What Is Brake Horsepower?
Brake horsepower (BHP) is the actual mechanical power delivered at a rotating shaft — originally measured with a friction device called a Prony brake, hence the name. For pumps, it answers a very practical question: how much power must the motor supply to move this fluid at this flow and pressure, given that the pump wastes some energy along the way?
That last part is what makes BHP worth calculating. Moving fluid takes a certain amount of ideal, textbook power — but real pumps lose energy to friction, turbulence and internal leakage. An undersized motor will struggle, overheat and trip out; an oversized one costs more to buy and runs inefficiently. Calculating BHP lets you match the motor to the job with confidence.
The Brake Horsepower Formula
For flow in US gallons per minute and head in feet, the standard formula is:
[
\text{BHP} = \frac{Q \times H \times SG}{3960 \times \eta}
]
Where:
- Q is the flow rate in gallons per minute (gpm)
- H is the total dynamic head in feet (ft) — the effective height the pump lifts the fluid once pipe friction is included
- SG is the specific gravity of the fluid (dimensionless; water is 1.0)
- η is the pump efficiency as a decimal (for example, 0.75 for 75 percent)
The constant 3,960 quietly converts the units into horsepower: one horsepower is 33,000 ft·lb/min and a US gallon of water weighs about 8.34 lb, so 33,000 ÷ 8.34 ≈ 3,960.
A handy intermediate quantity is the water horsepower (WHP) — the same formula without the efficiency term:
[
\text{WHP} = \frac{Q \times H \times SG}{3960}
]
Water horsepower is the ideal power reaching the fluid; brake horsepower is what you pay for. Dividing WHP by efficiency gives BHP, so a less efficient pump simply demands more shaft power for exactly the same job.
Worked Example: Sizing a Pump Motor
A centrifugal pump operates under these conditions:
- Flow rate: 500 gpm
- Total dynamic head: 150 ft
- Specific gravity: 1.1
- Pump efficiency: 75%
Start from the formula:
[
\text{BHP} = \frac{Q \times H \times SG}{3960 \times \eta} = \frac{500 \times 150 \times 1.1}{3960 \times 0.75}
]
Work out the numerator step by step:
[
500 \times 150 = 75{,}000
]
[
75{,}000 \times 1.1 = 82{,}500
]
And the denominator:
[
3960 \times 0.75 = 2970
]
Divide:
[
\text{BHP} = \frac{82{,}500}{2970} \approx 27.78 \text{ HP}
]
So the motor must deliver about 27.78 horsepower (roughly 20.7 kW). Notice the water horsepower here is 82,500 ÷ 3960 ≈ 20.83 WHP — the extra 6.95 HP exists purely to overcome losses inside the pump. Applying a typical 15 percent safety margin, you would select a standard 32–40 HP motor rather than a 30 HP one running flat-out all day.
Working in Metric Units
The 3,960 constant assumes gpm and feet. If your data is metric, convert first, then apply the same formula — exactly what the calculator does internally:
| Quantity | Multiply by |
|---|---|
| Litres per minute → gpm | 0.264172 |
| Metres → feet | 3.28084 |
Take the same pump expressed in metric units:
- Flow rate: 1,800 L/min → 1800 × 0.264172 = 475.51 gpm
- Total dynamic head: 45 m → 45 × 3.28084 = 147.64 ft
- Specific gravity: 1.1, Efficiency: 75%
Substituting into the formula:
[
\text{BHP} = \frac{475.51 \times 147.64 \times 1.1}{3960 \times 0.75} = \frac{77{,}224}{2970} \approx 26.0 \text{ HP}
]
Both routes — entering metric values straight into the calculator, or converting by hand first — land on the same answer because the calculator performs these identical conversions behind the scenes.
Typical Pump Efficiencies
If you don't have a manufacturer's curve handy, these ranges are useful ballparks for estimating:
| Pump type | Typical efficiency |
|---|---|
| Small centrifugal (< 5 HP) | 50–65% |
| Large centrifugal (well-matched duty point) | 75–88% |
| Positive displacement | 80–90% |
| Slurry or abrasive-service pumps (worn) | 50–70% |
Remember that efficiency depends on where on its curve the pump runs. A pump operated well away from its best efficiency point (BEP) can be dramatically worse than its nameplate figure, and wear pushes efficiency down further over the years — which quietly raises the true BHP long before anything visibly breaks.
Quick Recap
- BHP = (Q × H × SG) ÷ (3960 × η), with Q in gpm, H in ft, η as a decimal.
- Water horsepower drops the η term — it's the ideal power the fluid receives; the rest is lost inside the pump.
- Metric inputs? Convert L/min → gpm (× 0.264172) and m → ft (× 3.28084) first.
- Add a 10–25 percent service margin when choosing the motor nameplate rating.
Once you've sized the pump side, the RPM to horsepower calculator shows how shaft speed and torque connect to the horsepower figure you've just computed.