh
Answer

7,980 MWh: 1 MW × 8,760 h × 0.911. The full 8,760 MWh would need every hour at full size.

Numbers, sources and what’s next

Numbers to remember

Number What it means Source
91.1% Average capacity factor of U.S. nuclear plants in 2025. EIA, Electric Power Monthly, Table 6.07.B · 2025 data (final), released October 2026
33.8% Average capacity factor of U.S. wind farms in 2025. EIA, Electric Power Monthly, Table 6.07.B · 2025 data (final), released October 2026
24.0% Average capacity factor of U.S. utility-scale solar photovoltaic farms in 2025. EIA, Electric Power Monthly, Table 6.07.B · 2025 data (final), released October 2026
18–24 months How often U.S. reactors typically refuel, mostly in spring and fall. EIA, Today in Energy · as of October 2022
10,791 kWh Electricity bought in a year by an average U.S. residential customer (a yearly total, not an hourly need). EIA, Frequently Asked Questions · data for 2022

Next on the starter path

Lesson 6 · Cheap energy, firm capacity, flexibility: which plant does which job?

Related lab: compute capacity factors from a year of hourly data in Python (bridge B2).

In the real world

EIA publishes these capacity factors every month for every kind of plant. Turning a wind farm's scattered measurements into a power curve with honest error bars is still a research question (Li et al., 2023).

Case file CF8: learning a wind turbine's power curve from scarce data.

Sources and further reading

Spotted an error, or stuck? Write to hlli@ksu.edu. Corrections are made in place and dated here.

Text licensed CC BY 4.0, code MIT: teachers and students may reuse and adapt it, with credit to Honglin Li.