Wind Turbine Calculator
A wind turbine is an argument with the weather, settled by one equation. The wind carries kinetic energy through the disc the rotor sweeps; the turbine keeps a fraction of it, and that fraction has a hard physical ceiling discovered a century ago. This calculator runs the full arithmetic — swept area, the cube of wind speed, and an honest efficiency — then turns the instantaneous power into the numbers that decide real projects: energy per year at a realistic capacity factor, and revenue at your electricity price. Enter a home turbine or a utility machine; the physics does not change, only the number of zeroes.
The Formula and the Betz Limit
Moving air carries kinetic energy, and the power crossing a disc of area A at wind speed v is P = ½ × ρ × A × v³ — air density ρ (1.225 kg/m³ at sea level), area in square metres, speed in metres per second, power in watts. A turbine multiplies that flow by its power coefficient Cp, the share it actually converts to electricity. In 1919–1926 Albert Betz (and, independently, others) proved the ceiling: a rotor that stopped the wind completely would block all flow, so the optimum slows the wind to a third of its upstream speed, capturing at most 59.3% — Cp can never exceed 0.593, whatever the marketing says. Real rotors, paying for blade drag, tip losses, gearbox and generator losses, deliver Cp of 0.25 (small or ageing machines) to 0.45 (the best modern blades). Any calculator or brochure implying more than 0.593 is not optimistic; it is wrong, and now you can check in seconds.
Worked Example: A 10-Metre Farm Turbine
The defaults price a serious farm or large-home machine: rotor diameter 10 m (swept area π × 5² = 78.5 m²) in an 8 m/s wind (a fresh breeze, about 29 km/h) at Cp 0.35. Step by step: 0.5 × 1.225 × 78.54 × 512 × 0.35 = 8,621 W ≈ 8.62 kW at that moment. At the Betz limit the same wind and rotor could give at most 14.6 kW — the physical wall. Run the year at a 30% capacity factor (a good inland site): 8.62 × 8,760 hours × 0.30 = 22,655 kWh per year, worth about $3,398 at $0.15/kWh — which is why the hub item "wind turbine profit calculator" folds into this page: the profit question is this question, with a price attached. Scale sense: raise the wind to 12 m/s and power leaps to 29.1 kW — the cube at work — while a utility rotor of 100 m at 12 m/s and Cp 0.42 makes about 3.49 MW, one machine supplying a small town.
The Cube Law: Why Site Selection Is Everything
Power scales with the cube of wind speed, the most consequential exponent in renewable energy. Double the wind and the same turbine makes eight times the power; a site averaging 9 m/s is not 12.5% better than one at 8 m/s — it is 42% better (1.125³ = 1.42). This is why developers measure a candidate site for a full year before spending on steel, why turbines live on ridges and coasts rather than in sheltered valleys, and why raising a home turbine from a 10 m mast to an 18 m mast — climbing out of the slow, turbulent air dragged by the ground — can double its output without touching the rotor. It is also why this calculator asks for wind speed so prominently: a 1 m/s error in your estimate is a 30–40% error in the answer at small scales, and honesty about the input is worth more than precision in the arithmetic.
Capacity Factor: From a Moment to a Year
The kilowatt figure is an instant; bills and business cases run on years, and the bridge is the capacity factor — actual annual energy divided by the energy the machine would make running at that power non-stop. Wind is variable, so factors run 20–35% onshore, 35–50% offshore, and under 20% for small turbines in turbulent suburban air. Nameplate games exploit the gap: a "10 kW" home turbine rated at 12 m/s may average under 2 kW at a real 6 m/s site, producing less in a year than a quality 5 kW machine at a better mast height. The defence is this page's workflow: compute power at your site's average wind (not the brochure's rating speed), apply a sober capacity factor, and compare annual kilowatt-hours — the only currency the meter accepts.
