Formula
- Tip speed = π D N / 60
- λ (TSR) = tip speed / wind speed
- P_ideal = ½ ρ A v³
- Cp = P_actual / P_ideal (Betz limit 0.593)
About this calculator
Part of our EV & Renewable Calculators collection. Battery sizing, solar panel tilt, wind turbine performance, and EV drivetrain estimates.
How it works
Tip speed ratio compares blade tip speed to wind speed. Ideal wind power uses swept area and air density. Power coefficient Cp is actual output divided by ideal power. The Betz limit of 0.593 is the theoretical maximum Cp for any wind turbine.
Enter your values in the inputs above and click CALCULATE. Results appear on the right without a page reload. No login and no server upload.
Worked example
10 m/s wind, 20 m rotor at 60 rpm, 50 kW output.
- Tip speed = π × 20 × 1 = 62.8 m/s
- TSR = 6.28
- Ideal power ≈ 192 kW, Cp = 50/192 = 26%
Result: TSR 6.3, Cp 26% (below Betz limit 59.3%).
When to use
- Checking tip speed ratio for blade design
- Comparing actual power to ideal wind power
- Evaluating power coefficient Cp
Limitations
- Ideal power uses ρ = 1.225 kg/m³ at sea level
- Does not include gearbox, generator, or availability losses
- Cp > 0.593 indicates input power exceeds physical limit
FAQ
- What is the Betz limit?
- No wind turbine can capture more than 59.3% of wind kinetic energy in the stream tube. Real Cp is typically 0.35–0.45.
- Typical TSR?
- Modern horizontal-axis turbines often operate at TSR 6–8 at rated wind speed.
Privacy and accuracy
Every calculation runs locally in your browser. Your design data never leaves your device. Results are intended for preliminary engineering work. Always verify critical designs with qualified review and applicable standards before production use.
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