Conversion of Power Units

Conversions of power units •
Power conversion P
Power P is the quotient of done work W = energy and the taken time t
P = W / t; W = work, t = time. The SI unity of power is watt W

	W	kW	kcal/s	kcal/h	kgf m/s	PS	HP
1 W = Nm/s = J/s	1	0.001	2.39×10^-4	0.860	0.102	0.00136	0.001359
1 kW =	1000	1	0.239	860	102	1.36	1.3596
1 kcal/s =	4190	4.19	1	3600	427	5.69	5.685
1 kcal/h =	1.16	0.00116	0.00028	1	0.119	0.00158	0.001606
1 kgf m/s =	9.81	0.00981	0.00234	8.43	1	0.0133	0.01335
1 PS =	736	0.7360	0.176	623	75	1	0.98632
1 HP =	735.5	0.7355	0.1759	622.577	74.905	1.01387	1

Power conversion chart

To convert from:	to:	multiply by
erg per second (erg/s)	watt W	1.0×10^-7
foot pound-force per hour (ft·lbf/h)	watt W	3.766161×10^-4
foot pound-force per minute (ft·lbf/min)	watt W	2.259697×10^-2
foot pound-force per second (ft·lbf/s)	watt W	1.355818
horsepower (550 ft·lbf/s) HP or BHP	watt W	745.699872 W
horsepower (boiler)	watt W	9809.50
horsepower (electric)	watt W	746
horsepower (metric) = 75 kgf·m/s	watt W	735.4987
horsepower (UK) HP or Break HP	watt W	745.699872 W
horsepower (water)	watt W	746.043

Powerunits conversion chart

Sorted from small to large

Name of Power Unit, P	Symbol	Definition	Relation to SI unit watt, W
watt (SI unit)	W	≡ J/s = N·m/s	= kg·m²/s³
lusec	lusec	≡ 1 L·µmHg/s	≈ 1.333 224×10^⁻⁴ W
foot-pound-force per hour	ft lbf/h	≡ 1 ft lbf/h	≈ 3.766 161×10^⁻⁴ W
atmospherecubic centimetre per minute	atm ccm	≡ 1 atm × 1 cm³/min	= 1.688 75×10⁻³ W
foot-pound-force per minute	ft lbf/min	≡ 1 ft lbf/min	= 2.259 696 580 552 334×10⁻² W
atmosphere–cubiccentimetre per second	atm ccs	≡ 1 atm × 1 cm³/s	= 0.101 325 W
BTU (International Table) per hour	BTUIT/h	≡ 1 BTUIT/h	≈ 0.293 071 W
atmosphere–cubic foot per hour	atm cfh	≡ 1 atm × 1 cu ft/h	= 0.797 001 244 704 W
foot-pound-force per second	ft lbf/s	≡ 1 ft lbf/s	= 1.355 817 948 331 400 W
litre-atmosphere per minute	L·atm/min	≡ 1 atm × 1 L/min	= 1.688 75 W
calorie (International Table) per second	calIT/s	≡ 1 calIT/s	= 4.1868 W
BTU (International Table) per minute	BTUIT/min	≡ 1 BTUIT/min	≈ 17.584 264 W
atmosphere-cubic foot per minute	atm·cfm	≡ 1 atm × 1 cu ft/min	= 47.820 074 682 24 W
square foot equivalent direct radiation	sq ft EDR	≡ 240 BTUIT/h	≈ 70.337 057 W
litre-atmosphere per second	L·atm/s	≡ 1 atm × 1 L/s	= 101.325 W
horsepower (metric)	hp	≡ 75 m kgf/s	= 735.498 75 W
horsepower (European electrical)	hp	≡ 75 kp·m/s	= 736 W
horsepower (Imperial mechanical)	hp	≡ 550 ft lbf/s	= 745.699 871 582 270 22 W
horsepower (Imperial electrical)	hp	-	≡ 746 W
ton of air conditioning	-	≡ 1 t × 1005 J/kg × 1 °F/K ÷ 10 min	= 844.2 W
poncelet	p	≡ 100 m kgf/s	= 980.665 W
BTU (International Table) per second	BTUIT/s	≡ 1 BTUIT/s	= 1.055 055 852 62×10³ W
atmosphere-cubic foot per second	atm cfs	≡ 1 atm × 1 cu ft/s	= 2.869 204 480 934 4×10³ W
ton of refrigeration (IT)	-	≡ 1BTUIT × 1 sh tn/lb ÷ 10 min/s	≈ 3.516 853×10³ W
ton of refrigeration (Imperial)	-	≡ 1BTUIT × 1 lng tn/lb ÷ 10 min/s	≈ 3.938 875×10³ W
boiler horsepower	bhp	≈ 34.5 lb/h × 970.3 BTUIT/lb	≈ 9.810 657×10³ W

History of the term "horsepower"

The term"horsepower" was invented by James Watt to help market his improvedsteam engine. He determined that a horse could turn a mill wheel 144 times in an hour (or 2.4 times a minute). The wheel was 12 feet in radius, thus in a minute the horse travelled 2.4 × 2π × 12 feet. Watt judged that the horse could pull with a force of 180 pounds (just assuming that the measurements of mass were equivalent to measurements of force in pounds-force, which were not well-defined units at the time). So:
$power = \frac{work}{time} = \frac{force \times distance}{time} = \frac{(180 \mbox{ lbf})(2.4 \times 2 \pi \times 12 \mbox{ ft})}{1\ \mbox{min}}=32,572 \frac{\mbox{ft} \cdot \mbox{lbf}}{\mbox{min}}$
This was rounded to an even 33,000 ft·lbf/min.
Others recount that Watt determined that a pony could lift an average 220 pounds 100 feet (30.48 m) per minute over a four-hour working shift. Watt then judged a horse was 50% more powerful than a pony and thus arrived at the 33,000 ft·lbf/min figure.
Engineering in history recounts that John Smeaton initially estimated that a horse could produce 22,916 foot-pounds per minute. John Desaguliers increased that to 27,500 foot-pounds per minute. "Watt found by experiment in 1782 that a ’brewery horse’ was able to produce 32,400 foot-pounds per minute". James Watt and Matthew Boulton standardized that figure at 33,000 the next year.
Put into perspective, a healthy human can sustain about 0.1 horsepower, and trained athletes can manage up to about 0.3 horsepower for a period of several hours. Most observers familiar with horses and their capabilities estimate that Watt was either a bit optimistic or intended to underpromise and overdeliver; few horses can maintain that effort for long. Regardless, comparison to a horse proved to be an enduring marketing tool.

Conversion of historical definition to watts

The historical value of 33,000 ft∙bf/min may be converted to the SI unit of watts by using the following conversion of units factors:
1 ft = 0.3048 m
1 lbf = g × 1 lb = 9.80665 m/s² ×1 lb × 0.45359237 kg/lb = 4.44822 kg·m/s² = 4.44822 N
60 seconds = 1 minute
$33,000 \frac{\mbox{ft} \cdot \mbox{lbf}}{\mbox{min}} \times \frac{0.3048 \mbox{ m}}{\mbox{ft}}\times \frac{4.44822 \mbox{ N}}{\mbox{lbf}}\times \frac{\mbox{min}}{60 \mbox{ s}}=745.69987158227022 \ \frac{\mbox{N} \cdot \mbox{m}}{\mbox{s}}$
And the watt is defined as $1\ \mbox{W} = 1 \frac{\mbox{N} \cdot \mbox{m}}{\mbox{s}}$ so the historical figure of 33,000 ft·lbf/min converts exactly to the modern definition.