Foot pounds-force second to Horsepower (Water)
ft·lbf/s
hp
Conversion History
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Quick Reference Table (Foot pounds-force second to Horsepower (Water))
| Foot pounds-force second (ft·lbf/s) | Horsepower (Water) (hp) |
|---|---|
| 1 | 0.00181734557972540457 |
| 10 | 0.01817345579725404568 |
| 100 | 0.18173455797254045678 |
| 200 | 0.36346911594508091357 |
| 550 | 0.99954006884897251231 |
| 1,000 | 1.81734557972540456783 |
| 5,000 | 9.08672789862702283917 |
About Foot pounds-force second (ft·lbf/s)
Foot pounds-force per second (ft·lbf/s) is the fundamental mechanical power unit in the US customary system, equal to approximately 1.356 watts. It is the rate of doing work when a force of one pound-force moves through one foot per second. The unit is directly related to the mechanical horsepower: one horsepower equals exactly 550 ft·lbf/s. It appears in US mechanical engineering, ballistics, and machinery design texts.
One mechanical horsepower equals 550 ft·lbf/s (~746 W). A person climbing stairs moderately expends about 200–300 ft·lbf/s of mechanical power.
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 second – Frequently Asked Questions
Why is horsepower defined as exactly 550 ft·lbf/s?
James Watt calculated that a mill horse could turn a mill wheel 144 times per hour, doing 32,572 ft·lbf of work per minute — he rounded up to 33,000 ft·lbf/min (550 ft·lbf/s) for marketing purposes. He wanted to sell steam engines by comparing them to horses, so he likely overestimated the horse to make his engines look like better value. A real horse sustains closer to 350–500 ft·lbf/s, so Watt's "1 HP" is actually more than one horse.
How do you calculate ft·lbf/s from torque and RPM?
Power (ft·lbf/s) = Torque (ft·lbf) × RPM × 2π / 60. This is the workhorse formula (pun intended) of US mechanical engineering. For example, an engine producing 200 ft·lbf of torque at 3,000 RPM delivers 200 × 3,000 × 6.2832 / 60 = 62,832 ft·lbf/s ≈ 114 hp. The formula works because angular velocity in rad/s times torque in ft·lbf gives power directly in ft·lbf/s.
What everyday forces produce 1 ft·lbf/s of power?
Pushing with 1 pound of force at 1 foot per second — roughly the effort of slowly sliding a light book across a table against friction. Lifting a 1-pound weight 1 foot in 1 second. Turning a doorknob with a very light touch. It's about 1.36 watts — enough to dimly light an LED. In human terms, it's almost effortless: casual walking produces about 50–80 ft·lbf/s of mechanical power, and you don't even notice.
Is ft·lbf/s still used in modern American engineering?
Yes, particularly in ballistics (muzzle energy rates), mechanical testing (dynamometer output), agricultural machinery specs, and industrial equipment designed for the US market. However, even in the US, many engineering firms are switching to SI units for international compatibility. The automotive industry increasingly quotes power in both hp and kW. Aerospace has been mostly metric since the 1990s. Ft·lbf/s survives mainly in traditional mechanical and manufacturing industries.
How does ft·lbf/s relate to bullet kinetic energy?
Bullets are rated in ft·lbf of muzzle energy (not per second), but the power of a firearm is the muzzle energy divided by barrel time. A .308 rifle bullet exits with about 2,600 ft·lbf of energy over a barrel transit time of ~0.001 seconds, meaning the instantaneous power is roughly 2,600,000 ft·lbf/s (about 3,500 hp). That's why rifle recoil feels punchy — for a millisecond, you're absorbing the reaction force of a truck engine.
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.