Units, Dimensions, Conversions

Units and Dimensions

Table C.1: SI units with c.g.s. and British system equivalents

Quantity	Dimensions	SI	c.g.s.	British
Basic
Length	L	1 m	= 102 cm	= 3.281 ft
Mass	M	1 kg	= 103 g	= 2.205 lb
Time	T	1 s	= 1 s	= 2.778 x 10-4 h
Temperature	$\theta$	1 K	= 1 K	= 1.8 o F
Derived
Area	L2	1 m2	= 104 cm2	= 10.76 ft2
Volume	L3	1 m3	= 106 cm3	= 35.31 ft3
Density	M L-3	1 kg m-3	= 10-3 g cm-3	= 6.243 x 10-2 lb ft-3
Velocity	L T-1	1 m s-1	= 102 cm s-1	= 3.281 ft s-1
Acceleration	L T-2	1 m s-2	= 102 cm s-2	= 3.281 ft s-2
Force	ML T-2	1 kg m s-2	= 105 g cm s-2	= 0.225 lb f
		= 1 N (Newton)	= 105 dynes	(lb force)
Pressure	M L-1 T-2	1 kg m-1 s-2	= 10 g cm-1 s-2	= 0.021 lb f ft-2
		= 1 Pa (Pascal)	= 10-2 hPa (or mb)
Work, energy	ML2 T-2	1 kg m2 s-2	= 107 g cm2 s-2	= 0.738 ft lb f
		= 1 J (Joule)	= 107 ergs
Power	ML2 T-3	1 kg m2 s-3	= 107 g cm2 s-3	= 0.738 ft lb f s-1
		= 1 W (Watt)	= 107 ergs s-1
Heat, energy	Q (= ML2 T-2 )	1 J	= 0.2388 cal	= 9.487 x 10-4 BTU
Heat flux	QT-1	1 W	= 0.2388 cal s-1	= 3.412 BTU h-1
Heat flux density	QL-2 T-1	1 W m-2	= 2.388 x 10-5	= 0.317
			cal cm-2 s-1	BTU ft-2 h-1
Latent heat	QM-1	1 J kg-1	= 2.388 x 10-4	4.29 x 10-4
			cal g-1	BTU lb-1
Specific heat	QM-1 $\mbox{$\theta$}$-1	1 J kg-1 K-1	= 2.388 x 10-4	= 2.388 x 10-4
			cal g-1 K-1	BTU lb-1 o F-1
Thermal	QL-1 $\mbox{$\theta$}$-1 T-1	1 W m-1 K-1	= 2.388 x 10-3	= 0.578
conductivity			cal cm-1 s-1 K-1	BTU ft-1 h-1 o F-1
Thermal	L2 T-1	1 m2 s-1	= 104 cm2 s-1	= 10.8 ft2 s-1
diffusivity

Useful Metric to English Conversions

Length: 		  1 kilometer (km) = 1000 meters (m) = 0.6214 miles (mi) = 3281 feet (ft) 


1 meter = 100 centimeters (cm) = 1.0936 yards (yd) = 3.281 feet = 39.37 inches (in) 


1 centimeter = 10 millimeters (mm) = 0.3937 inches 


1 micron ($\mu$

m)= 10-6

 meters = 10-4

 centimeters = 3.937 
x 10-5

 inches 




Area: 		   1 square kilometer (1 km2

) = 106

 sq. meters (m2

)  = 0.3861 sq. miles (mi2

)  = 247.1 acres 


1 m2

 = 104

 sq. centimeters (cm2

) = 1.196 sq. yards = 10.764 sq. feet = 1550.0 sq. inches 




Volume: 		         1 cubic kilometer = 109

 cubic meters (m3

) = 0.2399 cubic miles 


1 cubic meter = 106

 cubic centimeters = 1.308 cubic yards =  35.31 cubic feet = 61024 cubic inches 


1 litre (1) = 1000 cm3

 = 10-3

 cubic meters = 0.264 US gallons (US gal) = 61.024 in3

 




Mass: 		   1 metric ton (tonne) = 1000 kilograms = 2204.6 avoirdupois pounds (means pound of mass not force) 


1 kilogram (kg) = 1000 grams (g) = 2.2046 avoirdupois pounds 




Time: 		   1 day = 86400 seconds (s)  


1 year (yr) = 
3.156 x 107

 seconds 




Velocity / 		    1 meter/second (same as m/s, read meter per second) = 3.281 feet/second = 2.24 miles/hour 

Speed: 		        1 m/s = 3.6 kilometers /hour = 2.237 miles/hour 


1 kilometer/hour = 0.62 miles/hour (mi/hr) 


1 knot = 1 nautical mile/hour = 1.151 miles/hour = 0.51 m/s = 1.85 km/hr 




Force: 		  1 newton (N) =  1 kilogram meter/(sq. second) 


1 newton (N) = 1 kg m s-2

 = 0.2248 pounds force 




Pressure: 		  1 atmosphere  = 1013.2 hectopascals (hPa) = 101.32  kilopascals (kPa) 


1 atmosphere  = 14.7 pounds/ sq. inch (lb/in2

) 


1 atmosphere = 760 millimeters of mercury (mm Hg) =  29.92 inches of mercury 


10 millibars (hPa) = 1 kilopascal (kPa) 


1  Pascal (Pa) = 1 newton /meter2

 = 0.01 millibars (mb) = 0.01 hectopascals (hPa) 


1 millibar (mb) = 1 hectopascal (hPa) 




Temperature: 


Temperature in  o

C = 5/9(temperature in o

F - 32) 


Temperature in  o

F = 9/5(temperature in o

C) + 32 


Temperature in   K = temperature in o

C + 273.15 




Energy: 		   1 joule (J) = 1 newton meter (N m) = 1 kg m2

 s-2

 =  0.239 calories = 1 watt sec (W s) 


1 calorie (cal)= 4.186 joules (J) 


1 langley = 1 calorie /square centimeter 


1 kilowatt hour = 
3.6 x 106

 J 




Power: 		          1 watt (W) = 1 joule / second  (J / s) =  14.3353 calories /minute (cal/min) 


1 calorie/second = 4.186 joules /second (J/s) = 4.186 watts (W) 


1 calorie/minute = 0.06973 watts (W) 


1 horsepower (hp) = 746 watts (W)