Every pump must lift a flow of liquid against a head. The power it gives the fluid is ρgQH; the motor must supply more to cover losses. Specific speed classifies impellers – radial, mixed or axial flow.
How to use the Pump Horsepower Calculator
- Flow rate Q
- Total head H
- Fluid density ρ
- Pump efficiency (%)
- Pump speed (rpm)
- Gravitational acceleration
Results update as you type, every field has its own unit menu, and everything is calculated in your browser.
How it works
Enter the flow, total head, fluid density, efficiency and pump speed.
Inputs explained
| Field | What to enter |
|---|---|
| Flow rate Q | Units: m³/h, L/s, L/min, US gpm, m³/s |
| Total head H | Units: m, cm, mm, km, in, ft … |
| Fluid density ρ | Units: kg/m³, g/cm³, g/mL, lb/ft³, lb/in³ |
| Pump efficiency (%) | A number |
| Pump speed (rpm) | A number |
| Gravitational acceleration | Units: m/s², ft/s², g, cm/s² |
What each result means
- Hydraulic power = [Fluid density ρ]×[Gravitational acceleration]×[Flow rate Q]×[Total head H]
- Shaft (brake) power = [Fluid density ρ]×[Gravitational acceleration]×[Flow rate Q]×[Total head H]÷([Pump efficiency (%)]÷100)
- Specific speed (US units) = [Pump speed (rpm)]×sqrt([Flow rate Q]÷6.30901964e-5)÷([Total head H]÷0.3048)^0.75
Example values
How the main result changes when Flow rate Q changes and everything else stays at the example values above:
| Flow rate Q (m³/h) | Shaft (brake) power (W) |
|---|---|
| 10 | 1,165.1234 |
| 15 | 1,747.6851 |
| 20 | 2,330.2468 |
| 25 | 2,912.8085 |
| 30 | 3,495.3703 |
| 40 | 4,660.4937 |
Formula
P_h = ρ·g·Q·H, P_shaft = P_h / η, N_s = N·√Q / H^{3/4} (US: rpm, gpm, ft)
Worked example
Inputs — Flow rate Q: 20 m³/h; Total head H: 30 m; Fluid density ρ: 998 kg/m³; Pump efficiency (%): 70; Pump speed (rpm): 2,900; Gravitational acceleration: 9.80665 m/s².
Results — Hydraulic power = 1,631.1728 W; Shaft (brake) power = 2,330.2468 W; Specific speed (US units) = 871; Impeller type = Radial flow.
Key terms
- Head
- Energy per unit weight of fluid, in metres.
Frequently asked questions
What is the difference between hydraulic and brake power?
Brake power includes pump losses.
What efficiency should I assume?
50–85% depending on size and type.
What is total head?
Static lift plus friction and pressure differences, in metres of fluid.
Do I need to oversize the motor?
Usually by 10–25% over shaft power.