Water Wheel Power Calculator (Head, Flow & Output)

Calculate how much power a water wheel can produce from flow and head with typical wheel efficiencies, plus annual energy, or solve for flow or head.

Solve for

Use net head after conveyance losses and your estimated efficiency of the remaining conversion stages.

Water flow reaching the wheel

Net head

Wheel type (typical efficiency)

Typical shaft efficiencies. Choose Custom to include generator losses or use your own figure.

Result unit and planning assumptions

Power result unit

Water density (kg/m³)

Default 1,000 kg/m³ (fresh water); blank uses 1,000.

Operating hours per day

Default 24 h/day. Enter 0 for no operation.

Operating days per year

Default 365 days at the calculated output; not a seasonal flow model.

Low-flow rate as % of entered flow

Default 50%, with head and efficiency unchanged.

Related Calculators

Water Wheel Power Formula

The calculator reports delivered power using net head, flow and your entered conversion efficiency. It also shows hydraulic power at the net head before those conversion losses. The equations below first describe that hydraulic reference, then its efficiency adjustment. Gravity is approximated as9.81 m/s² and the editable density default is1000 kg/m³.

P ww = ρ g Q H

For fresh water, the density is usually taken as approximately 1000 kg/m³. In standard SI units, the equation is commonly written as:

P ww \approx 9810QH

In that form, Q is in m³/s and H is in meters. If flow is entered in liters per second, the formula becomes:

P ww \approx 9.81QH

In this simplified form, Q is in L/s, H is in meters, and the result is in watts.

Input or Output	Meaning	Common Units
Water wheel power	Theoretical power available from the water	W, HP
Net head	Usable vertical drop after subtracting losses	m, ft, cm, in
Flow rate	Volume of water reaching the wheel each second	L/s, GPM, m³/h
Water density	Usually treated as fresh water for site estimates	about 1000 kg/m³

Rearranged Forms

The following rearrangements use hydraulic power P. In the interface, target power is delivered power, so the flow and head denominators also include your efficiency fraction η:

H = (P) / (ρ g Q)

Q = (P) / (ρ g H)

This is useful when you want to determine how much flow is required to reach a target power level, or how much head is needed at a given flow.

What Net Head Means

Net head is not the same as gross elevation drop. Gross head is the total vertical difference between the water source and wheel. Net head is the portion that remains after accounting for losses in channels, pipes, gates, screens, and other conveyance components.

Hₙₑₜ = H gross - hₗₒₛₛ

Using gross head instead of net head will overestimate power. For realistic results, always use the head available at the wheel.

Actual Output vs. Theoretical Power

The primary result includes your entered efficiency; do not multiply it by efficiency again. The separate hydraulic result is the ideal reference at the stated net head. Use remaining wheel, drivetrain and generator losses consistently, avoiding double counting any conveyance loss already subtracted from net head.

P actual = etaρ g Q H

Here, η is the overall efficiency of the system. That efficiency may include hydraulic capture losses, wheel efficiency, bearing losses, gearing or belt losses, and generator efficiency if electrical output is being estimated.

Loss Area	Why It Matters
Intake and channel losses	Reduce the effective head or flow reaching the wheel
Wheel inefficiency	Not all water energy is converted into shaft power
Mechanical friction	Bearings, shafts, and drivetrains consume part of the power
Electrical conversion losses	Generators and power electronics further reduce output

How to Use the Calculator

Measure or estimate the net head at the wheel location.
Measure the available water flow rate during the operating condition you care about.
Choose power, flow or head to solve for and enter the two known quantities plus overall conversion efficiency.
Select the correct units for each field.
Calculate the missing value.
Open the optional settings to choose the result unit or adjust density, operating hours, annual days and the low-flow scenario. Defaults are1000 kg/m³,24 h/day,365 days/year and50% flow.

Annual energy equals delivered kW × entered hours/day × entered operating days, assuming constant output. Low-flow and125% flow scenarios hold head and efficiency fixed and do not change annual energy or account for capacity limits. Actual seasonal estimates require flow-duration and equipment-performance data.

Example 1

If a site has a net head of 3 m and a flow rate of 100 L/s, the theoretical hydraulic power is:

Pww =9.81 \times100 \times3 =2943 W

That is approximately 2.94 kW of hydraulic power. Entering70% conversion efficiency gives2.0601 kW delivered,49.4424 kWh/day at24 hours and18,046.476 kWh/year at365 such days.

Example 2

If the net head is 5 m and the flow rate is 140 L/s, then:

Pww =9.81 \times140 \times5 =6867 W

To convert watts to horsepower:

HP = (P) / (745.7)

HP = (6867) / (745.7) \approx 9.21

This corresponds to about 6.87 kW or 9.21 HP of theoretical hydraulic power.

Useful Unit Notes

1 kW = 1000 W
1 HP = 745.7 W
1 m³/s = 1000 L/s
1 m³/h = 0.2778 L/s
1 ft = 0.3048 m

Practical Design Notes

Power increases linearly with both head and flow, so doubling either one doubles the theoretical power available.

P\propto QH

That means a small change in available head or a seasonal reduction in flow can have a direct and noticeable effect on output. In general, low-head systems need more flow to reach the same power level, while higher-head sites can produce meaningful power with less water. This head-based model applies when a usable hydraulic head is defined. It does not estimate free-stream wheel power from current velocity; DOE distinguishes kinetic turbines from head-based systems.