Bar shows net head as a share of gross head. Pipe friction uses Darcy-Weisbach with the Swamee-Jain friction factor and water at 10 °C. A feasibility estimate only.
Formula and breakdown
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This micro hydro calculator estimates how much electricity a small stream could generate from its flow and head, after the friction loss in the pipe that feeds the turbine, and turns that into kWh and value per year. It is meant for landowners, smallholders and off-grid homes in the UK, Ireland and Europe weighing up a hydro scheme, and works in metric or US units.
Quick answer: A micro hydro calculator uses P = ρ x g x Q x H x η: water density 1,000 kg/m³, gravity 9.81 m/s², flow in m³/s, net head in metres and efficiency. 20 litres a second falling 25 m gives 4.9 kW of water power; at 60% efficiency and after pipe losses, about 2.5 kW of electricity.
What Is a Micro Hydro Calculator?
A micro hydro calculator is a tool that converts the flow and vertical drop of a stream into the electrical power a small turbine could produce. In plain words: power in watts equals 1,000 x 9.81 x flow in cubic metres per second x net head in metres x overall efficiency.
The Wikipedia article on hydropower gives this formula with η for turbine efficiency, ρ for water density, Q for volumetric flow, g for gravity and Δh for the height difference. Net head is the gross drop minus the energy lost to friction in the pipe, which is where many quick estimates go wrong: they use the gross head and overstate output. This micro hydro calculator works out that loss from the pipe’s length, internal diameter and roughness.
The size names matter for expectations. According to the Wikipedia article on micro hydro, micro hydro typically produces 5 to 100 kW, and installations below 5 kW are called pico hydro. Most domestic streams fall into the pico range.
How Do You Use the Micro Hydro Calculator?
- Choose metric or US units.
- Enter the design flow: the flow you can divert through the turbine, after leaving the water that must stay in the stream.
- Enter the gross head, the vertical height from the intake water surface down to the turbine.
- Enter the pipe length, internal diameter and roughness, or set length to 0 to see the result before pipe losses.
- Enter the overall water-to-wire efficiency and a capacity factor from your flow records.
- Read the electrical output, net head, pipe loss, water speed and energy per year.
How Much Power Can a Small Stream Generate?
Each litre per second falling through one metre carries 9.81 W of water power, so at 60% efficiency it yields about 5.9 W of electricity. The table shows electrical output at 60% overall efficiency before pipe losses, for common combinations of head and flow.
| Gross head | 5 L/s | 10 L/s | 20 L/s | 50 L/s | 100 L/s |
|---|---|---|---|---|---|
| 5 m | 0.15 kW | 0.29 kW | 0.59 kW | 1.47 kW | 2.94 kW |
| 10 m | 0.29 kW | 0.59 kW | 1.18 kW | 2.94 kW | 5.89 kW |
| 25 m | 0.74 kW | 1.47 kW | 2.94 kW | 7.36 kW | 14.71 kW |
| 50 m | 1.47 kW | 2.94 kW | 5.89 kW | 14.71 kW | 29.43 kW |
| 100 m | 2.94 kW | 5.89 kW | 11.77 kW | 29.43 kW | 58.86 kW |
Head and flow trade off directly: 10 L/s over 50 m gives the same power as 50 L/s over 10 m, but the low-head site needs five times the water and a larger, more expensive turbine and intake. Wikipedia notes that high-head sites suit Pelton wheels, while low-head sites use Francis or propeller turbines, water wheels or Archimedes screws, and that a drop of at least about 0.6 m is needed for a system to be feasible.
How Do You Measure Head and Flow at a Site?
Measure head as the vertical drop from the water surface at the intake to the turbine, not the length of the slope; a pressure gauge on a full, closed pipe gives it directly, because 1 bar of static pressure equals about 10.2 m of head (pressure divided by water density and gravity).
- Head by survey: a surveyor’s level or a laser level and staff, stepped down the slope, is the most precise method. Phone GPS and map contours are fine for a first look but are much less precise, and a small head error matters on a low-head site.
- Head by pressure: run a hose or pipe from the intake point to the turbine site, fill it, close the bottom end and read the gauge with no water flowing. Multiply bar by 10.2 for metres.
- Flow by bucket: for small streams, catch the whole flow in a container of known volume and divide litres by seconds.
- Flow by weir or meter: for larger streams a temporary weir plate or a flow meter gives better figures; record them in wet and dry months.
Use the dry-season flow you can take after any hands-off flow as the design flow, not a winter peak. Work in streams only when water levels are safe, and get the landowner’s agreement before surveying.
How Much Head Does the Pipe Lose?
Pipe friction can take a large share of the head, and it rises with roughly the square of the water speed, so a pipe one size too small can cost a third of the output. The micro hydro calculator uses the Darcy-Weisbach equation, head loss = f x (L / D) x v² / 2g, with the friction factor from the Swamee-Jain equation (or 64 / Re in laminar flow), and water at 10 °C.
