Renewable Power Calculator: Hydro Power, Wind Turbine Power with the Betz Limit, and Solar Array Size

Work out the power from water, the power from the wind, or the size of the solar array you need.

Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.

How this calculator works

Choose hydro, wind or solar. For hydro enter the flow, the net head and the efficiency. The power is rho g Q H times the efficiency.

For wind enter the rotor diameter, the wind speed, the power coefficient and the air density. It gives the power in the wind, the Betz limit of 59.3 percent, and the power of your turbine.

For solar enter the daily energy, the peak sun hours, the performance ratio and the panel size. It gives the array size, the number of panels, and the area.

Formulas used

  • P = \eta\rho g Q H
  • P_w = \tfrac12\rho A v^3
  • P = C_p P_w,\quad C_p \le 0.593
  • P_{pk} = \frac{E_d}{\mathrm{PSH}\times\mathrm{PR}}

Worked example

With the default numbers in the calculator above:

  1. Power in the water: 2943.00 kW
  2. Electrical power out: 2501.55 kW (2.50 MW)
  3. Energy in a year if it ran all the time: 21.91 GWh (multiply by the capacity factor for the real figure)

Change the numbers in the calculator to see the full working, every step, for your own case.

A second worked example

A different case, with these numbers: What do you want? Wind turbine power.

  1. Swept area of the rotor: 5026.55 m2
  2. Power in the wind through the rotor: 3078.76 kW
  3. Betz limit: the most any turbine can take (59.3 percent): 1825.71 kW
  4. Power from the turbine: 1231.50 kW (1.23 MW)
  5. Energy in 24 hours at this wind speed: 29556.10 kWh

Common questions

What is the Betz limit?

No wind turbine can take more than 59.3 percent of the power in the wind, because the air has to keep moving past the rotor.

What are peak sun hours?

The number of hours a day of full sun, 1 kW per square metre, that would give the same energy as the real day.

Why does wind power vary so much?

It goes as the cube of the wind speed, so a small change in speed changes the power a great deal.

Does the solar answer include batteries?

No. It sizes the array for the daily energy only. A battery is sized for the nights and cloudy days.

Related calculators

Got a question about this? Ask an engineering question and get a plain-language answer with references.

Further reading: Twidell and Weir, Renewable Energy Resources; Clean Energy Council guidelines for solar design.

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