Foot-Pounds per Second to Horsepower: the 550 Definition

Why One Horsepower Is 550 Foot-Pounds per Second

Almost every mechanics problem set arrives at the same shape: something heavy is moved a measured distance in a measured time, the answer comes out in foot-pounds per second, and the marking scheme wants horsepower. The bridge between the two is not a measured constant to be looked up to eight figures — it is a definition, fixed at 550, and knowing where that number came from makes the whole topic easier to hold on to.

Conversion factor: 1 ft·lb/s = 1/550 hp = 0.0018181818 hp, so divide the work rate by 550. A hoist raising a 150 lb load 20 ft in 10 s does 3 000 ft·lb of work at 300 ft·lb/s, which is 300 ÷ 550 = 0.5455 hp.

What Watt Was Actually Measuring

The mill horse he timed

Watt watched draught horses walking a circular gin at a brewery, leaning into the bar with roughly 180 lbf of pull at about 181 ft/min. That is 543 ft·lb/s — a whisker under the round figure he went on to publish.

Work is force times distance

Lifting 550 lb through 1 ft costs 550 ft·lb whether it takes a second or an afternoon. Nothing in that figure says how quickly it happened, which is exactly why a second unit is needed.

Power divides work by time

Put that same 550 ft·lb into one second and you have 550 ft·lb/s, the definition of one mechanical horsepower. Spread it over ten seconds and the identical job needs a tenth of the machine.

The 33 000 per minute twin

Older textbooks quote the same definition on a per-minute clock: 550 × 60 = 33 000 ft·lb/min. It is one horsepower written two ways, and mixing the two clocks is the commonest lost mark.

Working a Power Problem from Load, Height and Time

Get the work rate first, in whatever units the question gives you, and leave the horsepower step until last. Doing it in that order keeps the physics and the bookkeeping apart.

Multiply weight by the height raised

A 240 lb crate taken 5 ft up a ramp gains 1 200 ft·lb of potential energy. Use the vertical rise, not the length of the slope — the ramp changes the force you push with, not the work done against gravity.

Divide by the elapsed seconds

Eight seconds for that crate gives 1 200 ÷ 8 = 150 ft·lb/s. If the question runs on a per-minute clock, either turn the minutes into seconds now or plan to divide by 33 000 later — pick one and stay with it.

Type the work rate and read the horsepower

Put 150 in the left field and 0.27272727 hp appears as you type. A comma works in place of a decimal point and spaces are ignored, so a pasted figure such as 1 200 still parses. The copy button hands over the bare number for a worked-solution write-up.

Reverse it when the rating is the given

If the question hands you the horsepower and asks for a time or a height, press the swap button (↔) to run hp → ft·lb/s. A quarter-horsepower winch becomes 137.5 ft·lb/s, and dividing the job's work by that number gives the seconds directly.

Weight in pounds-force, please: the foot-pound of work pairs a foot with a pound-force. If a problem states mass in slugs or kilograms, turn it into lbf before multiplying, or the work rate comes out wrong by a factor of roughly 32.2.

Classic Work-Rate Problems in ft·lb/s and Horsepower

Eight situations of the kind that fill a mechanics chapter, each carried through to a work rate and then to horsepower. Every figure in the last column is simply the ft·lb/s value divided by 550.

Situation	Work done	Time	Work rate (ft·lb/s)	Power (hp)
The definition itself	550 lb raised 1 ft = 550 ft·lb	1 s	550 ft·lb/s	1.0000 hp
Watt's brewery mill horse	180 lbf on the bar, 181 ft walked per minute	Continuous	543.0 ft·lb/s	0.9873 hp
Pit pony on a mine gin	132 lbf on the rope, 165 ft per minute	Continuous	363 ft·lb/s	0.6600 hp
Pumping against a 50 ft head	100 gal/min × 8.33 lb/gal × 50 ft	Per minute	694.2 ft·lb/s	1.2621 hp
Load raised by a hoist	150 lb through 20 ft = 3 000 ft·lb	10 s	300 ft·lb/s	0.5455 hp
Climbing one storey of stairs	180 lb through 12 ft = 2 160 ft·lb	8 s	270 ft·lb/s	0.4909 hp
Crate pushed up a ramp	240 lb through 5 ft of rise = 1 200 ft·lb	8 s	150 ft·lb/s	0.2727 hp
Bucket drawn from a well	40 lb through 60 ft = 2 400 ft·lb	25 s	96 ft·lb/s	0.1745 hp

