# Capacity factor The **capacity factor** of a power plant is the ratio of the [[Energy|energy]] it actually delivers over a period, usually a year, to the energy it would have delivered running at its full rated power the whole time. Hydroelectric plants in the United States average about 40%, because their water arrives with the seasons; wind farms average about 33% and solar photovoltaic plants about 20%.[^murphy-cf] Rating tells how large a plant is; capacity factor tells how much it produces. For [[Hydroelectricity|hydroelectricity]] the figure is set as much by the [[Hydrology|hydrology]] of the river as by the machines. <div class="microsim-player"> <iframe src="https://wikitube-3d-microsims.netlify.app/Capacity_factor.html" width="100%" height="620" frameborder="0" loading="lazy" sandbox="allow-scripts allow-same-origin" allow="accelerometer; gyroscope" title="Capacity factor — p5.js microsim"></iframe> </div> *Microsim (THY-105): run a year of daily output from hydro, wind and solar and watch each capacity factor settle to its average. ILLUSTRATIVE: synthetic daily series scaled to the cited averages.* Videos: [16:9](https://wikitube-3d-microsims.netlify.app/media/Capacity_factor_16x9.mp4) · [9:16](https://wikitube-3d-microsims.netlify.app/media/Capacity_factor_9x16.mp4) ## Formula CF = E_actual / (P_rated × T), where T is the length of the period; for a year, T = 8,760 hours. Equivalently, the capacity factor is the average output divided by the rated output.[^murphy-11] ## Sample calculations Each calculation divides a year's energy by the rating times 8,760 hours. ### Hydroelectric dam Hoover Dam is listed at 2,080 MW with annual production of about 4.2 TWh. Dividing 4.2 × 10¹² Wh by 8,760 h gives an average of about 480 MW, a capacity factor of about 23%.[^murphy-11] ### Wind farm A wind farm whose output averages one third of its rating has a capacity factor of about 33%, typical of U.S. wind.[^murphy-cf] ### Photovoltaic power station A solar plant producing the equivalent of about 4.8 full-sun hours a day has a capacity factor of about 20%; the best U.S. states reach about 27%, equal to about 6.5 full-sun hours.[^murphy-cf] ## Determinants of a plant capacity factor A plant runs below its rating because its fuel or resource is not always available (water, wind, sunlight), because it is shut down for maintenance or faults, or because the grid does not need its output and it is dispatched down. For hydroelectric plants, seasonal flow is the main factor, and a dam may be deliberately sized to produce high power for a few hours rather than steady power all day. ## Capacity factor of renewable energy Variable renewable sources have capacity factors set by nature: solar by night, season and cloud; wind by the weather; run-of-river hydro by the river's flow. In a database of 1,317 U.S. dams with 77.6 GW installed, the average output was 28.1 GW, a capacity factor of 0.36; weighted by generation the national average is about 0.4.[^murphy-11] Washington, with 20.7 GW installed across 65 dams, delivers an average of 8.9 GW; Iowa has only 0.153 GW installed but a high capacity factor, with an average of 0.114 GW dominated by the Keokuk dam.[^murphy-11] ## Capacity factors by energy source Typical U.S. values are about 40% for hydroelectric, 33% for wind and 20% for solar photovoltaic plants.[^murphy-cf] ### United States U.S. hydroelectric dams deliver about 40% of their rated capacity over a year, subject to seasonal water flow; U.S. wind capacity factors are around 33%, and photovoltaic capacity factors are around 20%.[^murphy-cf] ## See also - [[Run-of-the-river_hydroelectricity]] - [[Hydroelectricity]] - [[Grid_energy_storage]] - [[Electrical_grid]] ## References [^murphy-cf]: Murphy, Tom W., Jr. (2021). *Energy and Human Ambitions on a Finite Planet*, ch. 11–13 (capacity factors of hydroelectric, wind and solar installations). eScholarship, University of California. https://escholarship.org/uc/item/9js5291m [^murphy-11]: Murphy, Tom W., Jr. (2021). *Energy and Human Ambitions on a Finite Planet*, ch. 11 "Hydroelectric Energy," pp. 173–181. eScholarship, University of California. https://escholarship.org/uc/item/9js5291m ### Portal Books - Murphy, Tom W., Jr. (2021). *Energy and Human Ambitions on a Finite Planet* — [eScholarship](https://escholarship.org/uc/item/9js5291m); on the [[PORTAL_Energy]] shelf. <!-- SPINEPATH:BEGIN g20 — shortest chain of Wikipedia links between local articles to a Compendium Main article; do not hand-edit inside --> *Connected to the Apex Spine:* Capacity factor → [[Hydroelectricity|Hydroelectricity]] — [[WT!Thury_Hydrodynamics_Compendium|Compendium]] section 16, *Hydroelectricity*. <!-- SPINEPATH:END --> ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Capacity_factor) : [Wikitube](https://en.wikitube.io/wiki/Capacity_factor) · pinned revision [1329986954](https://en.wikipedia.org/w/index.php?oldid=1329986954) · 2026-09-10 ## Previous hub tags Hubs: `Life_Physics`, `Systems`. Portals: [[PORTAL_Thury_Hydrodynamics_Apex_Spine]], [[PORTAL_Energy]]. --- *Thury station wave · 2026-09-10 · drafted · microsim THY-105 (p5.js) · parent [[Hydroelectricity]].*