Horsepower Calculator

power = force × distance / time

F

The force doing the work, in pounds-force, with newtons, kilonewtons and kilogram-force in the same field. The default 550 lbf is the definition of mechanical horsepower and is not a coincidence. It must be positive: a force of zero moves nothing and the power is meaningless rather than zero

d

The distance the force moves the object through, in feet, with metres, centimetres, kilometres, inches and miles in the same field. It is the distance along the direction of the force, so lifting a load is the case this fits exactly and dragging it across a floor is not. The default of one foot completes the definition of horsepower

t

How long the movement takes, in seconds, minutes or hours. It sits in the denominator, so the same force over the same distance is twice the power if it happens in half the time — which is the whole meaning of power as opposed to work. It must be positive; zero seconds is a division by zero, and there is no such thing as moving something in no time

P

The power, given as mechanical horsepower (hp), metric horsepower (PS) and kilowatts. The first is the one defined by 550 ft·lbf/s and is the page's main result; the second is 75 kgf·m/s, which is 735.49875 W and therefore 1.4 percent smaller; the third is the SI unit and is the only one of the three that is not called horsepower at all. The three rows are the same power, not three results

Use this page when you have a force and a distance and a time — a winch lifting a load, a motor driving a carriage along a rail, a person carrying something up a flight of stairs — and you want to know how fast that work is being done, in the unit the equipment is sold in. It is also the page to read backwards: 100 hp is a familiar figure from a car brochure, and the three output rows say what it is in kilowatts and in metric horsepower, which is where most of the confusion about horsepower comes from. Two warnings. First, decide which horsepower you mean before you quote a number to anyone, because a 224.7 hp engine and a 224.7 PS engine are not the same engine — the second is about 221.6 hp. Second, the force has to be along the displacement. Moving something sideways against friction is a perfectly good power calculation, but the force in the formula is then the friction force, not the weight. An engine's power can also be worked out from its torque and rotational speed rather than from a force and a distance; that is the same physical quantity reached by the other route and it has its own page.

1. The definition itself: 550 lbf through one foot in one second

   1. Force 550 lbf, distance 1 ft, time 1 s — this is where the unit comes from
   2. Convert to SI first, because the product only comes out in watts in newtons and metres: 550 lbf = 2446.5 N
   3. 2446.5 N × 0.3048 m = 745.7 J of work
   4. Done in one second, that is 745.7 W
   5. Mechanical horsepower: 745.7 ÷ 745.6999 = 1.0 hp
   6. Metric horsepower: 745.7 ÷ 735.49875 = 1.0139, which the page shows as 1.0 PS

   The unit is a definition, not a measurement: James Watt picked 550 foot-pounds per second so that a horse would compare favourably with the steam engines he was selling, and every horsepower figure in the world descends from that choice. It is worth noticing that this row cannot show the difference between the two horsepowers — 1.0139 rounds to 1.0 either way — and that is exactly why the comparison has to be made at a larger number. The next example does that.

2. 100 hp, and the 1.4 percent that makes metric horsepower a different unit

   1. 1100 lbf = 4893.04 N, and 100 ft = 30.48 m
   2. Work: 4893.04 × 30.48 = 149140 J
   3. Over 2 seconds: 149140 ÷ 2 = 74570 W
   4. Mechanical horsepower: 74570 ÷ 745.6999 = 100.0 hp
   5. Kilowatts: 74570 ÷ 1000 = 74.57, shown as 74.6 kW
   6. Metric horsepower: 74570 ÷ 735.49875 = 101.39, shown as 101.4 PS

   This is the only row on the page that tells the two horsepowers apart, and it does it by a margin nobody would notice on a single unit: 100.0 hp against 101.4 PS. The reason is that the two units were defined twice, independently — 550 ft·lbf/s in Britain and 75 kgf·m/s in continental Europe — and 745.7 against 735.5 is a 1.4 percent gap that compounds into a real error at the sizes people quote. It is worth being concrete about the direction: for the same power the metric number is always the larger one, so a car advertised as 100 PS is about 98.6 hp, and an engine rated 224.7 hp is 227.8 PS.

