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Pump Calculator

This pump calculator returns hydraulic horsepower, brake horsepower at the pump shaft, required motor horsepower with service factor, and the next standard NEMA motor size. It uses the Hydraulic Institute formula HP = Q x H x SG / 3960 for any centrifugal or positive-displacement pump moving water, seawater, fuel, brine, or sludge. Use it to size a booster pump, pool pump, transfer pump, sump pump, or irrigation pump.

Pump Calculator Formula

The core equation from the Hydraulic Institute pump engineering handbook:

Hydraulic HP = Q x H x SG / 3960

Where:

  • Q = flow rate in gpm (US gallons per minute)
  • H = total dynamic head in feet
  • SG = specific gravity of the fluid (water = 1.00)
  • 3960 = conversion constant

Hydraulic HP is the theoretical power transferred to the fluid. Real pumps are 50-85% efficient, so you need more shaft power than the hydraulic HP.

From Hydraulic HP to Brake HP to Motor HP

Brake HP (BHP) = Hydraulic HP / pump efficiency

BHP is the shaft power the pump actually needs. A 10 HP hydraulic load on a 70% efficient pump needs 14.3 HP at the shaft.

Motor HP = Brake HP / service factor

NEMA standard service factor on open-drip-proof motors is 1.15, meaning the motor can run 15% over nameplate briefly. A 14.3 BHP load can use a 12.4 HP motor (14.3 / 1.15) but the next standard size is 15 HP.

Common Pump Efficiencies

Pump Type Typical Efficiency
End-suction centrifugal 65-80%
Multi-stage centrifugal 60-75%
Submersible well pump 55-70%
Sump pump (small residential) 40-55%
Pool circulation pump 60-70%
Positive displacement (gear, piston, diaphragm) 80-90%
Progressive cavity 70-80%

Lower efficiency means more brake HP for the same hydraulic output. Submersibles have lower efficiency because motor cooling losses and the confined geometry hurt performance.

Specific Gravity Adjustment

Specific gravity (SG) scales the horsepower proportionally. Seawater (SG 1.03) needs 3% more HP than freshwater. 30% solids sludge (SG 1.30) needs 30% more HP. Sulfuric acid 98% (SG 1.84) nearly doubles the required HP vs water.

Fluid SG
Water 1.00
Seawater 1.03
Brine (20% salt) 1.20
Milk 1.03
Diesel fuel 0.85
Gasoline 0.72
Sludge 30% solids 1.30
Sulfuric acid 98% 1.84

Total Dynamic Head

Total dynamic head (TDH) is the total "lift" work the pump must do:

  • Static lift = vertical height from source water level to discharge
  • Friction losses in the pipe (Hazen-Williams or Darcy-Weisbach)
  • Pressure head at the discharge (1 psi = 2.31 ft of water head)
  • Elevation change from start to end
  • Velocity head (usually small, often ignored)

Example: A pump moves 100 gpm from a lake 20 ft below grade to a tank 50 ft above grade, through 500 ft of 4-inch pipe, delivering 30 psi at the tank.

  • Static lift: 20 ft
  • Elevation rise: 50 ft
  • Friction loss at 100 gpm in 4" pipe: 1.5 ft per 100 ft x 5 = 7.5 ft
  • Pressure head: 30 psi x 2.31 = 69.3 ft
  • Total TDH = 146.8 ft

At 100 gpm and 147 ft TDH moving water at 70% pump efficiency: hydraulic HP = 100 x 147 / 3960 = 3.71 HP. BHP = 3.71 / 0.70 = 5.3 HP. With a 1.15 service factor (motor can run 15 percent above nameplate), required motor HP = 5.3 / 1.15 = 4.6. Standard motor: 5 HP (next NEMA size up from 4.6).

When to Oversize

  • High-viscosity fluid: add 20% to HP
  • Frequent startups: add 10-15%
  • Long pipe runs with valves and elbows: verify friction loss calculation
  • Future capacity: one size up if expansion is likely

When NOT to Oversize

  • Oversized pumps run "off the curve" at low efficiency, waste energy, and destroy seals and impellers via cavitation.
  • A 7.5 HP motor on a 3 HP pump load runs the motor at 40% load, poor efficiency (85% vs 92% at full load), and the larger contactor cycles more.
  • Right-size the pump first, then size the motor for that pump at the actual operating point.

Pump Calculator Examples

Pool pump: 50 gpm, 30 ft TDH, water, 65% efficiency = 0.38 hydraulic HP, 0.58 BHP. Standard: 3/4 HP single-speed or 1.5 HP variable-speed (VS pumps save 60-80% on energy).

Irrigation pump: 150 gpm, 80 ft TDH, water, 70% efficiency = 3.0 hydraulic HP, 4.3 BHP. Standard: 5 HP.

Transfer pump (diesel fuel): 100 gpm, 50 ft TDH, SG 0.85, 75% efficiency = 1.07 hydraulic HP, 1.43 BHP. Standard: 2 HP.

Municipal booster pump: 500 gpm, 120 ft TDH, water, 80% efficiency = 15.2 hydraulic HP, 19 BHP. Standard: 20 HP.

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