Quick answer
Wind power is P = ½ρAv³C_p with ρ = 1.225 kg/m³. An 80 m rotor in an 8 m/s wind with a power coefficient of 0.35 produces about 551.7 kW; the Betz-limit maximum is 934.1 kW.
Enter the rotor diameter, wind speed and power coefficient. The calculator returns the power in watts and kilowatts and the Betz limit. Use this wind power estimate calculator to check your own figures.
Related tools: Power Calculator: Mechanical power from work and time, or force and velocity. Potential Energy Calculator: Gravitational potential energy from mass, height and gravity. Solar Panel Output Calculator: Daily, monthly and yearly energy from a solar array.
How to use the Wind Power Estimate Calculator
- Enter rotor diameter (m) (above 0).
- Enter wind speed (m/s) (above 0).
- Enter power coefficient (between 0 and 0.593). It starts at 0.35.
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Rotor diameter | A number, in m | > 0 |
| Wind speed | A number, in m/s | > 0 |
| Power coefficient | A number. Cannot exceed the Betz limit of 0.593 | > 0, ≤ 0.593, starts at 0.35 |
Formula and method
Formula
P = ½ ρ A v³ C_p (ρ = 1.225 kg/m³)
IEEE-754 double precision; shown to the decimals indicated.
Air density is sea-level standard; the Betz limit caps C_p at 16/27 ≈ 0.593.
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Rotor diameter = 80; Wind speed = 8; Power coefficient = 0.35.
| Result | Value |
|---|---|
| Power | 551,713.94 W |
| Kilowatts | 551.714 |
| Betz-limit maximum | 934.119 kW |
Example 2
Inputs: Rotor diameter = 2.5; Wind speed = 12; Power coefficient = 0.4.
| Result | Value |
|---|---|
| Power | 2,078.16 W |
| Kilowatts | 2.078 |
| Betz-limit maximum | 3.079 kW |
Example 3
Inputs: Rotor diameter = 126; Wind speed = 10; Power coefficient = 0.45.
| Result | Value |
|---|---|
| Power | 3,436,762.95 W |
| Kilowatts | 3,436.763 |
| Betz-limit maximum | 4,525.778 kW |
The first line is the headline result (power). Below it the wind Power Estimate Calculator lists kilowatts and betz-limit maximum, which describe the same case from other angles. IEEE-754 double precision; shown to the decimals indicated.
Cube of wind speed
Power rises with the cube of wind speed: at 10 m/s the same turbine would produce (10/8)³ = 1.95 times as much, about 1,078 kW. That is why sites with higher wind are so valuable.
The Betz limit
No turbine can capture more than 16/27 (59.3%) of the wind's power. Real turbines reach C_p of 0.35 to 0.45. The estimate ignores cut-in and cut-out speeds and the turbine's rated power.
How the result changes with rotor diameter
Holding every other input at the first worked example, this table changes only rotor diameter. It shows how sensitive the answer is to that one value; each row was produced by running this calculator.
| Rotor diameter | Power | Kilowatts | Betz-limit maximum |
|---|---|---|---|
| 40 | 137,928.48 W | 137.928 | 233.53 kW |
| 80 | 551,713.94 W | 551.714 | 934.119 kW |
| 160 | 2,206,855.74 W | 2,206.856 | 3,736.475 kW |
| 320 | 8,827,422.97 W | 8,827.423 | 14,945.901 kW |
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Rotor diameter: entering "0" shows "Rotor diameter must be greater than 0." beside that field and no result.
- Power coefficient: entering "0.9" shows "Power coefficient must be at most 0.593." beside that field and no result.
Choosing between the Wind Power Estimate Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Power Calculator](/science/power-calculator/) | use | Power |
| [Potential Energy Calculator](/science/potential-energy-calculator/) | mass, height and gravitational acceleration | Potential energy |
| [Solar Panel Output Calculator](/science/solar-panel-output-calculator/) | panel rating, number of panels and peak sun hours per day | Energy |
| [Solar Payback Calculator](/science/solar-payback-calculator/) | system cost and annual savings | Payback period |
| [Work Calculator](/science/work-calculator/) | force, distance and angle between force and motion | Work |
Background: motion and mechanics
For constant acceleration the standard relations are v = u + at, s = ut + ½at², v² = u² + 2as and s = ½(u + v)t. Pick the equation that contains your three known quantities and the one you want. Use SI units (metres, seconds, kilograms, newtons, joules) throughout or the answer will be off by a factor.
These equations stop applying when acceleration changes during the motion, as with a rocket burning fuel; that needs calculus or numerical methods.
Assumptions and limitations
- Power rises with the cube of wind speed
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for rotor diameter and power coefficient to confirm this.
Frequently asked questions
What is Cp?
The fraction of wind power captured.
Why do turbines have long blades?
Power scales with swept area.
What is the capacity factor?
Average output relative to rated output.
What does the Wind Power Estimate Calculator calculate?
Power from a wind turbine rotor at a wind speed. It returns Power, Kilowatts and Betz-limit maximum.
What formula does the Wind Power Estimate Calculator use?
P = ½ ρ A v³ C_p (ρ = 1.225 kg/m³). Air density is sea-level standard; the Betz limit caps C_p at 16/27 ≈ 0.593.
What do I need to enter in the wind Power Estimate Calculator?
You enter Rotor diameter (m), Wind speed (m/s) and Power coefficient.
How is the result rounded or limited?
IEEE-754 double precision; shown to the decimals indicated. Power rises with the cube of wind speed.
What is an example of a wind Power Estimate result?
With rotor diameter 80, wind speed 8 and power coefficient 0.35, the power is 551,713.94 W.
Where does the method come from?
The method follows: Betz limit; ICAO International Standard Atmosphere (1.225 kg/m³).
Related calculators
- Power Calculator — Mechanical power from work and time, or force and velocity.
- Potential Energy Calculator — Gravitational potential energy from mass, height and gravity.
- Solar Panel Output Calculator — Daily, monthly and yearly energy from a solar array.
- Solar Payback Calculator — Simple payback period of an installation after incentives.
- Work Calculator — Work done by a force over a distance at an angle.
- Wind Chill Calculator — Wind chill temperature (°F, mph).
Sources
- Betz limit; ICAO International Standard Atmosphere (1.225 kg/m³)
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.