UNIT CONVERSION NOTES
Dimensions – characterize any physical
quantity
Units – magnitudes assigned to the
dimensions
Primary or Fundamental Dimension –
dimensions such as mass (m), length
(L), time (t) and temperature (T)
Secondary or Derived Dimensions –
dimensions such as velocity (v),
acceleration (a) and energy (E).
International System or SI or Metric SI
– units such as meter, kilogram and
Newton.
English Engineering System/USCS
(United States Customary System) –
units such as feet, pound mass and
pound force.
Metric Prefix
Yotta
Zetta
Exa
Peta
Tera
Giga
Mega
Kilo
Hecto
deka
deci
centi
Milli
Micro
Nano
Pico
Femto
Atto
Zepto
yocto
1
Symbol
Y
Z
E
P
T
G
M
k
h
dk
d
c
m

n
p
f
a
z
y
Value
1024
1021
1018
1015
1012
109
106
103
102
101
10-1
10-2
10-3
10-6
10-9
10-12
10-15
10-18
10-21
10-24
Length
1 meter = 3.28 feet
1 meter = 100 centimeters
1 kilometer = 1000 meters
1 inch = 2.54 centimeters
1 foot = 12 inches
1 yard = 3 feet
1 mile, nautical = 6080 feet
1 mile, statute = 5280 feet
1 league, nautical = 3 nautical miles
1 league, statute = 3 statute miles
1 fathom = 6 feet
1 furlong = 220 yards
1 cable = 120 fathoms
1 micron = 10-6 meter
1 mil = 10-3 inch
1 angstrom = 10-10 m
1 chain, surveyor’s = 66 feet
1 link, surveyor’s = 7.92 inches
1 hand = 4 inches
1 pace = 30 inches
1 rod = 5.5 yards
1 span = 9 inches
Area
1 sq. ft = 144 sq. inches
1 acre = 43,560 sq. ft. = 160 sq. rods
1 sq. mile (statute) = 640 acres
1 are = 100 sq. m.
1 hectare = 10,000 sq. m
1 Section (US) = 1 sq. statute mile
1 Township (US) = 36 sq. statute miles
Volume
1 cubic meter = 1000 liters
1 cubic yard = 27 cubic feet
1 gallon (US) = 3.7854 liters
1 gallon (UK) = 4.54609 liters
1 stere = 1 cubic meter
1 bushel (US) = 2, 150.42 cubic inches
1 bushel (UK) = 2, 219.36 cubic inches
Mass
1 kgm (kilogram mass) = 2.2046 lbm
(pound mass)
1 tonne or metric ton = 1,000 kg
1 slug = 32.2 lbm
Mass (Avoirdupois) *for general
weighing
1 short ton (US) = 2000 lbm
1 long ton (UK) = 2,240 lbm
1 lbm = 16 ounce
1 ounce = 28.3495 grams = 437.5 grains
Mass (Troy) *for precious metal/gems
1 carat = 3.086 grains
1 ounce = 20 pennyweights
1 pennyweight = 24 grains
1 lbm = 12 ounce
Liquid Measure (Capacity)
1 tablespoon = 3 teaspoons
1 fluid ounce = 2 tablespoon
1 cup = 8 fluid ounce
1 pint = 2 cups
1 quart = 2 pints
1 gallon = 4 quarts
2
Dry Measure (Capacity)
1 peck = 8 quarts
1 bushel = 4 pecks
1 UK dry quart = 1.032 US dry quarts
Angular or Circular Measures
1 minute = 60 seconds
1 degree = 60 minutes
1 rev = 360 degrees
= 2 radian
= 6400 mil
= 400 gon or centesimal degree
1 zodiac sign = 30 degrees
Wood Measure
1 board foot = 1 cu. ft.
1 cord foot = 16 cu. ft.
1 cord = 8 cord ft.
Weight or Force
1 Newton (N) = 1 kgm m /s2
1 Newton = 105 dynes
1 kgf (kilogram force) = 9.81 N
1 pound force (lbf) = 32.2 lbm ft/s2
1 pound force (lbf) = 4.4482 N
1 pound force (lbf) = 32.2 poundal (pdl)
1 kip = 1000 lbf
Pressure
1 Pa = 1 N/m2
1 atm (atmosphere) = 101.325 kPa
101.325 kPa = 14.696 psi (lbf per sq. in.)
