Wind Speed at Height Calculator
Extrapolate a wind speed measured at one height to a different height using the wind-profile power law. Handy for scaling a 10 m weather-station reading up to a turbine hub, a crane jib or a rooftop.
Enter Values
How to use this calculator
- Enter the known wind speed in m/s and the height it was measured at (h1, in metres).
- Enter the target height h2 you want the wind speed for.
- Optionally set the roughness exponent α — leave it at 0.143 for open terrain, or raise it for rougher, built-up ground. Read the extrapolated speed in m/s and km/h.
How it works
Wind speeds up with height because ground friction slows the air near the surface. The power law models this profile as v2 = v1 × (h2 / h1)^α, where α is the wind-shear exponent set by surface roughness. The ratio (h2 / h1)^α is the multiplying factor applied to the known speed, and the km/h figure is simply the m/s result multiplied by 3.6.
Worked example
Worked example. A 10 m mast reads 5 m/s over open terrain (α = 0.143). To estimate the wind at a 50 m hub height, the factor is (50/10)^0.143 = 5^0.143 ≈ 1.2588, so v2 ≈ 5 × 1.2588 = 6.294 m/s, which is about 22.66 km/h.
Common mistakes
- Leaving α at 0.143 over rough or urban ground — friction there is far stronger, so use roughly 0.25–0.40 to avoid overestimating the high-level wind.
- Mixing up h1 and h2 — h1 is where the wind was measured, h2 is where you want it; swapping them inverts the result.
- Using it in complex terrain or right next to buildings, where the smooth power-law profile breaks down.
Frequently asked questions
What is the one-seventh power law?
It is the special case α = 1/7 ≈ 0.143, a long-standing engineering approximation for the wind profile over flat, open terrain and open water under neutral atmospheric stability.
How do I choose the right α?
Match it to the ground upwind: about 0.10–0.14 for water and open flat land, ~0.20 for crops and scattered obstacles, and 0.25–0.40 for suburbs, forest and city centres. Rougher surfaces produce stronger shear and a larger α.
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Tip: Enter any known values to calculate the remaining results.
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