Fillable Printable Conversion Tables for Units
Fillable Printable Conversion Tables for Units
Conversion Tables for Units
Chapter 1
-
1
1.6 Conversion tables for units
The table below gives conversion factors from a variety of units to the corresponding SI unit.
Examples of the use of this table have already been given in the preceding section. For each
physical quantity the name is given, followed by the recommended symbol(s). The SI unit is
given, followed by the esu, emu, Gaussian unit (Gau), atomic unit (au), and other units in
common use, with their conversion factors to SI. The constant ζ which occurs in some of the
electromagnetic conversiton factors is the (exact) pure number 2.997 924 58
×
10
10
= c
0
/(cm s
-1
).
The inclusion of non-SI units in this table should not be taken to imply that their use is to be
encouraged. With some exceptions, SI units are always to be preferred to non-SI units.
However, since may of the units below are to be found in the scientific literature, it is
convenient to tabulate their relation to the SI.
For convenience units in the esu and Gaussian systems are quoted in terms of the four
dimensions length, mass, time, and electric charge, by including the franklin (Fr) as an
abbreviation for the electrostatic unit of charge and 4
π
ε
0
as a constant with dimensions
(charge)
2
/(energy
×
length). This gives each physical quantity the same dimensions in all
systems, so that all conversion factors are pure numbers. The factors 4
π
ε
0
and the Fr may be
eliminated by writing Fr = esu of charge = erg
½
cm
½
= cm
3/2
g
½
s
-1
, and 4
π
ε
0
= ε
ir)
= 1 Fr
2
erg
-1
cm
-1
= 1, to recover esu expressions in terms of three base units (see section 7.3 below). The
symbol Fr should be regarded as a compact representation of (esu of charge).
Conversion factors are either given exactly (when the = sign is used), or they are given to the
approximation that the corresponding physical constants are known (when the
≈
sign is used). In
the latter case the uncertainty is always less than ±5 in the last digit quoted.
Chapter 1
-
2
Name Symbol Relation to SI
length, l
metre (SI unit) m
centimetre (cgs unit) cm = 10
-2
m
ångström Å = 10
-10
m
micron µ = µm = 10
-6
m
millimicron mµ = nm = 10
-9
m
x unit X
≈
1.002
×
10
-13
m
fermi f, fm = fm = 10
-15
m
inch in = 2.54
×
10
-2
m
foot ft = 12 in = 0.3048 m
yard yd = 3 ft = 0.9144 m
mile mi = 1760 yd = 1609.344 m
nautical mile = 1852 m
astronomical unit AU = 1.496 00
×
10
11
m
parsec pc
≈
3.085 68
×
10
16
m
light year l.y.
≈
9.460 528
×
10
15
m
light second = 299 792 458 m
area, A
square metre (SI unit) m
2
barn b = 10
-28
m
2
acre
≈
4046.856 m
2
are a = 100 m
2
hectare ha = 10
4
m
2
volume, V
cubic metre (SI unit) m
3
litre l, L = dm
3
= 10
-3
m
3
lambda λ = µl = 10
-6
dm
3
barrel (US)
≈
158.987 dm
3
gallon (US) gal (US) = 3.785 41 dm
3
gallon (UK) gal (UK) = 4.546 09 dm
3
Chapter 1
-
3
Name Symbol Relation to SI
mass, m
kilogram (SI unit) kg
gram (cgs unit) g = 10
-3
kg
electron mass (au) m
e
≈
9.109 39
×
10
-31
kg
unified atomic mass u, Da = m
a
(
12
C)/12
≈
1.660 540
×
10
-27
kg
unit, daltonS
gamma
γ
= µg
tonne t = Mg = 10
3
kg
pound (avoirdupois) lb = 0.453 592 37 kg
ounce (avoirdupois) oz
≈
28.3495 g
ounce (troy) oz (trou)
≈
31.1035 g
grain gr = 64.798 91 mg
time, t
second (SI, cgs unit) s
au of time h/E
h
≈
2.418 88
×
10
-17
s
minute min = 60 s
hour h = 3600 s
day
1
d = 86 400 s
year
2
a
≈
31 556 952 s
svedberg Sv = 10
-13
s
(1) Note that the day is not exactly in terms of the second since so-called leap-seconds are
added or subtracted from the day semiannually in order to keep the annual average
occurrence of midnight at 24:00 on the clock.
