Wind Turbine Swept Area Power P = ½ρAv³·Cp & Betz Limit (59.3%) Calculator

Compute wind turbine swept area, cubic wind power ½ρAv³, Betz limit, and net electrical kW.

Turbine Rotor Shaft Power (@ Cp)
2,281.98 kW
Theoretical Betz Limit Max (59.26%) 3,073.37 kW
Raw Kinetic Wind Power (½ρAv³) 5,186.32 kW
Rotor Swept Area (πR²) 6,361.73 m²
Inputs
⚡ Scenarios:
m
Wind turbine rotor radius R in meters.
m/s
Freestream wind velocity v in m/s.
kg/m³
Air density ρ in kg/m³ (1.225 kg/m³ at sea level 15 °C).
C_p
Rotor aerodynamic power coefficient C_p (max 0.5926 Betz limit).
Results & Graph
Turbine Rotor Shaft Power (@ Cp)
2,281.98 kW
Theoretical Betz Limit Max (59.26%)
3,073.37 kW
Raw Kinetic Wind Power (½ρAv³)
5,186.32 kW
Rotor Swept Area (πR²)
6,361.73 m²

Turbine Rotor Shaft Power (@ Cp)

Graph 1 • Wind Turbine Betz Power • Domain Architecture & Live Telemetry Maps Rotor Blade Radius Meters, Wind Speed Meters Per Sec, Air Density Kg M3 through Wind Turbine Betz Power Formula.
Wind Turbine Betz Power • Generation → Conversion → Storage Bus 1. SOURCE / ARRAY 45 m Rotor Blade Radius Met 2. DELIVERED RATING 2,281.98 kW Turbine Rotor Shaft Powe 3. SECONDARY OUTPUT 3,073.37 kW Theoretical Betz Limit M
Graph 2 • Turbine Rotor Shaft Power (@ Cp) Across Rotor Blade Radius Meters Sweep (40% → 160%) Evaluates A = π·R²; P_wind = 0.5 × ρ × A × v³; P_Betz = (16/27) × P_wind; P_ across 7 operating points (current input highlighted).
0 kW 3.2k kW 6.4k kW 365.1 18m 821.5 27m 1.5k 36m 2.3k 45m 3.3k 54m 4.5k 63m 5.8k 72m
Graph 3 • Joint Sensitivity: Rotor Blade Radius Meters × Wind Speed Meters Per Sec Compares Turbine Rotor Shaft Power (@ Cp) when Wind Speed Meters Per Sec is shifted +25% (solid) vs. −25% (dashed).
0 kW 4.1k kW 8.3k kW --- Wind Speed Meters Per Sec @ 75% 2.2k -30% 3.2k -15% 4.5k +0% 5.9k +15% 7.5k +30%
Summary: Across 6362 m² swept area at 11 m/s, raw kinetic wind power is 5186 kW, the 59.3% Betz limit ceiling is 3073 kW, and rotor power at Cp=0.44 is 2282 kW.
Summary: Across 6362 m² swept area at 11 m/s, raw kinetic wind power is 5186 kW, the 59.3% Betz limit ceiling is 3073 kW, and rotor power at Cp=0.44 is 2282 kW.
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Formula & Mathematical Methodology: Wind Turbine Betz Power Formula

A = π·R²
Pwind = 0.5 × ρ × A × v³
PBetz = (16/27) × Pwind
Pelec = Pwind × Cp × ηgen
A = π·R²; P_wind = 0.5 × ρ × A × v³; P_Betz = (16/27) × P_wind; P_elec = P_wind × C_p × η_gen
  • rotorBladeRadiusMeters: Rotor Blade Radius Meters (m)
  • windSpeedMetersPerSec: Wind Speed Meters Per Sec (m/s)
  • airDensityKgM3: Air Density Kg M3 (kg/m³)
  • powerCoefficientCp: Power Coefficient Cp (C_p)

Rounding: Engineering outputs round to 2–3 decimal places; discrete material bag/unit counts round up via ceiling.

Worked Example: Engineering Scenario: Wind Turbine Betz Power

Compute wind turbine swept area, cubic wind power ½ρAv³, Betz limit, and net electrical kW.

  1. Enter your system dimensions, electrical/RF ratings, or environmental conditions.
  2. Evaluate the governing equation: A = π·R²; P_wind = 0.5 × ρ × A × v³; P_Betz = (16/27) × P_wind; P_elec = P_wind × C_p × η_gen.
  3. Inspect the primary design output, supporting allowances, and 3 SVG schematics.
Result: Computes Wind Turbine Betz Power via A = π·R²; P_wind = 0.5 × ρ × A × v³; P_Betz = (16/27) × P_wind; P_elec = P_wind × C_p × η_gen.

Frequently Asked Questions

How does the Wind Turbine Swept Area Power P = ½ρAv³·Cp & Betz Limit (59.3%) Calculator calculate results?

It evaluates A = π·R²; P_wind = 0.5 × ρ × A × v³; P_Betz = (16/27) × P_wind; P_elec = P_wind × C_p × η_gen directly in your browser and updates three custom SVG visualizations in real time.

Can I use Goal Seek to solve backwards for a required dimension or rating?

Yes. Click "🎯 Goal Seek" in the results toolbar to solve backwards for any numeric input parameter.

Does this engineering calculator work offline?

Yes. All calculations run 100% locally in your browser and work offline via the CalculatorGraph PWA.

Science & Engineering · Renewable Energy & Battery Engineering

Wind Turbine Swept Area Power P = ½ρAv³·Cp & Betz Limit (59.3%) Calculator: inputs, method, and how to read the result

Compute wind turbine swept area, cubic wind power ½ρAv³, Betz limit, and net electrical kW.

Choose inputs for the case you are checking

The defaults are illustrative. Replace them with values for your case and keep the units shown beside each field.

  • Rotor Blade Radius Meters: Wind turbine rotor radius R in meters.
  • Wind Speed Meters Per Sec: Freestream wind velocity v in m/s.
  • Air Density Kg M3: Air density ρ in kg/m³ (1.225 kg/m³ at sea level 15 °C).
  • Power Coefficient Cp: Rotor aerodynamic power coefficient C_p (max 0.5926 Betz limit).

What the calculation includes

With the default values shown, Turbine Rotor Shaft Power (@ Cp) is 2,281.98 kW. The calculation follows Wind Turbine Betz Power Formula; the formula and variable definitions above show how the inputs combine.

One-input check: With the other defaults held constant, changing Rotor Blade Radius Meters from 45 m to 50 m changes Turbine Rotor Shaft Power (@ Cp) from 2,281.98 kW to 2,817.26 kW. This is a comparison inside the calculator's stated model, not a prediction.

Where to use caution

  • Uses standard NREL, IEEE, ASHRAE, and IRC design equations.
  • Verify final structural, electrical, and mechanical specifications against local building codes.

Scope: Global Engineering & Building Code Standard Check the assumptions and limitations against your situation before relying on the estimate.

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