The table shows the example site of 20 L/s, 25 m gross head and a 120 m pipe with 0.01 mm roughness, at 60% efficiency and a 50% capacity factor.
| Pipe internal diameter | Water speed | Friction loss | Share of head | Electrical output | Energy per year |
|---|---|---|---|---|---|
| 90 mm | 3.14 m/s | 10.93 m | 43.7% | 1.66 kW | 7,253 kWh |
| 110 mm | 2.10 m/s | 4.10 m | 16.4% | 2.46 kW | 10,778 kWh |
| 125 mm | 1.63 m/s | 2.20 m | 8.8% | 2.68 kW | 11,757 kWh |
| 160 mm | 0.99 m/s | 0.66 m | 2.7% | 2.86 kW | 12,548 kWh |
Going from 90 mm to 125 mm adds about 4,500 kWh a year at this site. Wider pipe costs more, so the right size is a balance a hydro designer will work out, but the micro hydro calculator shows quickly when a pipe is clearly too narrow. Pipe makers publish roughness figures for their products; change the default to match.
How Much Electricity Will a Micro Hydro System Make in a Year?
Annual energy equals output in kW x 8,760 hours x capacity factor, so a 2.46 kW turbine running at an average 50% of full output makes about 10,800 kWh a year. Unlike solar, a hydro turbine can run day and night whenever the stream has enough water.
The capacity factor depends on how the stream’s flow varies through the year against the turbine’s design flow, so it should come from flow measurements over at least a year. The default of 50% is an example value only. If you plan to store hydro power in batteries for an off-grid home, the battery bank size calculator sizes the bank, and the off-grid solar calculator helps when solar is added for summer low flows. Long cable runs from turbine to house also need checking with the voltage drop calculator.
Do You Need Permission for a Micro Hydro Scheme in the UK?
Yes. The Energy Saving Trust says all hydropower systems need planning permission, and in England the GOV.UK guidance on new hydropower schemes lists permissions from the Environment Agency: an abstraction licence if you divert water, an impounding licence for a dam or weir, approval for fish passes, and an environmental permit for flood risk activities. The licence sets a hands-off flow that must stay in the river while the turbine runs.
The Energy Saving Trust notes that in Scotland you may also need a water abstraction licence; each UK nation has its own environment regulator and rules. Talk to the regulator before buying equipment, because the permitted flow sets the design flow and so the output. Intakes, weirs and fast water are dangerous places to work, and the generator, controller and any connection to a building or the grid must be installed by a qualified electrician; in the UK the work must meet BS 7671.
Worked Example: A Hillside Stream With a 110 mm Pipe
Example: a farm stream can supply 20 L/s through the turbine after the hands-off flow. The intake sits 25 m above the turbine site, reached by 120 m of plastic pipe with a 110 mm internal diameter. Overall efficiency is taken as 60% and the capacity factor as 50%.
- Flow: 20 L/s = 0.02 m³/s. Water power at gross head: 1,000 x 9.81 x 0.02 x 25 = 4,905 W.
- Water speed: 0.02 / (π x 0.11² / 4) = 2.10 m/s.
- Friction factor (Swamee-Jain, Reynolds number about 177,000): 0.0166.
- Head loss: 0.0166 x (120 / 0.11) x 2.10² / 19.62 = 4.10 m, so net head is 20.90 m.
- Electrical output: 1,000 x 9.81 x 0.02 x 20.90 x 0.60 = 2,461 W, about 2.46 kW, which is pico hydro.
- Energy: 2.46 kW x 8,760 h x 0.50 = 10,778 kWh a year, worth about £2,837 at the Ofgem cap of 26.32p per kWh if it all replaces bought electricity.
A 125 mm pipe would cut the friction loss to 2.2 m and add about 980 kWh a year, which is worth pricing before the pipe is ordered.
Frequently Asked Questions
How do you calculate micro hydro power?
Multiply 1,000 kg/m³ by 9.81 m/s² by the flow in m³/s by the net head in metres by the overall efficiency. For 0.02 m³/s, 20.9 m net head and 60% efficiency that gives about 2,460 W. Net head is the gross drop minus pipe friction loss.
How much flow and head do I need for 1 kW?
At 60% overall efficiency, flow in litres per second times head in metres must be about 170. That could be 17 L/s over 10 m, 6.8 L/s over 25 m, or 3.4 L/s over 50 m, before pipe losses. Higher heads need less water and smaller turbines.
What efficiency should I use for a small hydro turbine?
Wikipedia gives turbine efficiency as generally 50 to 80% for micro hydro. The overall water-to-wire figure is lower, because the generator, controller and wiring also lose some energy. Use the manufacturer’s figure for your flow and head where available; 50 to 60% overall is a cautious starting point.
What is the difference between gross head and net head?
Gross head is the vertical drop from the intake water surface to the turbine. Net head is what remains after friction in the pipe. A narrow or long pipe can lose a large share, which is why this micro hydro calculator works out the loss from pipe size, length and roughness.
Is micro hydro better than solar panels?
On a good site a turbine runs day and night, so 2.46 kW at a 50% capacity factor makes about 10,800 kWh a year; at an example solar yield of 900 kWh per kWp, matching that needs about 12 kWp of panels. Few homes have a suitable stream, and hydro needs permits and civil works.
How do I measure the flow of a stream?
For small streams, time how long the full flow takes to fill a bucket of known volume at a point where it can all be caught, and divide litres by seconds. Repeat across seasons, because the design flow and capacity factor depend on how flow changes through the year.
Checked October 2026 by the Solaxyra Editorial Team. Sources: Wikipedia: Hydropower, Wikipedia: Micro hydro, Wikipedia: Darcy friction factor formulae, GOV.UK: New hydropower scheme, Energy Saving Trust: Hydroelectricity.