# Hydroelectric Power Calculator

Created by Bogna Szyk
Reviewed by Dominik Czernia, PhD and Jack Bowater
Last updated: Nov 02, 2022

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! And if renewable energy topics are your hobby, we also have the solar panel calculator and wind turbine calculator.

## 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:

$P = 0.5 × η × ρ × Q × v^2$

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 = 35,245,368 W ≈ 35,245 kW

## What's my revenue?

Once you know the dam's power output, 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 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 × 35,245 × 24 × 150 = $10,147,561 Is that enough to justify the construction cost? Check it with our ROI calculator! Bogna Szyk Turbine type Hydroelectric dam Cross-sectional area ft² Flow velocity ft/s Flow discharge cu ft /s Head ft Expected output power Efficiency % Power output kW Revenue Operating days /year Tariff$/
kWh
Revenue
\$/
yr
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