(2) The year is not commensurable with the day and not a constant. Prior to 1967, when the
atomic standard was introduced, the tropical year 1900 served as the basis for the
definition of the second. For the epoch 1900.0. it amounted to 365.242 198 79 d
≈
31
556 925.975 s and it decreases by 0.530 seconds per century. The calendar years are
exactly defined in terms of the day:
Julian year = 365.25 d
Gregorian year = 365.2425 d.
The definition in the table corresponds to the Gregorian year. This is an average based
on a year of length 365 days, with leap years of 366 days; leap years are taken either
when the year is divisible by 4 but is not divisible by 100, or when the year is divisible
by 400. Whether the year 3200 should be a leap year is still open, but this does not have
to be resolved until sometime in the middle of the 32nd century.
Chapter 1
-
4
Name Symbol Relation to SI
acceleration, a
SI unit m s
-2
standard acceleration of g
n
= 9.806 65 m s
-2
free fall
gal, galileo Gal = 10
-2
m s
-2
force, F
newton (SI unit)
3
N = kg m s
-2
dyne (cgs unit) dyn = g cm s
-2
= 10
-5
N
au of force E
h
/a
0
≈
8.238 73
×
10
-8
N
kilogram-force kgf = 9.806 65 N
energy, U
joule (SI unit) J = kg m
2
s
-2
erg (cgs unit) erg = g cm
2
s
-2
= 10
-7
J
rydberg Ry = E
h
/2
≈
2.179 87
×
10
-18
J
electronvolt eV = e
×
V
≈
1.602 18
×
10
-19
J
calorie, thermochemical cal
th
= 4.184 J
calorie, international cal
IT
= 4.1868 J
15
°
C calorie cal
15
≈
4.1855 J
litre atmosphere l atm = 101.325 J
British thermal unit Btu = 1055.06 J
pressure, p
pascal (SI unit) Pa = N m
-2
= kg m
-1
s
-2
atmosphere atm = 101 325 Pa
bar bar = 10
5
Pa
torr Torr = (101 325/760) Pa
≈
133.322 Pa
millimetre of mercury mmHg = 13.5951
×
980.665
×
10
-2
Pa
≈
133.322 Pa
(conventional)
pounds per squere inch psi
≈
6.894 757
×
10
3
Pa
power, P
watt (SI unit) W = kg m
2
s
-3
horse power hp = 745.7 W
(3) 1 N is approximately the force exerted by the earth upon an apple.
Chapter 1
-
5
Name Symbol Relation to SI
action, L, J (angular momentum)
SI unit J S = kg m
2
s
-1
cgs unit erg s = 10
-7
J s
au of action
2π/h=h
≈
1.054 57
×
10
-34
J s
dynamic viscosity, η
SI unit Pa s = kg m
-1
s
-1
poise P = 10
-1
Pa s
centipoise cP = mPa s
kinematic viscosity, v
SI unit m
2
s
-1
stokes St = 10
-4
m
2
s
-1
thermodynamic temperature, T
kelvin (SI unit) K
degree Rankine
4
°
R = (5/9) K
entropy, S
heat capacity, C
SI unit J K
-1
clausius Cl = cal
th
/K = 4.184 J K
-1
molar entropy, S
m
molar heat capacity, C
m
SI unit J K
-1
mol
-1
entropy unit e.u. = cal
th
K
-1
mol
-1
= 4.184 J K
-1
mol
-1
(4) T/
°
R = (9/5) T/K. Also, Celsius temperature θ is related to thermodynamic temperature
T by equation
θ/
°
C = T/K - 273.15
Similarly Fahrenheit temperature θ
F
is related to Celsius temperature θ by the equation
θ
F
/
°
F = (9/5) (θ/
°
C) + 32
Chapter 1
-
6
Name Symbol Relation to SI
molar volume, V
m
SI unit m
3
mol
-1
amagat amagat = V
m
of real gas at 1 atm and 273.15 K
≈
22.4
×
10
-3
m
3
mol
-1
plane angle, α
radian (SI unit) rad
degree
°
= rad
×
2π/360
≈
(1/57.295 78) rad
minute
′
= degree/60
second