101.325 kPa =760 mm Hg (millimeter of
mercury) =760 Torr = 1.0332 kgf/cm2
1 Bar = 100 kPa
Viscosity
Absolute Viscosity
1 Poise = 1 dyne∙s/cm2
1 Pa∙s = 10 poise
Kinematic Viscosity
m2/s
Energy
1 J (Joule) = 1 N∙m
1 cal (calorie) = 4.1858 J
1 Btu (British Thermal Unit) = 1055 J
1 Btu = 778 ft∙lbf
1 erg = 10-7 J
1 US Therm = 105 Btu
1 kW∙h = 3413 Btu
1 J = 6.2415 x 1018 eV (electronvolt)
Power
1 W (Watt) = 1 N m/s = 1 J/s
1 hp (horsepower) = 746 W
1 hp = 33,000 ft lbf/min
1 hp = 2545 Btu/hr
1 boiler hp = 9.81 kW
1 TOR (ton of refrigerant) = 3.516 kW
1 TOR = 12,000 Btu/hr
Frequency
1 Hz (Hertz) = 1 cycle / second
Coefficient of Performance (COP) to
Energy Efficiency Ratio (EER)
EER = 3.412 COP
3
Temperature Conversions
F = 1.8(C) + 32 (Celsius to Fahrenheit
and vice versa)
R = F + 460 (Fahrenheit to Rankine)
Re = (4/5) (C) (Celsius to Reaumur)
K = C + 273
R = F
K =C
F = 1.8(C)
Electricity and Magnetism
1 Volt = 1 Joule/Coulomb
1 Ampere = 1 Coulomb/second
1 Ohm = 1 Volt/Ampere
1 Watt = Ampere ∙Volts
1 Tesla = 1 Newton/ Ampere ∙meter
= 1 Weber/meter2
Computer Memory
1 character = 1 byte = 8 bits
1 kilobyte = 210 bytes
1 megabyte = 220 bytes
1 giga byte = 230 bytes
Other and Special Conversions
1 Knot = 1 nautical mile per hour
=1.852 kph = 1.151 statute miles/hour
1 Btu/lbm·R = 4.187 kJ/kgm·K
8.314 kJ/kmol·K = 1545 ft·lbf/lbmol·R
0.287 kJ/kg∙K = 53.34 ft·lbf/lbm·R
Fundamental Constants
Gravitational Acceleration
g = 9.80665 m/s2=32.2 ft/s2 (Earth)
g = 1.67 m/s2= 5.47 ft/s2 (Moon)
Gravitational Constant
gc=32.2 lbm ft/lbf∙sec2
G = 6.673 x 10-11 N∙m2/kg2
Mass
mass of Earth = 6 x 1024 kg
mass of Moon = 7.36 x 1022 kg
mass of Sun = 1.99 x 1030 kg
mass of electron (rest)= 9.109 x 10-31 kg
mass of proton (rest)= 1.673 x 10-27 kg
mass of neutron (rest)= 1.675 x 10-27 kg
atomic mass unit = 1.6606 x 10-27 kg
Charge
electron = -1.6022 x 10-19 C
proton = +1.6021 x 10-19 C
Density
air (STP@0C and 1 atm)= 1.29 kg/m3
water = 1000 kg/m3
seawater = 1025 kg/m3
mercury = 13,600 kg/m3
Velocity
c (speed of light) = 3.0 x 108 m/s
sound (air, STP) = 331 m/s
4
Specific Heat
Cpwater =4.187 kJ/kgm·K=1 Btu/lbm·R
Cpair =1.0062 kJ/kgm·K (ideal gas)
k = cp/cv, cp-cv=R; for ideal gas, k=1.4
Specific Weight (Water)
ʸ= 9.81 kN/m3 = 62.4 lbf/ft3
Gas Constant
R (Universal) = 8.314 kJ/kmol·K
R (Specific) = 0.287 kJ/kg∙K
(*see Other and Special Conversion
for equivalent units)
Physical Constants
Avogadro’s Number = 6.022 x 1023 mol-1
Boltzmann Constant = 1.3807 x 10-23 J/K
Stefan-Boltzmann Constant
= 5.67 x 10-8 W/m2∙K4
Planck’s Constant =6.6256 x 10-34 J∙s
Faraday Constant = 96485 C/mol
Absolute Zero = 0 K = -273 C
Mechanical Equivalent of Heat
= 4.186 J/cal
Volume of Ideal Gas (STP)
=22.4207 m3/ kg∙mol
Latent Heat of Vaporization (water)
@ 1 atm= 2256.5 kJ/kg
Latent Heat of Fusion (water) @ 1 atm
= 334 kJ/kg
Boiling Point of Water @ 1 atm = 100C
Freezing Point of Water @ 1 atm =0C