# Hydroelectric Power Calculator

By Bogna Szyk
Last updated: May 12, 2021

Whether you're designing a mini hydro turbine or the next Three Gorges Dam, this hydroelectric power calculator will help you estimate the power output of your project. Our tool finds the expected power for three different types of hydroelectric turbines from just the basic flow characteristics: the channel cross-section, flow velocity, and (for a dam) the so-called head - the usable fall height.

If you're interested in hydropower, check out the pipe flow calculator as well!

## Hydropower turbine types

Our hydroelectric power calculator is able to find the output of three different types of turbines: a dam, a "run-of-river" installation, and a tidal power turbine.

• Dams are huge barriers that block the flow of water, creating a large reservoir. Water falls from the dam, and its potential energy is converted into mechanical energy during the fall. The fall height is called the head, and is the most important characteristic of a dam.

• Run-of-river installations don't have a reservoir of water, but use the kinetic energy of the flow and convert it into mechanical energy. The requirement for such a turbine is a steady inflow of water.

• Tidal power stations use the daily rise and fall of ocean water, or the tides, to generate energy.

## Hydropower formulas

The power output of a dam is calculated using the potential energy of the water and can be found using the following hydropower formula:

`P = η * ρ * g * h * Q`

where:

• P is the power output, measured in Watts
• η is the efficiency of the turbine
• ρ is the density of water, taken as 998 kg/m³ (you can change it in advanced mode)
• g is the acceleration of gravity, equal to 9.81 m/s² (you can change it in advanced mode)
• h is the head, or the usable fall height, expressed in units of length (meters or feet)
• Q is the discharge (also called the flow rate), calculated as `Q = A * v`
• A is the cross-sectional area of the channel
• v is the flow velocity

Run-of-river installations and tidal power stations take advantage of the kinetic energy of the flow, so the formula is slightly different:

`P = 0.5 * η * ρ * Q * v²`

The efficiency of the turbine is the ratio of available energy of water to the actual power output of the turbine. It's usually expressed as a percentage. The efficiencies of such turbines can reach up to 59.3%, as they're limited by the Betz limit.

## Hydro turbine calculations: an example

Let's assume you want to build a dam on a small river. The cross-sectional area of the channel is 150 m², and the speed of the river is 2 m/s. The height of the dam is 15 m.

1. Calculate the discharge: `Q = A * v = 150 * 2 = 300 m³/s`.
2. Find the efficiency of your hydro turbine. We can assume it's equal to 80%.
3. Find the power output of the dam with the hydropower formula:

`P = η * ρ * g * h * Q = 0.8 * 998 * 9.81 * 15 * 300 = 39,639 * 10³ W = 39,639 kW`

## What's my revenue?

Once you know the power output of the dam, you can use our hydroelectric power calculator to determine the revenue it will bring you. All you have to do is multiply the power output by the electricity tariff and by the number of hours when the dam is in operation.

For example, let's assume that you get paid \$0.08 per kWh power for your electricity. The dam will be operating 150 days a year. After 365 days, you're going to secure the following revenue:

`revenue = \$0.08 * 39,639 * 24 * 150 = \$11,416,000`

Is that enough to justify the construction cost? Check it with our ROI calculator!

Bogna Szyk
Turbine type
Hydroelectric dam
Cross-sectional area
ft²
Flow velocity
ft/s
Flow discharge
cu ft
/s
ft
Expected output power
Efficiency
%
Power output
kW
Revenue
Operating days
/year
Tariff
\$/
kWh
Revenue
\$/
per year
People also viewed…

### Fish mercury

The fish mercury calculator will tell you how much mercury is in the fish you eat and how much you can safely consume in a week.

### Lost socks

Socks Loss Index estimates the chance of losing a sock in the laundry. 