Hydraulic Turbine Power Calculator

Calculate turbine shaft power from fluid density, flow rate, net head, gravity, and efficiency.

Pt = ρgQHη

Density ρ (kg/m³)

Gravity g (m/s²)

Flow rate Q (m³/s)

Net head H (m)

Turbine efficiency (%)

Enter valid values in all required fields.

What this formula means

A hydraulic turbine converts the potential and pressure energy represented by net head into shaft power. Efficiency accounts for hydraulic, mechanical, leakage, and other losses between the water and the shaft.

Use this equation for hydroelectric plants, water turbines, energy recovery devices, and preliminary turbine sizing. The result should be interpreted with consistent units and with the assumptions of the underlying model in mind.

Worked example

Water flowing at 2 m³/s through 50 m net head at 90% efficiency produces about 883 kW.

Applications

Use this equation for hydroelectric plants, water turbines, energy recovery devices, and preliminary turbine sizing. It is also useful as an independent check when comparing hand calculations, laboratory measurements, simulations, or preliminary engineering estimates.

Assumptions and common mistakes

Important: Use net head at the turbine, not gross elevation difference, and enter efficiency as a realistic value between zero and 100 percent.

Use SI units unless the field label states otherwise. Keep significant figures appropriate to the accuracy of the inputs, and do not treat a simplified calculator as a replacement for codes, detailed design standards, or professional review.

Frequently asked questions

What equation does this calculator use?Pt = ρgQHη. The calculator evaluates the displayed relationship using the values entered above.

Are the results unit-sensitive?Yes. The input labels use SI units so the displayed output follows the corresponding SI unit.

Can I use this for engineering design?Use it for learning and preliminary checks. Final designs require validated data, applicable standards, safety factors, and professional judgment.