Home Wind Turbine Output Calculator

The cube law: why wind speed dominates everything

A home wind turbine looks like a simple fan in reverse, but its output follows a rule that surprises everyone the first time they meet it: power grows with the cube of wind speed. Double the wind speed and you get eight times the power; halve it and you get one eighth. That single fact explains why site selection matters more than turbine brand, why a turbine on a windy hill outperforms a larger one in a sheltered garden, and why manufacturers' headline wattages — quoted at a brisk 12 metres per second — rarely match what a sheltered rooftop actually delivers. This calculator makes the cube law tangible: enter a rotor radius and a wind speed and it returns instant power plus daily and annual energy if that wind blew constantly, so you can compare sites and turbines honestly.

The formula is P = ½ × ρ × A × v³ × Cp, where ρ is air density (about 1.225 kilograms per cubic metre at sea level), A is the swept area of the rotor (π × radius²), v is wind speed, and Cp is the power coefficient — the fraction of the wind's energy the turbine actually captures. This calculator uses Cp = 0.35, a realistic value for a good small turbine; the theoretical maximum, the Betz limit, is 0.593, because air must retain some speed to move away after passing the rotor. A turbine that captured 100 percent of the wind's energy would stop the air dead, and no more air could arrive. Real turbines therefore live well below the Betz limit, and cheap ones well below that.

Why swept area matters as much as wind

Swept area grows with the square of rotor radius: double the radius and the area quadruples. A 1 metre rotor sweeps 3.14 square metres; a 2 metre rotor sweeps 12.57 square metres. Combined with the cube law, that means a modest increase in both size and wind transforms output. At 8 metres per second, a 1 metre rotor at Cp 0.35 gives about 345 watts. At 10 metres per second, a 1.5 metre rotor gives about 1,515 watts — more than four times as much, from a 25 percent wind increase and a 50 percent radius increase working together. This is why turbine makers emphasise rotor diameter and why planning rules that cap height or diameter cap energy far more than they appear to.

Read the table as instant power at a constant wind speed, not as a promise. Real wind gusts, lulls and changes direction, and a turbine spends much of its life below its rated speed. Annual energy therefore depends on the wind speed distribution at your site, not a single speed. The calculator's annual figure — daily energy at the entered speed times 365 — is an upper bound for that speed, useful for comparing turbines and sites, but a proper site assessment uses a year's wind data or a local wind atlas. If your average wind speed is 5 metres per second, do not size your expectations from the 12 metres per second row.

A worked example

Take a 1 metre rotor in an 8 metres per second wind. Swept area is π × 1² = 3.14 square metres. Power is 0.5 × 1.225 × 3.14 × 8³ × 0.35. Since 8³ = 512, that is 0.6125 × 3.14 × 512 × 0.35 = 344.8 watts. Running at that speed all day gives 344.8 × 24 ÷ 1000 = 8.28 kilowatt-hours per day, and all year gives about 3,020 kilowatt-hours. A typical home uses roughly 8–10 kilowatt-hours per day, so this turbine at a constant 8 metres per second would roughly cover a home — but wind is not constant, so real annual output at an average of 8 metres per second with gusts and calms would be lower, often by a third or more. The calculator's job is to show the physics clearly, not to replace a site survey.

Now the larger case: a 1.5 metre rotor at 10 metres per second. Swept area is π × 2.25 = 7.07 square metres. Power is 0.6125 × 7.07 × 1000 × 0.35 = 1,515.3 watts. Daily energy at that speed is 36.37 kilowatt-hours, annual is about 13,274 kilowatt-hours — far more than a home needs, which is why larger turbines are often grid-connected and export surplus. The jump from the first example to the second is the cube law plus the square law working together, and it is the reason a slightly bigger, slightly windier installation can look disproportionately better on paper. Check both inputs before believing any headline figure.

Site factors that make or break a turbine

• Average wind speed: the dominant factor. Below about 5 m/s average, most small turbines struggle to justify their cost; above 7 m/s they start to shine.
• Height above obstacles: wind speeds rise with height. A turbine should clear nearby trees and roofs by a good margin, typically with the rotor at least 9 metres above anything within 150 metres.
• Turbulence: rooftops and trees create gusty, swirling wind that reduces output and wears bearings. Smooth, laminar wind from open ground or water is far better.
• Direction: prevailing wind direction matters for placement relative to obstacles; a turbine downwind of a house sits in its turbulent wake.
• Air density: cold, sea-level air is denser and carries more energy than warm, high-altitude air. The difference is modest but real.

Practical and legal checks before buying

• Check planning permission, permitted development rules, and any height or noise limits in your area before ordering.
• Talk to neighbours early: noise, flicker and visual impact cause more disputes than technical failures.
• Get a wind assessment: a year of anemometer data, or at least a reputable wind atlas, beats a manufacturer's brochure.
• Budget for tower, inverter, cabling, and maintenance, not just the turbine. The tower often costs as much as the turbine.
• Plan for shutdown: most turbines need a brake or furling system for storms, and a safe way to lower the tower for servicing.

Common mistakes

The most expensive mistake is installing a turbine where the wind is poor — a sheltered garden, a rooftop in a built-up area, or a valley — and expecting brochure output. The second is confusing peak watts with average watts: a turbine rated at 1,000 watts at 12 metres per second may average 150 watts at a real site. The third is underestimating turbulence damage: a turbine that shakes in gusty rooftop wind will fail early, and its warranty may exclude turbulent sites. The fourth is ignoring the tower: a short tower on a cheap pole saves money and loses most of the energy. Wind energy rewards height, exposure and patience; it punishes shortcuts in all three.

Wind versus solar for a home

Wind and solar complement each other seasonally: wind is often stronger in winter when solar is weakest, and solar peaks in summer when wind may fall. A home with both can smooth its renewable output across the year, but only if the wind site is genuinely good. If your site is sheltered, solar panels on a clear roof will almost always give more energy per pound than a small turbine. Use this calculator to test your site honestly — enter your real average wind speed, not the brochure speed — and let the cube law give you the answer before you spend anything.