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Wind calculator

Wind power density calculator (W/m²) with NREL wind classes

Wind power density is the single best number for comparing wind sites. Enter a mean speed, height and Weibull k to get W/m², the NREL wind power class and how much energy hides in strong winds.

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Results

397 W/m² at 50 m: NREL wind power class 3 (“Fair”). Usable with modern low-specific-power rotors on tall towers. Using the mean speed alone (½ρv̄³) would underestimate it by 48%.
Wind power density at 50 m
397W/m²
3,476 kWh/m² of rotor area per year
NREL wind power class
3 · Fair
397 W/m² equiv. at 50 m
Air density
1.212kg/m³
-1.1% vs sea-level standard
Energy pattern factor
1.91
mean(v³) ÷ mean(v)³
Naive ½ρv̄³ (wrong)
208W/m²
ignores the speed distribution
Weibull scale c
7.9m/s
Most frequent speed
5.59m/s
Speed carrying most energy
11.17m/s
size rated speed around 1.2–1.5× this
Energy from winds ≥ 12 m/s
46.4%
mostly clipped by turbines at rated power
Equivalent at 10 m
199W/m²
IEC turbine class at 100 m: II
Where the energy is: time vs energy by wind speed

NREL wind power classes (Elliott et al., 1986)

ClassRatingW/m² at 10 mm/s at 10 mW/m² at 50 mm/s at 50 m
1Poor0–1000–4.40–2000–5.6
2Marginal100–1504.4–5.1200–3005.6–6.4
3 ◀ youFair150–2005.1–5.6300–4006.4–7
4Good200–2505.6–6400–5007–7.5
5Excellent250–3006–6.4500–6007.5–8
6Outstanding300–4006.4–7600–8008–8.8
7Superb400+7+800+8.8+
  • NREL class speeds assume sea-level air density and a Rayleigh distribution (k = 2); the class is assigned here from power density, which also accounts for your k and air density.
  • Wind power density is the power in the wind, not what a turbine extracts. Real rotors capture at most 59.3% (Betz limit), in practice 40–50% at the best speeds.

How this calculator works

The power in moving air grows with the cube of its speed: double the wind and you get eight times the power. That makes the mean wind speed a misleading number on its own: a gusty site and a steady site with the same average speed can carry very different energy. Wind power density (WPD) solves this by averaging the cube of the speed over the whole distribution, weighted by air density.

The calculator assumes the wind follows a Weibull distribution with your mean speed and shape factor k (k = 2 is the Rayleigh case used when nothing better is known). It computes air density from your elevation and temperature, the exact power density, the NREL wind power class, the energy pattern factor and the speeds where the energy actually sits. The chart separates time from energy: the wind spends most hours at moderate speeds, but much of the energy arrives in the less frequent strong winds.

The formula

WPD = ½ × ρ × mean(v³) = ½ × ρ × c³ × Γ(1 + 3/k)

c = v̄ / Γ(1 + 1/k) (Weibull scale) EPF = Γ(1 + 3/k) / Γ(1 + 1/k)³ (energy pattern factor) WPD = EPF × ½ × ρ × v̄³ ρ = p / (287.05 × T), p = 101,325 × (1 − 2.2558×10⁻⁵ × z)^5.2559

Γ is the gamma function, p the air pressure at altitude z (m) and T the absolute temperature in kelvin. For k = 2 the energy pattern factor is 1.91; for gusty inland winds with k = 1.5 it rises to 2.7, for steady trade winds with k = 3 it falls to 1.4.

Worked example: 7 m/s at 50 m

With the defaults (mean speed 7.0 m/s at 50 m, k = 2, a site at 200 m elevation with a mean temperature of 10 °C), air density at measurement height is about 1.21 kg/m³, 1% below standard.

  • Weibull scale c = 7.0 / Γ(1.5) = 7.90 m/s
  • WPD = ½ × 1.21 × 7.90³ × Γ(2.5) ≈ 397 W/m²
  • Naive estimate ½ρv̄³ = 208 W/m², almost 50% too low

397 W/m² at 50 m falls in NREL class 3 (“fair”), just short of class 4. The most frequent wind speed is only 5.6 m/s, but the speed carrying the most energy is 11.2 m/s, and nearly half the energy comes from winds of 12 m/s or more, speeds at which a turbine is already at rated power and spills the excess. That is why modern turbines with large rotors and modest generators capture a larger share of a site’s energy.