″
= degree/3600
grade grad = rad
×
2π/400
≈
(1/63.661 98) rad
radioactivity, A
becquerel (SI unit) Bq = s
-1
curie Ci = 3.7
×
10
10
Bq
absorbed dose of radiation
5
gray (SI unit) Gy = J kg
-1
rad rad = 0.01 Gy
dose equialent
sievert (SI unit) Sv = J kg
-1
rem rem
≈
0.01 Sv
(5) The unit röntgen, employed to express exposure to X or
γ
radiation, is equal to: R =
2.58 x 10
-4
C kg
-1
Chapter 1
-
7
Name Symbol Relation to SI
electric current, I
ampere (SI unit) A
esu, Gau (10/ζ)A
≈
3.335 64
×
10
-10
A
biot (emu) Bi = 10 A
electric charge, Q
coulomb (SI unit) C = A s
franklin (esu, Gau) Fr = (10/ζ)C
≈
3.335 64
×
10
-10
C
emu (abcoulomb) = 10 C
proton charge (au) e
≈
1.602 18
×
10
-19
C
≈
4.803 21
×
10
-10
Fr
charge density, ρ
SI unit C m
-3
esu, Gau Fr cm
-3
= 10
7
ζ
-1
C m
-3
≈
3.335 64
×
10
-4
C m
-3
electrical potential, V, φ
volt (SI unit) V = J C
-1
= J A
-1
s
-1
esu, Gau erg Fr
-1
= Fr cm
-1
/4πε
0
= 299.792 458 V
mean international volt = 1.00034 V
US international volt = 1.000 330 V
electric resistance, R
ohm (SI unit) Ω = V A
-1
= m
2
kg s
-3
A
-2
mean international ohm = 1.000 49 Ω
US international ohm = 1.000 495 Ω
electric field, E
SI unit V m
-1
= J C
-1
m
-1
esu, Gau Fr cm
-2
/4πε
0
= 2.997 924 58
×
10
4
V m
-1
electric field gradient, E
β
, q
αβ
SI unit V m
-2
= J C
-1
m
-2
esu, Gau Fr cm
-3
/4πε
0
= 2.997 924 58
×
10
6
V m
-2
electric dipol moment, p, µ
SI unit C m
esu, Gau Fr cm
≈
3.335 64
×
10
-12
C m
debye D = 10
-18
Fr cm
≈
3.335 64
×
10
-30
C m
Chapter 1
-
8
Name Symbol Relation to SI
electric quadrupole moment,
Q
αβ
, Θ
αβ
, eQ
SI unit C m
2
esu, Gau Fr cm
2
≈
3.335 64
×
10
-14
C m
-2
magnetic flux density, B
(magnetic field)
tesla (SI unit) T = J A
-1
m
-2
= V s m
-2
= Wb m
-2
gauss (emu, Gau) G = 10
-4
T
magnetic flux, Φ
weber (SI unit) Wb = J A
-1
= V s
maxwell (emu, Gau) Mx = G cm
-2
= 10
-8
Wb
magnetic field, H
(volume) magnetization, M
SI unit A m
-1
= C s
-1
m
-1
oersted (emu, Gau) Oe = 10
3
A m
-1
[But note: in practice the oersted, Oe, is only used as a unit for H
(ir)
= 4πH; thus when
H
(ir)
= 1 Oe, H = (10
3
/4π) A m
-1
.]
magnetic dipole moment, m, µ
SI unit A m
2
= J T
-1
emu, Gau erg G
-1
= 10 A cm
2
=10
-3
J T
-1
Bohr magneton
6
µ
B
= eh/2m
e
≈
9.274 02
×
10
-24
J T
-1
nuclear magneton µ
N
= (m
e
/m
p
)µ
B
≈
5.050 79
×
10
-27
J T
-1
magnetizability, ξ
SI unit J T
-2
= C
2
m
2
kg
-1
(6) The Bohr magneton µ
B
is sometimes denoted BM (or B.M.), but this is not
recommended.
Chapter 1
-
9
Name Symbol Relation to SI
magnetic susceptibility, χ, κ
SI unit 1
emu, Gau 1
[But note: in practice susceptibilities quoted in the context of emu or Gaussian units are
always values for χ
(ir)
= χ/4π; thus when χ
(ir)
= 10
-6
, χ = 4π
×
10
-6
.]
molar magnetic susceptibility, χ
m
SI unit m
3
mol
-1
emu, Gau cm
3
mol
-1
= 10
-6
m
3
mol
-1
[But note: in practice the units cm
3
mol
-1
usually imply that the irrational molar
susceptibility is being quoted, χ
m
(ir)
= χ
m
/4π; thus, for example if χ
m
(ir)
= -15
×
10
-6
cm
3
mol
-1
, which is often written as '-15 cgs ppm', then χ
m
= -1.88
×
10
-10
m
3
mol
-1
.]