3. A small crane: 2000 lbf through 10 ft in 2 seconds

   1. 2000 lbf = 8896.44 N, and 10 ft = 3.048 m
   2. Work: 8896.44 × 3.048 = 27116 J
   3. Over 2 seconds: 27116 ÷ 2 = 13558 W
   4. Mechanical horsepower: 13558 ÷ 745.6999 = 18.18, shown as 18.2 hp
   5. Kilowatts: 13.558, shown as 13.6 kW
   6. Metric horsepower: 13558 ÷ 735.49875 = 18.43, shown as 18.4 PS

   None of the three numbers is round, and that is the point of the row: it pins the route through SI rather than a shortcut. The tempting implementation is to fold the pound and the foot into a single factor of 550 and skip the conversion, and it gives the right answer for the first example and drifts by a few tenths here — which is invisible until someone checks the third digit against a catalogue. The other thing this row shows is how modest a real machine is: a crane pulling a short ton through three metres in two seconds is under twenty horsepower, which is why a 100 hp winch is a serious piece of equipment rather than an ordinary one.

Power is a rate, so this page says nothing about the total energy involved — the same 100 hp for ten seconds and for ten hours is the same number here, and the difference is what the fuel or the battery has to supply. It also assumes the force is constant and along the direction of travel. A real hoist accelerates at the start and decelerates at the end, so its peak force is larger than the average this page computes, and the answer is the average power over the whole movement rather than the peak the motor has to survive. Friction is not in the formula at all: if the object is being dragged, the number you want is the friction force and not the weight, and if it is being lifted, the pulley and rope losses are a real correction on top. Nothing here accounts for efficiency, so a 20 hp figure for a lifting job is the power delivered to the load, not the power drawn from the supply — an electric motor would need half again as much. And the unit itself carries a warning rather than a limitation: mechanical horsepower and metric horsepower differ by 1.4 percent, so a rating quoted without saying which one is ambiguous by more than the tolerance of most machinery.

What is the horsepower formula?

For a force moving something, P = F × d / t: the force in pounds-force, times the distance in feet it moves, divided by the time in seconds. That gives watts once the force and distance are converted to newtons and metres, and the page divides by 745.6999 to report horsepower. The unit itself is that expression with the numbers filled in — 550 lbf through one foot in one second — so the default row on this page is not an example of horsepower so much as its definition.

Which horsepower do you mean — mechanical or metric?

Both are shown, and the main result is mechanical horsepower, the one defined as 550 ft·lbf/s and equal to 745.6999 W. Metric horsepower, written PS, is 75 kgf·m/s and equals 735.49875 W, so it is 1.4 percent smaller. For the same amount of power the metric figure is therefore the larger number: 100 hp is 101.4 PS, and a car sold as 100 PS is about 98.6 hp. Always check which one a specification means before comparing two machines, because 1.4 percent is larger than most people assume and it is invisible at 1.0 of either unit.

How do I convert watts to horsepower?

Divide by 745.6999 for mechanical horsepower, or by 735.49875 for metric horsepower. In the other direction, one horsepower is 745.7 W and one PS is 735.5 W, so a 1000 W motor is 1.34 hp or 1.36 PS. The kilowatt row of this page is the same division by 1000 and needs no memorising, which is why the SI unit is the one to convert through if you are doing several of these: the arithmetic is a factor of ten rather than a factor of 745.6999.

Is horsepower a measure of speed or of force?

Neither — it is a rate of doing work, and it combines both. The formula has a force and a distance in the numerator and a time in the denominator, so the same force over the same distance is twice the power when it happens in half the time, and a large force moving slowly can be the same horsepower as a small force moving quickly. That is why a tractor and a motorcycle can have similar power figures and behave nothing alike: the tractor converts its power into force at low speed and the motorcycle into speed at low force.

Do I use the weight of the object as the force?

Only when the movement is vertical, where the force needed is the weight — and then the distance is the height lifted and not the length of any path. Dragging something across a floor, the force in the formula is the friction force, which for a sliding object is the coefficient of friction times the normal force, and the distance is how far it is dragged. Using the weight in that second case overstates the power by whatever the coefficient of friction is, often by a factor of several.

Why is the third output in kilowatts if horsepower is the unit I asked for?

Because horsepower is a non-SI unit and the kilowatt is not, so the SI answer is the one that will still be meaningful in any other calculation you do with it. It is also the unit most of the world outside the United States quotes. And the metric horsepower row is there for the same reason the answer is spelled out at all: three names for nearly the same quantity is exactly how a 1.4-percent error gets into a specification, and showing all three on one line makes the size of the difference visible rather than something you have to take on trust.

• Horsepower — the 550 ft·lbf/s definition, the metric horsepower of 75 kgf·m/s, and why the two differ by 1.4 percent — Wikipedia
• Work, Energy, and Power in Humans (College Physics 2e, §7.8) — power as a rate of doing work, and the sustained output of a human being as a familiar reference point — OpenStax
• NIST Guide to the SI, Chapter 5: Units Outside the SI — the status of the horsepower and other non-SI units whose continued use is permitted but not preferred — National Institute of Standards and Technology