Wind Turbine Power Calculator
Power in the wind across a rotor and the electrical output after Cp and drive-train efficiency. With the formula, a worked example and typical values.
Try your own numbers
Estimate only. Not engineering or safety advice. Check the result against the applicable standard and the equipment data, and have a competent engineer review it before it is relied on. Terms of use.
Open in the calculator with these values
About this calculator
This page calculates swept area, power in the wind and electrical output from rotor diameter, wind speed, power coefficient Cp, air density and 1 more input. Change any value or its unit and the result updates. The steps below show the working for the default values, so you can check each line against your own method.
Limits of this calculator
Power rises with the cube of wind speed, so a small error in the wind speed gives a large error in output. Use the manufacturer power curve for real yield.
Cross-check: 6 reference cases, calculated from textbook formulas coded separately from the engine by the same author, agree with this calculator. This is not an independent review.
Verification status: Indicative
Indicative. Estimation only; further engineering checks are required. Basis: Idealised turbine power with an assumed power coefficient.
What this calculator checks
- The arithmetic of the simplified model for the values you entered.
What remains unverified
- Whether the simplifying assumptions listed on this page hold for your case.
- Any standard, manufacturer or site data. Treat the result as an estimate and confirm it by a further engineering check.
Verification register entry
| Calculation author | Rahul Sharma (author) |
|---|---|
| Technical review | No independent technical review has been carried out |
| Individual professional approval | Not recorded |
| Formula reference | not recorded |
| Standard and edition | Not applicable: The Betz/available-wind-power relationship is a physics equation. Wind-turbine standards govern power-performance measurement and turbine design, not this theoretical power estimate. |
| Standard review state | Not applicable |
| Scope-screening note | not recorded |
| Cross-check test cases | 6 reference vectors (tests/reference_vectors.json) |
| Review date | not recorded |
| Next review date | not recorded |
| Status | Indicative |
Needed before this calculator can be marked Verified: reviewer name, qualification and review date; exact formula reference; formula source (textbook or standard); next review date.
Formula
Worked example
| Input | Value |
|---|---|
| Rotor diameter | 90 m |
| Wind speed | 10 m/s |
| Power coefficient Cp | 0.4 |
| Air density (kg/m³) | 1.225 |
| Drive-train and generator efficiency | 0.95 |
- A = π × 90² / 4 = 6,361.7 m²
- Pwind = 0.5 × 1.225 × 6,361.7 × 10³ = 3,896.6 kW
- Pout = 3,896.6 × 0.4 × 0.95 = 1,480.7 kW
Assumptions
- Steady wind at hub height
- Cp is for this wind speed, taken from the power curve
- Standard sea-level air density 1.225 kg/m³
Power rises with the cube of wind speed, so a small error in the wind speed gives a large error in output. Use the manufacturer power curve for real yield.
Inputs and results
| Input | Unit | Allowed or shown | Note |
|---|---|---|---|
| Rotor diameter | m | greater than 0 m | |
| Wind speed | m/s | greater than 0 m/s | |
| Power coefficient Cp | (number) | greater than 0, up to 0.592593 | The Betz limit is 0.593 |
| Air density (kg/m³) | (number) | 0.5 or more, up to 1.5 | |
| Drive-train and generator efficiency | (number) | greater than 0, up to 1 |
| Result | Unit | Allowed or shown | Note |
|---|---|---|---|
| Swept area | m² | Shown to 0 decimal places | |
| Power in the wind | kW | Shown to 1 decimal place | |
| Electrical output | kW | Shown to 1 decimal place |
How it is calculated
Each input is converted to the base unit of its quantity, the formula above is applied in the order shown in the worked example, and each result is shown in the unit you choose. Results are held at full precision and rounded only for display, except where a step selects a standard size, as the worked example shows. A value outside its allowed range is refused with a message instead of giving a result.
How the result changes with rotor diameter
| Rotor diameter (m) | Swept area (m²) | Power in the wind (kW) | Electrical output (kW) |
|---|---|---|---|
| 9 | 64 | 39 | 14.8 |
| 22.5 | 398 | 243.5 | 92.5 |
| 45 | 1,590 | 974.1 | 370.2 |
| 90 | 6,362 | 3,896.6 | 1,480.7 |
| 180 | 25,447 | 15,586.2 | 5,922.8 |
| 360 | 101,788 | 62,344.9 | 23,691.1 |
| 900 | 636,173 | 389,655.7 | 148,069.2 |
Other inputs are the same as in the worked example above.
Standards and further reading
- IEC 62548 (photovoltaic array design requirements)
Module and battery limits come from the manufacturer data sheet; local grid codes set connection rules. These are named as background reading. Elecmetric does not embed clause text or rating tables, and the reviewer record for this calculator is separate from this list.
Frequently asked questions
What do I need to enter?
Enter rotor diameter, wind speed, power coefficient Cp, air density (kg/m³) and drive-train and generator efficiency. Change the unit of a value with its selector and the result stays the same.
What does this calculator assume?
Steady wind at hub height. Cp is for this wind speed, taken from the power curve. Standard sea-level air density 1.225 kg/m³.
Which calculators should I use next?
Common next steps are Solar PV Energy Yield and Appliance Running Cost (Energy and Cost). The related links at the bottom of this page open them.
How accurate are the results?
Every figure comes from the same tested engine as the Elecmetric calculators and is meant for estimating. 6 reference cases, calculated from textbook formulas coded separately from the engine by the same author, agree with this calculator. This is not an independent review. Check design values against the standard and the equipment data you work to.
Formula guides and reference
Longer explanations with worked examples and tables, written for the same topic.
- Wind Turbine Power Formulas: Betz Limit: Wind turbine power formulas: swept area, power in the wind, power with the power coefficient
More Renewable Energy calculatorsAll engineering calculatorsWind Turbine Power in Elecmetric