How to read the results

  • Wind power density is the headline number. Multiply by 8.76 to get kWh per m² of rotor per year passing through the swept area.
  • NREL class is assigned from power density converted to 50 m with the 1/7 power law, so measurements at any height can be compared with the table.
  • Energy pattern factor shows how much the speed distribution amplifies power over the mean-speed estimate.
  • Speed carrying most energy is a design guide: turbines are usually rated at 1.1–1.4× this speed.
  • IEC turbine class runs from I (high wind, 10 m/s mean) down to IV (6 m/s), based on the mean speed extrapolated to 100 m.

Typical values

NREL class Rating WPD at 50 m (W/m²) Speed at 50 m (m/s)
1 Poor 0–200 0–5.6
2 Marginal 200–300 5.6–6.4
3 Fair 300–400 6.4–7.0
4 Good 400–500 7.0–7.5
5 Excellent 500–600 7.5–8.0
6 Outstanding 600–800 8.0–8.8
7 Superb > 800 > 8.8

Speeds in the table assume sea-level density and k = 2. Typical real-world ranges at 100 m: inland Europe 250–450 W/m², windy coasts and plains 450–800 W/m², North Sea 800–1,000 W/m², Patagonia or exposed islands above 1,000 W/m².

Tips

  • Get k right. A k of 1.6 instead of 2.0 raises power density by 30% for the same mean speed. Fit k from measured data with the Weibull calculator.
  • Compare at the same height. Use the wind speed at height calculator before comparing sites measured at different heights.
  • Correct for altitude. Mountain and plateau sites lose 10–25% of power to thin air, which matters for small-turbine payback.
  • Remember the Betz limit. WPD is the resource, not the yield: use the wind turbine calculator for actual kWh.

Limitations

Real wind distributions are not always Weibull. Sea-breeze or monsoon climates can be bimodal, and very calm sites have more zero-wind hours than the model predicts. Density is taken at the annual mean temperature; seasonal correlation between cold air and strong winds (common in Europe) raises real power density by a few percent. The NREL classes assume a 1/7 power law, which may not match your terrain. For investment decisions, compute power density directly from at least one year of measured 10-minute data.

Method & assumptions

Power density of a Weibull wind regime: WPD = ½ ρ c³ Γ(1 + 3/k), with scale c = v̄ / Γ(1 + 1/k). This equals ½ ρ v̄³ × EPF, where the energy pattern factor EPF = Γ(1+3/k)/Γ(1+1/k)³ (1.91 for k = 2). Air density from the barometric formula at elevation + height and the temperature lapsed at 6.5 °C/km: ρ = p / (287.05 T). To compare with the NREL table, power density is moved to 10 m and 50 m with the power law (WPD ∝ h^{3α}).

Frequently asked questions

What is wind power density?
It is the kinetic power carried by the wind through one square metre perpendicular to the flow, averaged over time, in W/m². It combines mean speed, the speed distribution and air density into one number, which makes it the best single figure for comparing wind sites.
What is a good wind power density?
At 50 m height, below 200 W/m² is poor (NREL class 1), 300–400 W/m² is fair (class 3), 400–500 good (class 4) and above 500–600 W/m² excellent. Modern low-wind turbines make class 3 sites viable; offshore sites often exceed 700–900 W/m² at hub height.
Why can't I just use ½ρv³ with the average wind speed?
Because power depends on the cube of speed, and the average of cubes is larger than the cube of the average. For a typical Rayleigh distribution (k = 2) the true power density is 1.91 times ½ρv̄³, so using the mean speed alone underestimates it by almost half.
How does air density affect wind power?
Power is directly proportional to air density. Standard sea-level air at 15 °C is 1.225 kg/m³; at 1,500 m elevation density is about 15% lower, and hot air is thinner than cold air, so winter winds carry slightly more power than summer winds of the same speed.
How much of wind power density can a turbine capture?
At most 59.3% (the Betz limit). Real rotors capture 40–50% near their best wind speed, and much less above rated speed, where they deliberately shed power. Over a year a turbine typically converts 20–35% of the wind power passing through its rotor into electricity.
What are the NREL wind power classes?
Seven classes defined in the 1986 US Wind Energy Resource Atlas by power density at 10 m and 50 m: class 1 (poor) up to class 7 (superb). They were built for 1980s turbines at low heights, so today they are mainly used for broad comparisons; utility projects now look directly at hub-height speed and power density.

Sources & references

  1. Elliott, D.L. et al. (1986). Wind Energy Resource Atlas of the United States. DOE/CH 10093-4, Pacific Northwest Laboratory
  2. Global Wind Atlas (DTU / World Bank) — mean power density maps
  3. Manwell, J.F., McGowan, J.G., Rogers, A.L. — Wind Energy Explained, 2nd ed., Wiley
  4. Justus, C.G., Hargraves, W.R., Mikhail, A., Graber, D. (1978). Methods for estimating wind speed frequency distributions. Journal of Applied Meteorology 17

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