Small Turbines: The Honest Buyer's Arithmetic
The cube law writes the small-turbine industry's tragedy in one line. A machine advertised as "1,000 W" is rated at its rated wind speed — usually 11–13 m/s, a strong wind that most gardens see a few hours a year. At a realistic steady 6 m/s the same machine delivers 1,000 × (6/12)³ = 125 W — an eighth — and a full year of such wind would sum to about 1,095 kWh before turbulence, furling and downtime take their share. None of this makes small wind useless: on an exposed hill farm with 7–8 m/s average air, a well-sited small turbine on a tall mast is a serious machine (the worked example's 8.62 kW is exactly that class). It makes site honesty the whole purchase. The professional sequence is a year of measured wind at hub height, this calculator run at the measured mean — remembering that mean power needs the mean of cubes, which a proper wind assessment supplies — and deep suspicion of any quote that leads with the nameplate. Rooftop turbines on ordinary houses fail this arithmetic almost by definition: buildings sit in the slowest, roughest air in the landscape, and bolting a rotor to one advertises the address of the turbulence.
Offshore, and the Repowering Question
Move the same physics to sea and every term improves: winds are stronger and steadier, so capacity factors of 40–50% replace the onshore 25–35% — the worked example's machine at a 45% factor would yield about 34,000 kWh a year instead of 22,655 — and rotors have grown past 200 m across, with single offshore turbines now rated above the output of entire early wind farms. The other quiet revolution is repowering: replacing a 1990s 500 kW machine on an existing site — grid connection, permits, access roads already paid for — with a modern 4–5 MW rotor, multiplying the site's energy by roughly ten on the same land and often with fewer towers. Run the calculator both ways on any familiar site and the two-decade improvement in Cp, rotor size and capacity factor stops being an abstraction: it is the difference between the wind industry as a garnish on the grid and wind as one of its main courses.
Availability Is Not Capacity Factor
One confusion to retire before it costs you: a turbine's availability — the share of time it is mechanically ready to run, typically 97–99% for a modern machine — is not its capacity factor. A perfectly available turbine on a calm ridge still produces little; the wind's calendar, not the machine's health, writes the capacity factor. Brochures that blur the two are selling the 98 as if it were output. Keep them separate in every estimate you run here: availability trims the year by a few percent, the capacity factor you enter does the honest rest.
Related Tools
More from the Ecology Calculators hub: the Solar Panel Calculator for the other great renewable, the Hydroelectric Power Calculator for energy from falling water, the Carbon Footprint Calculator to weigh what the turbine displaces, and the CO2 Emissions Calculator for the emissions side of the ledger.
Frequently Asked Questions
Can a turbine beat the Betz limit of 59.3%?
No. The limit follows from conservation of mass and energy for a free-stream rotor: extracting all the wind's energy would require the air to stop dead behind the rotor, which blocks further flow. Ducted and shrouded designs advertise around it by enlarging the effective capture area — the 59.3% then applies to the shroud's area, not the rotor's, which is accounting, not magic.
Why does the calculator fix air density at 1.225?
That is sea-level air at 15°C, the standard reference. Air thins with altitude and heat: at 2,000 m density is about 1.0 kg/m³ and output falls roughly 18% at the same wind speed. Mountain users should scale the result by their local density ratio.
What wind speed should I enter?
Your site's measured or mapped average at hub height, for energy estimates — and remember the cube law punishes guesses. A year of anemometer data, or a reputable wind atlas figure for your exact location and height, is the professional standard.
How tall should a home turbine mast be?
The common rule: the rotor should clear everything within about 150 m by at least 9 m (30 ft). Turbulence from roofs and trees both starves and fatigues a turbine; height is usually the cheapest power a small system can buy.
What capacity factor should I assume?
25–30% is a fair planning figure for a good onshore site, 20% for a cautious one, and 40%+ belongs offshore. Manufacturers quoting small-turbine output at 35%+ for a backyard should be asked for the wind data behind the claim.
Does a bigger rotor always beat a bigger generator?
At real, moderate winds, yes, usually: energy comes from swept area and the wind that actually blows, so an oversized rotor on a modest generator (a low specific-power design) harvests more annual energy in light-wind regions than a small rotor straining behind a big nameplate.