NRL_FORMULARY_09-1

Dimensions

Physical

Sym-

SI

Conversion

Gaussian

Quantity

bol

SI

Gaussian

Units

Factor

Units

Force

F

ml

ml

newton

105

dyne

t2

t2

Frequency

f, ν

1

1

hertz

1

hertz

t

t

Impedance

Z

ml2

t

ohm

1

× 10−11

sec/cm

tq2

l

9

Inductance

L

ml2

t2

henry

1

× 10−11

sec2/cm

q2

l

9

Length

l

l

l

meter (m)

102

centimeter

(cm)

Magnetic

H

q

m1/2

ampere–

4π × 10−3

oersted

lt

l1/2t

intensity

turn/m

Magnetic flux

Φ

ml2

m1/2l3/2

weber

108

maxwell

tq

t

Magnetic

B

m

m1/2

tesla

104

gauss

tq

l1/2t

induction

Magnetic

m, µ

l2q

m1/2l5/2

ampere–m2

103

oersted–

t

t

moment

cm3

Magnetization

M

q

m1/2

ampere–

4π × 10−3

oersted

lt

l1/2t

turn/m

Magneto-

M,

q

m1/2l1/2

ampere–

4π

gilbert

t

t2

10

motance

Mmf

turn

Mass

m, M

m

m

kilogram

103

gram (g)

(kg)

Momentum

p, P

ml

ml

kg–m/s

105

g–cm/sec

t

t

Momentum

m

m

kg/m2–s

10−1

g/cm2–sec

l2t

l2t

density

Permeability

µ

ml

1

henry/m

1

× 107

—

q2

4π

Dimensions

Physical

Sym-

SI

Conversion

Gaussian

Quantity

bol

SI

Gaussian

Units

Factor

Units

Physical

Name

Symbol

Physical

Name

Symbol

Quantity

of Unit

for Unit

Quantity

of Unit

for Unit

*length

meter

m

electric

volt

V

potential

*mass

kilogram

kg

electric

ohm

Ω

*time

second

s

resistance

*current

ampere

A

electric

siemens

S

*temperature

kelvin

K

conductance

electric

farad

F

*amount of

mole

mol

capacitance

substance

magnetic flux

weber

Wb

*luminous

candela

cd

intensity

magnetic

henry

H

†plane angle

inductance

radian

rad

magnetic

tesla

T

†solid angle

steradian

sr

intensity

frequency

hertz

Hz

luminous flux

lumen

lm

energy

joule

J

illuminance

lux

lx

force

newton

N

activity (of a

becquerel

Bq

radioactive

pressure

pascal

Pa

source)

power

watt

W

absorbed dose

gray

Gy

(of ionizing

electric charge

coulomb

C

radiation)

