Conversion Factors, Front matter | University Physics Volume 1

Learning objectives

Length
	m	cm	km
1 meter	1	10²	10⁻³
1 centimeter	10⁻²	1	10⁻⁵
1 kilometer	10³	10⁵	1
1 inch	$2.540 \times 10^{−2}$	2.540	$2.540 \times 10^{−5}$
1 foot	0.3048	30.48	$3.048 \times 10^{−4}$
1 mile	1609	$1.609 \times 10^{5}$	1.609
1 angstrom	10⁻¹⁰
1 fermi	10⁻¹⁵
1 light-year			$9.460 \times 10^{12}$
	in.	ft	mi
1 meter	39.37	3.281	$6.214 \times 10^{−4}$
1 centimeter	0.3937	$3.281 \times 10^{−2}$	$6.214 \times 10^{−6}$
1 kilometer	$3.937 \times 10^{4}$	$3.281 \times 10^{3}$	0.6214
1 inch	1	$8.333 \times 10^{−2}$	$1.578 \times 10^{−5}$
1 foot	12	1	$1.894 \times 10^{−4}$
1 mile	$6.336 \times 10^{4}$	5280	1

Area

$1 {cm}^{2} = 0.155 {in.}^{2}$

$1 m^{2} = 10^{4} {cm}^{2} = 10.76 {ft}^{2}$

$1 {in.}^{2} = 6.452 {cm}^{2}$

$1 {ft}^{2} = 144 {in.}^{2} = 0.0929 m^{2}$

Volume

$1 liter = 1000 {cm}^{3} = 10^{−3} m^{3} = 0.03531 {ft}^{3} = 61.02 {in.}^{3}$

$1 {ft}^{3} = 0.02832 m^{3} = 28.32 liters = 7.477 gallons$

$1 gallon = 3.788 liters$

Time
	s	min	h	day	yr
1 second	1	$1.667 \times 10^{−2}$	$2.778 \times 10^{−4}$	$1.157 \times 10^{−5}$	$3.169 \times 10^{−8}$
1 minute	60	1	$1.667 \times 10^{−2}$	$6.944 \times 10^{−4}$	$1.901 \times 10^{−6}$
1 hour	3600	60	1	$4.167 \times 10^{−2}$	$1.141 \times 10^{−4}$
1 day	$8.640 \times 10^{4}$	1440	24	1	$2.738 \times 10^{−3}$
1 year	$3.156 \times 10^{7}$	$5.259 \times 10^{5}$	$8.766 \times 10^{3}$	365.25	1

Speed
	m/s	cm/s	ft/s	mi/h
1 meter/second	1	10²	3.281	2.237
1 centimeter/second	10⁻²	1	$3.281 \times 10^{−2}$	$2.237 \times 10^{−2}$
1 foot/second	0.3048	30.48	1	0.6818
1 mile/hour	0.4470	44.70	1.467	1

Acceleration

$1 {m/s}^{2} = 100 {cm/s}^{2} = 3.281 {ft/s}^{2}$

$1 {cm/s}^{2} = 0.01 {m/s}^{2} = 0.03281 {ft/s}^{2}$

$1 {ft/s}^{2} = 0.3048 {m/s}^{2} = 30.48 {cm/s}^{2}$

$1 mi/h \cdot s = 1.467 {ft/s}^{2}$

Mass
	kg	g	slug	u
1 kilogram	1	10³	$6.852 \times 10^{−2}$	$6.024 \times 10^{26}$
1 gram	10⁻³	1	$6.852 \times 10^{−5}$	$6.024 \times 10^{23}$
1 slug	14.59	$1.459 \times 10^{4}$	1	$8.789 \times 10^{27}$
1 atomic mass unit	$1.661 \times 10^{−27}$	$1.661 \times 10^{−24}$	$1.138 \times 10^{−28}$	1
1 metric ton	1000

Force
	N	dyne	lb
$1$ newton	1	10⁵	0.2248
$1$ dyne	10⁻⁵	1	$2.248 \times 10^{−6}$
$1$ pound	4.448	$4.448 \times 10^{5}$	1

Pressure
	Pa	dyne/cm²	atm	cmHg	lb/in.²
*Where the acceleration due to gravity is $9.80665 {m/s}^{2}$ and the temperature is $0 ° C$
1 pascal	1	10	$9.869 \times 10^{−6}$	$7.501 \times 10^{−4}$	$1.450 \times 10^{−4}$
1 dyne/centimeter²	10⁻¹	1	$9.869 \times 10^{−7}$	$7.501 \times 10^{−5}$	$1.450 \times 10^{−5}$
1 atmosphere	$1.013 \times 10^{5}$	$1.013 \times 10^{6}$	1	76	14.70
1 centimeter mercury*	$1.333 \times 10^{3}$	$1.333 \times 10^{4}$	$1.316 \times 10^{−2}$	1	0.1934
1 pound/inch²	$6.895 \times 10^{3}$	$6.895 \times 10^{4}$	$6.805 \times 10^{−2}$	5.171	1
1 bar	10⁵
1 torr				1 (mmHg)

Work, Energy, Heat
	J	erg	ft.lb
1 joule	1	10⁷	0.7376
1 erg	10⁻⁷	1	$7.376 \times 10^{−8}$
1 foot-pound	1.356	$1.356 \times 10^{7}$	1
1 electron-volt	$1.602 \times 10^{−19}$	$1.602 \times 10^{-12}$	$1.182 \times 10^{−19}$
1 calorie	4.186	$4.186 \times 10^{7}$	3.088
1 British thermal unit	$1.055 \times 10^{3}$	$1.055 \times 10^{10}$	$7.779 \times 10^{2}$
1 kilowatt-hour	$3.600 \times 10^{6}$
	eV	cal	Btu
1 joule	$6.242 \times 10^{18}$	0.2389	$9.481 \times 10^{−4}$
1 erg	$6.242 \times 10^{11}$	$2.389 \times 10^{−8}$	$9.481 \times 10^{−11}$
1 foot-pound	$8.464 \times 10^{18}$	0.3239	$1.285 \times 10^{−3}$
1 electron-volt	1	$3.827 \times 10^{−20}$	$1.519 \times 10^{−22}$
1 calorie	$2.613 \times 10^{19}$	1	$3.968 \times 10^{−3}$
1 British thermal unit	$6.585 \times 10^{21}$	$2.520 \times 10^{2}$	1

Power

$1 W = 1 J/s$

$1 hp = 746 W = 550 ft \cdot lb/s$

$1 Btu/h = 0.293 W$

Angle

$1 rad = 57.30 ° = 180 ° / π$

$1 ° = 0.01745 rad = π / 180 rad$

$1 revolution = 360 ° = 2 π rad$

$1 rev/min (rpm) = 0.1047 rad/s$

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