# Pump Horsepower Calculator

URL: https://speedycalculator.com/calculators/physics/pump-horsepower/
Last updated: 2026-10-30

> The pump horsepower calculator finds the hydraulic (water) power, the shaft (brake) power and the specific speed of a pump from the flow rate, head, fluid density and efficiency.

## Inputs

- Flow rate Q (m³/h, L/s, L/min, US gpm, m³/s)
- Total head H (m, cm, mm, km, in, ft, yd, mi)
- Fluid density ρ (kg/m³, g/cm³, g/mL, lb/ft³, lb/in³)
- Pump efficiency (%)
- Pump speed (rpm)
- Gravitational acceleration (m/s², ft/s², g, cm/s²)

## Results

- Hydraulic power
- Shaft (brake) power
- Specific speed (US units)
- Impeller type

## Formula

```
P_h = ρ·g·Q·H,  P_shaft = P_h / η,  N_s = N·√Q / H^{3/4} (US: rpm, gpm, ft)
```

## Explanation

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

FieldWhat to enterFlow rate QUnits: m³/h, L/s, L/min, US gpm, m³/sTotal head HUnits: m, cm, mm, km, in, ft …Fluid density ρUnits: kg/m³, g/cm³, g/mL, lb/ft³, lb/in³Pump efficiency (%)A numberPump speed (rpm)A numberGravitational accelerationUnits: 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)101,165.1234151,747.6851202,330.2468252,912.8085303,495.3703404,660.4937

## 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.

## FAQ

**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.


## Sources

- [The Engineering ToolBox](https://www.engineeringtoolbox.com/)
- [Hydraulic Institute](https://www.pumps.org/)