*SI base unit

†Supplementary unit

METRIC PREFIXES

Multiple

Prefix

Symbol

Multiple

Prefix

Symbol

10−1

deci

d

10

deca

da

10−2

centi

c

102

hecto

h

10−3

milli

m

103

kilo

k

10−6

micro

µ

106

mega

M

10−9

nano

n

109

giga

G

10−12

pico

p

1012

tera

T

10−15

femto

f

1015

peta

P

10−18

atto

a

1018

exa

E

Physical Quantity

Symbol

Value

Units

Boltzmann constant

k

1.3807 × 10−23

J K−1

Elementary charge

e

1.6022 × 10−19

C

Electron mass

me

9.1094 × 10−31

kg

Proton mass

mp

1.6726 × 10−27

kg

Gravitational constant

G

6.6726 × 10−11

m3s−2kg−1

Planck constant

h

6.6261 × 10−34

J s

h¯ = h/2π

1.0546 × 10−34

J s

Speed of light in vacuum

c

2.9979 × 108

m s−1

Permittivity of

ǫ0

8.8542 × 10−12

F m−1

free space

Permeability of

µ0

4π × 10−7

H m−1

free space

Proton/electron mass

mp/me

1.8362 × 103

ratio

Electron charge/mass

e/me

1.7588 × 1011

C kg−1

ratio

Rydberg constant

R∞ =

me4

1.0974 × 107

m−1

2

3

8ǫ0

ch

5.2918 × 10−11

Bohr radius

a0 = ǫ0h2/πme2

m

Atomic cross section

πa02

8.7974 × 10−21

m2

Classical electron radius

re = e2/4πǫ0mc2

2.8179 × 10−15

m

Thomson cross section

(8π/3)re

2

6.6525 × 10−29

m2

Compton wavelength of

h/me c

2.4263 × 10−12

m

electron

h/m¯ ec

3.8616 × 10−13

m

Fine-structure constant

α = e2/2ǫ0hc

7.2974 × 10−3

α−1

137.04

First radiation constant

c1 = 2πhc2

3.7418 × 10−16

W m2

Second radiation

c2 = hc/k

1.4388 × 10−2

m K

constant

Stefan-Boltzmann

σ

5.6705 × 10−8

W m−2K−4

constant

Physical Quantity

Symbol

Value

Units

Wavelength associated

λ0 = hc/e

1.2398 × 10−6

m

with 1 eV

Frequency associated

ν0 = e/h

2.4180 × 1014

Hz

with 1 eV

Wave number associated

k0 = e/hc

8.0655 × 105

m−1

with 1 eV

Energy associated with

hν0

1.6022 × 10−19

J

1 eV

Energy associated with

hc

1.9864 × 10−25

J

1 m−1

Energy associated with

me3/8ǫ02h2

13.606

eV

1 Rydberg

Energy associated with

k/e

8.6174 × 10−5

eV

1 Kelvin

Temperature associated

e/k

1.1604 × 104

K

with 1 eV

Avogadro number

NA

6.0221 × 1023

mol−1

Faraday constant

F = NA e

9.6485 × 104

C mol−1

Gas constant

R = NA k

8.3145

J K−1mol−1

Loschmidt’s number

n0

2.6868 × 1025

m−3

(no. density at STP)

Atomic mass unit

mu

1.6605 × 10−27

kg

Standard temperature

T0

273.15

K

Atmospheric pressure

p0 = n0kT0

1.0133 × 105

Pa

Pressure of 1 mm Hg

1.3332 × 102

Pa

(1 torr)

Molar volume at STP

V0 = RT0/p0

2.2414 × 10−2

m3

Molar weight of air

Mair

2.8971 × 10−2

kg

calorie (cal)

4.1868

J

Gravitational

g

9.8067

m s−2

acceleration

Physical Quantity

Symbol

Value

Units

Boltzmann constant

k

1.3807 × 10−16

erg/deg (K)

Elementary charge

e

4.8032 × 10−10

statcoulomb

(statcoul)

Electron mass

me

9.1094 × 10−28

g

Proton mass

mp

1.6726 × 10−24

g

Gravitational constant

G

6.6726 × 10−8

dyne-cm2/g2

Planck constant

h

6.6261 × 10−27

erg-sec

h¯ = h/2π

1.0546 × 10−27

erg-sec

Speed of light in vacuum

c

2.9979 × 1010

cm/sec

Proton/electron mass

mp/me

1.8362 × 103

ratio

Electron charge/mass

e/me

5.2728 × 1017

statcoul/g

ratio

Rydberg constant

R∞ =

2π2me4

1.0974 × 105

cm−1

ch3

Bohr radius

a0 = h¯2/me2

5.2918 × 10−9

cm

Atomic cross section

πa02

8.7974 × 10−17

cm2

Classical electron radius

re = e2/mc2

2.8179 × 10−13

cm

Thomson cross section

(8π/3)re

2

6.6525 × 10−25

cm2

Compton wavelength of

h/me c

2.4263 × 10−10

cm

electron

h/m¯ ec

3.8616 × 10−11

cm

Fine-structure constant

α = e2/hc¯

7.2974 × 10−3

α−1

137.04

First radiation constant

c1 = 2πhc2

3.7418 × 10−5

erg-cm2/sec

Second radiation

c2 = hc/k

1.4388

cm-deg (K)

constant

Stefan-Boltzmann

σ

5.6705 × 10−5

erg/cm2-

constant

sec-deg4

Wavelength associated

λ0

1.2398 × 10−4

cm

with 1 eV

Physical Quantity

Symbol

Value

Units

Frequency associated

ν0

2.4180 × 1014

Hz

with 1 eV

Wave number associated

k0

8.0655 × 103

cm−1

with 1 eV

Energy associated with

1.6022 × 10−12

erg

1 eV

Energy associated with

1.9864 × 10−16

erg

1 cm−1

Energy associated with

13.606

eV

1 Rydberg

Energy associated with

8.6174 × 10−5

eV

1 deg Kelvin

Temperature associated

1.1604 × 104

deg (K)

with 1 eV

Avogadro number

NA

6.0221 × 1023

mol−1

Faraday constant

F = NA e

2.8925 × 1014

statcoul/mol

Gas constant

R = NAk

8.3145 × 107

erg/deg-mol

Loschmidt’s number

n0

2.6868 × 1019

cm−3

(no. density at STP)

