03 // Bidirectional STEM Calculators // ENGINEERINGP = (ρ × 9.80665 × Q × H) / (η / 100)

Pump Shaft & Hydraulic Power Calculator

Centrifugal pump shaft brake power P equals the hydraulic fluid power (ρ × g × Q × H) divided by overall pump mechanical-hydraulic efficiency η.

P = (ρ × 9.80665 × Q × H) / (η / 100)

Pick which value you want to calculate (or type into any field):Solving for: P_shaft — Required Shaft Power

Required Shaft PowerCalculated

Brake power required at the pump shaft in Watts (switch to kW or hp)

105,000,000.00

Volumetric Flow Rate

Flow rate in m³/s (switch inline unit for L/s, L/min, or GPM)

0.000150

Total Dynamic Head (TDH)

Static lift plus friction head loss in meters

0.51,000.00

Fluid Density

Pumped liquid density in kg/m³ (Water = 1000)

5005,000.00

unit

Pump Efficiency

Best Efficiency Point (BEP) hydraulic efficiency in percent

1096

Calculated Result · Required Shaft Power (P_shaft)

16,344.42W

Converted units:

Step-by-Step Calculation

01Canonical Law: P = (ρ × 9.80665 × Q × H) / (η / 100)

02Given Inputs (Base Units): Q = 0.05 m³/s, H = 25 m, ρ (kg/m³) = 1,000, η (%) = 75

03Solve for P_shaft (Required Shaft Power): P_shaft = 16,344.42 W

Centrifugal pump shaft brake power P equals the hydraulic fluid power (ρ × g × Q × H) divided by overall pump mechanical-hydraulic efficiency η.

End-Suction Industrial Centrifugalη = 72% – 84% @ BEP

Standard ANSI / ISO process water pump

Small Fractional-HP Circulatorη = 45% – 62%

Hydronic heating loop pump

Pump Affinity Law (Power)P₂ / P₁ = (N₂ / N₁)³

VFD speed reduction to 80% cuts shaft power to 51.2%

Required Shaft Power (P_shaft) · Volumetric Flow Rate (Q)

Compare across:

Pump Shaft & Hydraulic Power Calculator — Volumetric Flow Rate → Required Shaft Power
#	Volumetric Flow Rate (m³/s)	Required Shaft Power (W)	Δ %
01	0.05 m³/sCurrent	16,344.42 W	0.00%
02	0.364568 m³/s	119,172.93 W	+629.14%
03	0.729035 m³/s	238,313.17 W	+1358.07%
04	1.0935 m³/s	357,453.40 W	+2087.01%
05	1.458 m³/s	476,593.64 W	+2815.94%
06	1.8224 m³/s	595,733.88 W	+3544.88%
07	2.1869 m³/s	714,874.12 W	+4273.81%
08	2.5514 m³/s	834,014.36 W	+5002.75%
09	2.9158 m³/s	953,154.59 W	+5731.68%
10	3.2803 m³/s	1,072,294.83 W	+6460.62%
11	3.6448 m³/s	1,191,435.07 W	+7189.55%
12	4.0092 m³/s	1,310,575.31 W	+7918.49%
13	4.3737 m³/s	1,429,715.55 W	+8647.42%
14	4.7382 m³/s	1,548,855.78 W	+9376.36%
15	5.1026 m³/s	1,667,996.02 W	+10105.30%
16	5.4671 m³/s	1,787,136.26 W	+10834.23%
17	5.8316 m³/s	1,906,276.50 W	+11563.17%
18	6.1961 m³/s	2,025,416.74 W	+12292.10%
19	6.5605 m³/s	2,144,556.98 W	+13021.04%
20	6.925 m³/s	2,263,697.21 W	+13749.97%

Was this tool helpful?

How do I read required pump power directly in Horsepower (hp) or Kilowatts (kW)?+

Use the inline unit selector on P_shaft to switch from Watts (W) to Kilowatts (kW) or Horsepower (hp).

How do I find pure Hydraulic Water Power?+

Set Pump Efficiency η (%) to 100% to display the exact hydraulic power transferred into the fluid stream.

Does motor VFD efficiency need to be included?+

P_shaft is mechanical power at the pump coupling. Divide P_shaft by electric motor efficiency (~92%–96%) to obtain electrical grid kW.