Pump Power Calculator with Steps - Hydraulic & Brake Power, Solved Examples

Flow Rate (Q) m³/h

Fluid Density (ρ) kg/m³

Total Head (H) m

Pump Efficiency (η) %

Brake (Shaft) Power — this is your motor sizing figure:

What is Pump Power?

Pump power is the rate of energy a pump must deliver to move a fluid against gravity (head) or pressure. There are two figures that matter:

Hydraulic power (Ph) — the actual work done on the fluid.
Brake (shaft) power (Pb) — the mechanical power the motor must supply, always higher than hydraulic power because no pump is 100% efficient. This is the number to use when selecting a motor.

Pb = Ph / η

Formulas Used

Mode	Hydraulic Power Formula
Using head (H)	Ph (kW) = (ρ × g × Q × H) / 3,600,000
Using pressure rise (ΔP)	Ph (kW) = (Q × ΔP) / 3600

where ρ is density (kg/m³), g = 9.81 m/s², Q is flow rate (m³/h), H is total head (m), and ΔP is pressure rise (kPa).

Why It Matters

Undersizing the motor against brake power (not hydraulic power) is a common beginner mistake — the motor must be rated for the higher brake power figure, with a safety margin, or it will overload and trip under real operating conditions.

Solved Examples (Practice Problems)

Click "Try This Example" to auto-fill the calculator above and see the full step-by-step working.

Example 1 — Water pump, using head

A centrifugal pump moves water (ρ = 1000 kg/m³) at 50 m³/h against a total head of 30 m, at 75% efficiency. Find the hydraulic and brake power.

Example 2 — Pump sized from a pressure rise

A pump must deliver 20 m³/h of fluid with a pressure rise of 250 kPa across it, at 70% efficiency. Find the hydraulic and brake power.

Example 3 — Viscous oil, using head

An oil transfer pump moves oil (ρ = 850 kg/m³) at 200 m³/h against a total head of 80 m, at 68% efficiency. Find the hydraulic and brake power.

Worked Solutions in Full

Each example is solved completely, and then taken one step further to a motor size, since that is the reason for doing the calculation.

Example 1 — Water pump, head known

Given: Q = 50 m³/h, ρ = 1000 kg/m³, H = 30 m, η = 75%

Step 1 — Hydraulic power formula: P_h (kW) = ρ × g × Q × H / 3,600,000, with Q in m³/h

Step 2 — Multiply the top line: 1000 × 9.81 × 50 × 30 = 14,715,000

Step 3 — Divide: 14,715,000 / 3,600,000 = 4.088 kW

Step 4 — Brake power: P_b = P_h / η = 4.088 / 0.75 = 5.450 kW

Step 5 — Motor selection: With a 15% margin, 5.45 × 1.15 = 6.27 kW, so the next standard motor is 7.5 kW.

Answer: Hydraulic power 4.09 kW, brake power 5.45 kW, choose a 7.5 kW motor.

Example 2 — Pressure rise known

Given: Q = 20 m³/h, ΔP = 250 kPa, η = 70%

Step 1 — Hydraulic power formula: P_h (kW) = Q × ΔP / 3600, with Q in m³/h and ΔP in kPa

Step 2 — Substitute: 20 × 250 / 3600 = 1.389 kW

Step 3 — Brake power: 1.389 / 0.70 = 1.984 kW

Step 4 — Motor selection: 1.98 × 1.15 = 2.28 kW, so choose 3 kW.

Answer: Hydraulic power 1.39 kW, brake power 1.98 kW, choose a 3 kW motor.

Example 3 — Oil pump, head known

Given: Q = 200 m³/h, ρ = 850 kg/m³, H = 80 m, η = 68%

Step 1 — Multiply the top line: 850 × 9.81 × 200 × 80 = 133,416,000

Step 2 — Hydraulic power: 133,416,000 / 3,600,000 = 37.060 kW

Step 3 — Brake power: 37.060 / 0.68 = 54.500 kW

Step 4 — Motor selection: 54.50 × 1.15 = 62.67 kW, so choose 75 kW.

Answer: Hydraulic power 37.06 kW, brake power 54.50 kW, choose a 75 kW motor.

Motor sizes above follow the common IEC rating series. A 15% margin is a typical rule of thumb, not a universal rule: check your project standard and the pump manufacturer's power curve.

Practical Notes and Common Mistakes

Pump duty comes from the process: the flow you need, and the total head the system demands (static lift, pressure difference and pipe friction). Get the friction part from the Friction Factor Calculator, and check the suction side is safe with the NPSH Calculator before you settle on a pump.

Mistakes that give wrong answers

Sizing the motor from hydraulic power. The motor must supply brake power, which is higher.
Forgetting density. Head-based power scales directly with density, so an oil or brine pump is not sized like a water pump.
Confusing pump and overall efficiency. The η here is the pump efficiency. Motor and drive losses are extra and make the electrical input larger still.
Wrong flow units. The formulas here take Q in m³/h. Using m³/s or L/min without converting gives a wildly wrong answer.
Leaving out friction. Static lift alone understates the head; pipe friction and fittings usually add a large share.
Ignoring the operating range. A pump can run at a different flow than its design point. Check power at the highest flow it may see.

Frequently Asked Questions

What's the difference between hydraulic power and brake power?

Hydraulic power is the useful work actually delivered to the fluid. Brake power is the mechanical power the pump shaft — and therefore the motor — must supply, which is always higher because of internal losses (friction, slip, recirculation). Motor sizing must always be based on brake power, not hydraulic power.

What's a typical pump efficiency?

Most centrifugal pumps operating near their best efficiency point fall between 60% and 85%, depending on size, design, and how close the operating point is to the pump's design flow. Small pumps and pumps running far from their design point trend toward the lower end.

Why does fluid density matter so much for pump power?

Power scales directly with density — pumping a denser fluid (like most oils vs. water) at the same flow rate and head requires proportionally more power. This is why the same pump curve can't be used across fluids without correcting for density.

Should I add a safety margin to the calculated brake power?

Yes — it's common practice to size the motor 10-20% above the calculated brake power to account for operating point variation, future capacity, and avoiding the motor running at its absolute limit continuously.

Related Tool

Before trusting this power figure, check whether your pump will actually get the flow it needs with the NPSH Calculator — confirms your suction side won't cavitate.