Atomic mass unit

mu

1.6605 × 10−24

g

Standard temperature

T0

273.15

deg (K)

Atmospheric pressure

p0 = n0kT0

1.0133 × 106

dyne/cm2

Pressure of 1 mm Hg

1.3332 × 103

dyne/cm2

(1 torr)

Molar volume at STP

V0 = RT0/p0

2.2414 × 104

cm3

Molar weight of air

Mair

28.971

g

calorie (cal)

4.1868 × 107

erg

Gravitational

g

980.67

cm/sec2

acceleration

Q in the third column. Thus aˆ0 = 4πǫ0h¯2/[(mˆ h/c¯

)(ˆe2ǫ0hc¯ )] = 4π/mˆ eˆ2. (In

transforming from SI units, do not substitute for ǫ0, µ0, or c.)

Physical Quantity

Gaussian Units to SI

Natural Units to SI

Capacitance

α/4πǫ0

ǫ0−1

Charge

(αβ/4πǫ0)1/2

(ǫ0hc¯ )−1/2

Charge density

(β/4πα5ǫ0)1/2

(ǫ0hc¯ )−1/2

Current

(αβ/4πǫ0)1/2

(µ0/hc¯ )1/2

Current density

(β/4πα3ǫ0)1/2

(µ0/hc¯ )1/2

Electric field

(4πβǫ0/α3)1/2

(ǫ0/hc¯ )1/2

Electric potential

(4πβǫ0/α)1/2

(ǫ0/hc¯ )1/2

Electric conductivity

(4πǫ0)−1

ǫ0−1

Energy

β

(¯hc)−1

Energy density

β/α3

(¯hc)−1

Force

β/α

(¯hc)−1

Frequency

1

c−1

Inductance

4πǫ0/α

µ0−1

Length

α

1

Magnetic induction

(4πβ/α3µ0)1/2

(µ0hc¯ )−1/2

Magnetic intensity

(4πµ0β/α3)1/2

(µ0/hc¯ )1/2

Mass

β/α2

c/h¯

Momentum

β/α

h¯−1

Power

β

(¯hc2)−1

Pressure

β/α3

(¯hc)−1

Resistance

4πǫ0/α

(ǫ0/µ0)1/2

Time

1

c

Velocity

α

c−1

Name or Description

SI

Gaussian

Faraday’s law

× E = −

∂B

× E = −

1 ∂B

∂t

c

∂t

Ampere’s law

× H =

∂D

× H =

1 ∂D

4π

+ J

+

J

∂t

c

∂t

c

Poisson equation

· D = ρ

· D = 4πρ

[Absence of magnetic

· B = 0

· B = 0

monopoles]

Lorentz force on

q (E + v

B)

1

×

q E + c v × B

charge q

Constitutive

D = ǫE

D = ǫE

relations

B = µH

B = µH

In a plasma, µ ≈ µ0

= 4π × 10−7 H m−1 (Gaussian units: µ ≈ 1).

The

permittivity satisfies

ǫ

≈ ǫ0 = 8.8542 × 10−12 F m−1 (Gaussian:

ǫ ≈ 1)

2

polarization charge density gives rise to a dielec-

v = E × B/B to calculate

9

2

2

2

tric constant K ≡ ǫ/ǫ0 = 1 + 36π ×10 ρ/B

(SI) = 1 + 4πρc /B

(Gaussian),

where ρ is the mass density.

The electromagnetic energy in volume V is given by

W =

1

ZV dV (H · B + E · D)

(SI)

2

=

1

ZV dV (H · B + E · D)

(Gaussian).

8π

Poynting’s theorem is

∂W

+ ZS N · dS = − ZV

dV J · E,

∂t