How do you calculate hydropower output?

Power is P = η·ρ·g·Q·H, where ρ is water density (1000 kg/m³), g = 9.81 m/s², Q is the flow in m³/s, H is the net head in metres and η is the combined turbine and generator efficiency: over 90% for large units, about 60–80% for small ones. A handy rule: each 1 m³/s falling 1 m gives about 9.8 kW of hydraulic power. A stream of 20 L/s with a 15 m drop gives roughly 1.5–2 kW after losses, more than 10,000 kWh a year.

How do you choose between Pelton, Francis and Kaplan turbines?

Mainly by head and flow. High head (hundreds to over a thousand metres) and small flow suit a Pelton wheel, where nozzles turn pressure into fast jets hitting buckets. Medium heads (about 20–700 m) suit Francis turbines, used at Three Gorges, Baihetan and Itaipu. Low head and large flow (2–70 m) suit axial machines, and a Kaplan can adjust its blade angle to stay efficient at part load. Crossflow turbines are simple and common in small schemes. The chart shows typical teaching ranges; real selection also uses specific speed and manufacturer data.

Why is there an economic penstock diameter?

A thinner pipe is cheaper, but the velocity rises and friction loss h_f = f·(L/D)·v²/2g grows fast (roughly as 1/D⁵), wasting head and energy. A thicker pipe loses less but costs more steel and construction. Converting the pipe cost into an annual payment using the interest rate and lifetime, and adding the yearly value of lost energy, the total annual cost has a minimum at some diameter. Large plants typically end up at 3–6 m/s; micro-hydro schemes usually keep losses under 10–15% of gross head.

What is a flow duration curve, and why are hydro capacity factors modest?

Sort a year of daily river flows from high to low and plot them against the share of time each flow is exceeded: that is the flow duration curve. A plant is built for a design flow Q_d: in the wet season the flow above Q_d is spilled, and in the dry season the turbine must stop below its minimum flow. A larger design flow captures more energy but leaves the machines part-loaded most of the year, lowering the capacity factor. That is why hydro usually runs at 40–50%; the steady Paraná at Itaipu reaches over 70%.

How much energy can pumped storage hold, and how efficient is it?

Stored energy is E = ρ·g·V·H·η. Lifting one tonne of water 100 m stores only about 0.27 kWh, so plants need millions of cubic metres and heads of hundreds of metres; 10 million m³ with 400 m of head gives about 10 GWh. Pumping and generating are each about 90% efficient, and with other losses the round trip is about 75–80%, below lithium-ion's ~90%. But plants last 50–100 years and reach several GW, and pumped hydro is still by far the largest form of grid storage.

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💧Hydropower Calculator - Turbine Selection, Penstock Loss, Pumped Storage, Dam

Enter flow and head to get the power and annual energy of a hydro plant, and see on a selection chart where Pelton, Francis and axial turbines fit best. The other pages work out penstock friction loss and the cheapest pipe diameter, annual energy and capacity factor from a river's flow duration curve, how much energy a pumped-storage plant holds, and the water force on a dam with its overturning and sliding safety factors.

Free · No sign-up · Runs in your browserLast updated: 2026-10-29

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How to use Hydropower calculator

1In Power & turbines, enter flow Q and head H (or use presets such as home micro-hydro or one Three Gorges unit) to see power, annual energy and suitable turbines
2In Penstock, set diameter, length and material to see the net head, and find the economic diameter from steel and electricity prices
3In Annual energy, set the mean flow, variability and design flow to see the duration curve, capacity factor and best design flow
4In Pumped storage, enter reservoir volume and head and compare with batteries and other storage
5In Dam pressure and Famous plants, see the pressure distribution, safety factors and data for Three Gorges, Baihetan and Itaipu

FAQ

How do you calculate hydropower output?: Power is P = η·ρ·g·Q·H, where ρ is water density (1000 kg/m³), g = 9.81 m/s², Q is the flow in m³/s, H is the net head in metres and η is the combined turbine and generator efficiency: over 90% for large units, about 60–80% for small ones. A handy rule: each 1 m³/s falling 1 m gives about 9.8 kW of hydraulic power. A stream of 20 L/s with a 15 m drop gives roughly 1.5–2 kW after losses, more than 10,000 kWh a year.
How do you choose between Pelton, Francis and Kaplan turbines?: Mainly by head and flow. High head (hundreds to over a thousand metres) and small flow suit a Pelton wheel, where nozzles turn pressure into fast jets hitting buckets. Medium heads (about 20–700 m) suit Francis turbines, used at Three Gorges, Baihetan and Itaipu. Low head and large flow (2–70 m) suit axial machines, and a Kaplan can adjust its blade angle to stay efficient at part load. Crossflow turbines are simple and common in small schemes. The chart shows typical teaching ranges; real selection also uses specific speed and manufacturer data.
Why is there an economic penstock diameter?: A thinner pipe is cheaper, but the velocity rises and friction loss h_f = f·(L/D)·v²/2g grows fast (roughly as 1/D⁵), wasting head and energy. A thicker pipe loses less but costs more steel and construction. Converting the pipe cost into an annual payment using the interest rate and lifetime, and adding the yearly value of lost energy, the total annual cost has a minimum at some diameter. Large plants typically end up at 3–6 m/s; micro-hydro schemes usually keep losses under 10–15% of gross head.
What is a flow duration curve, and why are hydro capacity factors modest?: Sort a year of daily river flows from high to low and plot them against the share of time each flow is exceeded: that is the flow duration curve. A plant is built for a design flow Q_d: in the wet season the flow above Q_d is spilled, and in the dry season the turbine must stop below its minimum flow. A larger design flow captures more energy but leaves the machines part-loaded most of the year, lowering the capacity factor. That is why hydro usually runs at 40–50%; the steady Paraná at Itaipu reaches over 70%.
How much energy can pumped storage hold, and how efficient is it?: Stored energy is E = ρ·g·V·H·η. Lifting one tonne of water 100 m stores only about 0.27 kWh, so plants need millions of cubic metres and heads of hundreds of metres; 10 million m³ with 400 m of head gives about 10 GWh. Pumping and generating are each about 90% efficient, and with other losses the round trip is about 75–80%, below lithium-ion's ~90%. But plants last 50–100 years and reach several GW, and pumped hydro is still by far the largest form of grid storage.

Features

P = ηρgQH power and annual energy with an animated reservoir–penstock–turbine scene
Selection chart and efficiency curves for Pelton, Francis, Kaplan, crossflow and propeller turbines
Darcy–Weisbach with Swamee–Jain friction and the diameter with the lowest annual cost
Annual energy, capacity factor and running time from a log-normal flow duration curve
Pumped-storage energy, round-trip efficiency and comparison with batteries
Gravity-dam pressure triangle, overturning moment and overturning/sliding safety factors

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