Foot pounds-force minute to Horsepower (Water)
ft·lbf/min
hp
Conversion History
| Conversion | Reuse | Delete |
|---|---|---|
| No conversion history to show. | ||
Quick Reference Table (Foot pounds-force minute to Horsepower (Water))
| Foot pounds-force minute (ft·lbf/min) | Horsepower (Water) (hp) |
|---|---|
| 100 | 0.00302890929954234541 |
| 1,000 | 0.03028909299542345414 |
| 5,000 | 0.15144546497711727072 |
| 10,000 | 0.30289092995423454144 |
| 33,000 | 0.99954006884897398675 |
| 100,000 | 3.02890929954234541441 |
| 330,000 | 9.99540068848973986754 |
About Foot pounds-force minute (ft·lbf/min)
Foot pounds-force per minute (ft·lbf/min) equals approximately 0.02260 watts. It is used in US mechanical engineering for low-power applications and in the historical definition of horsepower: one horsepower was defined by James Watt as 33,000 ft·lbf/min — the rate at which a horse could lift coal from a mine. This unit is now mostly encountered in legacy engineering references and historical machinery specifications.
One mechanical horsepower = 33,000 ft·lbf/min. A hand-cranked generator might produce 2,000–5,000 ft·lbf/min of mechanical power output.
About Horsepower (Water) (hp)
Water horsepower (hp(W)) equals 746.043 watts and is used specifically in pump engineering to express the hydraulic power delivered to a fluid, as distinct from the shaft power input to the pump. It accounts for the fact that a pump's mechanical input power always exceeds the hydraulic power delivered due to efficiency losses. Pump efficiency is calculated as water hp divided by input shaft hp. The difference between water hp and electric/mechanical hp is negligible (0.05%) for most calculations.
A pump delivering 100 gallons per minute at 50 feet of head produces approximately 1.26 water hp of hydraulic power. A pump rated at 2 shaft hp may deliver 1.6 water hp at 80% efficiency.
Foot pounds-force minute – Frequently Asked Questions
Where does the number 3,960 come from in US pump sizing formulas?
The pump horsepower formula HP = (GPM × Head in ft) / 3,960 hides a chain of unit conversions. Water weighs 8.33 lb per US gallon. Multiplying GPM × Head × 8.33 gives ft·lbf/min. Dividing by 33,000 ft·lbf/min per hp gives horsepower. So 33,000 ÷ 8.33 ≈ 3,960. The number is so ubiquitous in US mechanical engineering that pump designers recognize it on sight, yet few remember the derivation. It breaks down for fluids other than water — multiply by specific gravity for anything denser or lighter.
What real-world tasks produce 33,000 ft·lbf/min?
Lifting 330 lbs (150 kg) at 100 feet per minute — roughly the speed of a slow freight elevator. Or lifting 33 lbs at 1,000 ft/min (a fast dumbwaiter). A human on a bicycle sustainably produces about 5,000–10,000 ft·lbf/min (0.15–0.3 hp). A small outboard boat motor produces about 165,000 ft·lbf/min (5 hp). The unit makes intuitive sense for lifting and hoisting — the original application Watt cared about.
Why use ft·lbf/min instead of ft·lbf/s?
Historical convention and practical timescale. Mine hoists, waterwheels, and early steam engines operated at rates naturally measured per minute — the machinery completed one cycle every few seconds to minutes. Watt himself measured horses per minute because that's how mine work was timed. The per-minute unit also gives larger, more manageable numbers: "33,000 ft·lbf/min" is easier to work with than "550 ft·lbf/s" when you're doing longhand arithmetic in 1780.
How much ft·lbf/min can a human sustain?
A healthy adult can sustain about 4,000–6,000 ft·lbf/min (roughly 90–135 W or 0.12–0.18 hp) of useful mechanical work for hours — think steady cycling or rowing. Short bursts reach 15,000–25,000 ft·lbf/min (0.5–0.75 hp). Elite cyclists sustain 12,000+ ft·lbf/min (0.4 hp) for an hour. By Watt's definition, a horse sustains 33,000 ft·lbf/min, meaning one horse ≈ 5–8 sustained humans. The ancient rule of "ten slaves per horse" wasn't far off.
Is 33,000 ft·lbf/min still used in any modern calculations?
Yes — it's embedded in US pump and fan engineering. The formula for pump horsepower is: HP = (GPM × Head in ft × Specific Gravity) / 3,960, where 3,960 = 33,000 / (8.33 lb/gal). The number 33,000 ft·lbf/min lurks inside every US pump sizing calculation, even if the engineer never writes it explicitly. It also appears in ASME standards for hoists, cranes, and elevators — anywhere lifting power needs to be specified.
Horsepower (Water) – Frequently Asked Questions
How do you calculate water horsepower for a pump?
Water HP = (Flow in GPM × Total Head in feet) / 3,960. The magic number 3,960 comes from the weight of water (8.33 lb/gal) × 33,000 ft·lbf/min per hp ÷ 8.33 × the appropriate conversions. For example: 200 GPM at 80 feet of head = 200 × 80 / 3,960 = 4.04 water hp. If the pump is 75% efficient, you need 4.04 / 0.75 = 5.39 shaft hp, so you'd select a 7.5 hp motor (next standard NEMA size up).
Why does water horsepower matter when sizing a pump motor?
Because the motor must provide shaft hp, not water hp. If your application needs 3 water hp but the pump is only 65% efficient, you need 3 / 0.65 = 4.6 shaft hp — meaning a 5 hp motor minimum. Underestimating this gap leads to overloaded motors, overheating, and premature failure. Pump efficiency varies from 30% (tiny pumps) to 90% (large, well-designed centrifugal pumps), so the water-hp-to-shaft-hp gap ranges from 10% to 70%.
How does water horsepower differ from brake horsepower in pumps?
Water hp is the useful hydraulic output — the power actually delivered to the fluid as pressure and flow. Brake hp (bhp) is the shaft input power measured at the coupling. The ratio is pump efficiency: η = WHP / BHP. A pump rated at 10 bhp with 80% efficiency delivers 8 water hp; the other 2 hp is lost to friction, turbulence, and heat in the pump. When specifying pumps, you calculate the required water hp first, then divide by efficiency to find the necessary brake hp.
Is water horsepower used outside the United States?
Rarely. International pump engineering uses kilowatts for both hydraulic power and shaft power. The formula becomes: Hydraulic Power (kW) = (Flow in m³/h × Head in meters × density × g) / 3,600,000. European pump catalogs list "hydraulic efficiency" as a percentage relating input kW to output kW. The concept is identical — water hp is just the US customary wrapper around it. If you see "water horsepower" in a specification, it's almost certainly an American or Canadian document.
What pump applications require the most water horsepower?
Municipal water supply: 50–500 water hp per pump station. Oil pipeline pumping: 1,000–10,000 water hp per station. Mining dewatering: 100–5,000 water hp. Hydroelectric dam penstocks deliver thousands of water hp to turbines (in reverse — the water does the work). The largest single pump installations, like the pumps protecting New Orleans from flooding, can exceed 10,000 water hp each — moving millions of gallons per minute against levee heights.