Read the first three rows together and the definition stops looking arbitrary. A working horse came out at 543 ft·lb/s, a smaller pit pony at two-thirds of that, and Watt rounded upward to a figure no buyer could accuse him of overstating. The two human rows sit near half a horsepower for a few seconds of effort, and sustainable output is a good deal lower — which is why the animal, not the person, became the yardstick.

What the Converter Handles in a Problem Set

Both boxes stay live across a multi-part question

Retype the work rate for each part and the horsepower keeps pace, so a load-height-time table can be filled in a single pass with nothing to clear between parts.

Swap when the rating is the given quantity

The ↔ button turns the page into hp → ft·lb/s, the direction you need when a machine's rating is printed in the question and the unknown is the time or the height.

Reach ft·lb/min without rewriting the sum

The searchable dropdowns carry ft·lb/min beside every other power unit, so a question set on a per-minute clock — and its 33 000 constant — needs nothing more than a change of unit.

Eight decimals on a recurring 1/550

Dividing by 550 rarely lands neatly, so results carry up to eight decimals — enough to see whether 0.18181818 was meant to be written as 0.18 or 0.182 in the answer book.

Questions Students Ask About the 550 Figure

How did Watt arrive at 550 rather than some other number?

He needed a selling unit, not a scientific constant. His customers were replacing horses, so he timed horses at real work — walking a circular gin against a measured pull — and rounded upward so nobody could claim the engine under-delivered. The usual reconstruction, 180 lbf at about 181 ft/min, gives 543 ft·lb/s, which he published as 33 000 ft·lb/min, or 550 per second. It has been a fixed definition ever since, not a measurement anyone refines.

My answer is in foot-pounds — why will the marking scheme not take it?

Because a foot-pound is a quantity of work and the question asked for a rate. Raising a 40 lb bucket 60 ft is 2 400 ft·lb no matter who does it; doing it in 25 s is 96 ft·lb/s, and doing it in 5 s is 480 ft·lb/s. Only the second kind of figure can become horsepower. If there is no division by a time anywhere in your working, you stopped one step early.

Is a foot-pound of torque the same foot-pound as a foot-pound of work?

Dimensionally they look identical, yet they describe different things and are never added together. Work is a force moved along its own line of action; torque is a force acting at a perpendicular distance from an axis, and nothing has to move at all for it to exist. Careful texts write torque as lb·ft and work as ft·lb to keep the two apart. A torque figure only becomes power once a rotational speed is brought into it.

When should I divide by 33 000 instead of 550?

Use 33 000 when the work rate is already per minute and 550 when it is per second — the same definition on two clocks, since 550 × 60 = 33 000. Pump and fan questions usually arrive per minute, in gallons or cubic feet per minute, so the larger constant saves a step there. Choosing ft·lb/min in the left dropdown does the same job with no arithmetic at all.

The question gives the horsepower and asks for the time — how do I rearrange it?

Turn the rating into a work rate first, then divide the job into it. A 0.25 hp winch is 0.25 × 550 = 137.5 ft·lb/s; lifting 300 lb through 22 ft is 6 600 ft·lb, so the time is 6 600 ÷ 137.5 = 48 s. That is the ideal case. Real gear gives some of the input away to friction, so where an efficiency is stated it has to reduce the available work rate before you take the time.

Foot-pounds per Second to Horsepower