Wind Speed at Height Calculator (Wind Shear, Power Law and Log Law)

What this tool does

Wind slows near the ground because of friction, so a 10 m anemometer reading understates the wind at the height of a turbine hub. Two standard ways to scale it are the power law, with an exponent often taken as 1/7 for open ground, and the logarithmic law, which uses the roughness length z₀ of the terrain, from about 0.0002 m over open water to a metre or more over towns and forests. Because the power in wind goes with the cube of its speed, a modest rise in speed matters a lot: a 36 % faster wind carries two and a half times the power. Both laws are for neutral conditions, over flat terrain, and in the lowest few hundred metres.

Formula

power law: v₂ = v₁ (z₂ ÷ z₁)^α (α ≈ 1/7 = 0.143 in open country) · log law: v₂ = v₁ ln(z₂ ÷ z₀) ÷ ln(z₁ ÷ z₀)

Variables

Symbol	Meaning	Unit
`v1`	Wind speed measured	m/s
`z1`	Height of the measurement	m
`z2`	Height you want it at	m
`al`	Power-law exponent α	—
`z0`	Roughness length z₀ of the ground	m
`VP`	Wind speed there, power law	m/s
`VL`	Wind speed there, logarithmic law	m/s
`PG`	Wind power available there compared with the measured height (log law)	×

Worked example

Wind speed measured5 m/s
Height of the measurement10 m
Height you want it at80 m
Power-law exponent α0.143
Roughness length z₀ of the ground0.03 m

Wind speed there, power law6.73 m/s
Wind speed there, logarithmic law6.79 m/s
Wind power available there compared with the measured height (log law)2.50 ×

Limitations

The formula assumes ideal conditions: no friction losses, no air resistance and no efficiency losses unless you enter them.
The result is an estimate based only on the values you type. Real situations often include factors this calculator does not know about.