Enter any 2 values (net head, water flow rate, or power), select units, then calculate the missing value.

Water Wheel Power Calculator

Enter any 2 values to calculate the missing value (assumes water density ≈ 1.0 kg/L and 100% efficiency).

Related Calculators

Water Wheel Power Formula

The water wheel power calculator estimates the theoretical hydraulic power available from flowing water using the site’s net head and flow rate. This is the energy carried by the water before wheel losses, bearing friction, drivetrain losses, and generator inefficiency are applied.

P_{ww}=\rho 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}\approx9810QH

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}\approx9.81QH

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

If you know the power and one site variable, the same relationship can be rearranged to solve for the missing value:

H=\frac{P}{\rho g Q}
Q=\frac{P}{\rho 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.

H_{net}=H_{gross}-h_{loss}

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

This calculator assumes ideal conditions, so its result is best treated as an upper-bound hydraulic value. Real wheel output is lower because no water wheel system is 100% efficient.

P_{actual}=\eta\rho 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

  1. Measure or estimate the net head at the wheel location.
  2. Measure the available water flow rate during the operating condition you care about.
  3. Enter any two known values: head, flow, or power.
  4. Select the correct units for each field.
  5. Calculate the missing value.
  6. If you need realistic delivered output, multiply the theoretical result by an estimated overall efficiency.

Because stream flow often changes by season, it is smart to test both peak-flow and low-flow conditions when evaluating a site.

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:

P_{ww}=9.81\times100\times3=2943\text{ W}

That is approximately 2.94 kW of theoretical power available in the water.

Example 2

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

P_{ww}=9.81\times140\times5=6867\text{ W}

To convert watts to horsepower:

HP=\frac{P}{745.7}
HP=\frac{6867}{745.7}\approx9.21

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. Overshot, breastshot, and undershot wheels may use the water differently, but the hydraulic power relationship above still defines the site’s theoretical upper limit.