The Physics
Opus in profectus

Special Symbols

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Style sheet

These are the conventions used in this book.

Symbols for physical quantities and their international units

Space & Time
symbol quantity symbol unit
r, r position, separation, radius, radius of curvature m meter
s, s displacement, distance m meter
θ, φ, θ, φ angle, angular displacement, angular separation, rotation angle rad radian
x, y, z cartesian coordinates m meter
, , cartesian unit vectors unitless
r, θ, φ spherical coordinates m, rad meter, radian
r̂, θ̂, φ̂ spherical unit vectors unitless
r, θ, z cylindrical coordinates m, rad meter, radian
r̂, θ̂, ẑ cylindrical unit vectors unitless
normal unit vector unitless
tangential unit vector unitless
h height, depth m meter
ℓ, L length m meter
d distance, separation, thickness m meter
t thickness m meter
D diameter m meter
C circumference m meter
A, A area, cross-sectional area, projected area, surface area m2 square meter
V volume m3 cubic meter
t time, duration s second
T period, periodic time s second
τ time constant s second
f frequency Hz hertz
ω angular frequency rad/s radian per second
symbol quantity symbol unit
v, v velocity, speed m/s meter per second
a, a acceleration m/s2 meter per second squared
ac, ac centripetal acceleration, centrifugal acceleration m/s2 meter per second squared
g, g gravitational field, acceleration due to gravity m/s2 meter per second squared
m mass kg kilogram
F, F force N newton
Fg, W, W force of gravity, weight N newton
Fn, N, N normal force, normal N newton
Ff, fs, fk force of friction (static, kinetic) N newton
µs, µk coefficient of friction (static, kinetic) unitless
p, p momentum kg m/s kilogram meter per second
J, J impulse N s newton second
W work J joule
E energy, total energy J joule
K, Kt, Kr kinetic energy (translational, rotational) J joule
U, Ug, Us potential energy (gravitational, spring) J joule
Vg gravitational potential J/kg joule per kilogram
η efficiency unitless
P power W watt
ω, ω rotational velocity, rotational speed rad/s radian per second
α, α rotational acceleration rad/s2 radian per second squared
τ, τ torque N m newton meter
I moment of inertia kg m2 kilogram meter squared
L, L angular momentum kg m2/s kilogram meter squared per second
H, H angular impulse N m s newton meter second
k spring constant N/m newton per meter
P pressure Pa pascal
σ normal stress Pa pascal
τ shear stress Pa pascal
ρ density, volume mass density kg/m3 kilogram per cubic meter
σ area mass density, superficial mass density kg/m2 kilogram per square meter
λ linear mass density kg/m kilogram per meter
FB, B, B buoyancy, buoyant force N newton
qm mass flow rate kg/s kilogram per second
qV volume flow rate m3/s cubic meter per second
FD, R, R drag, aerodynamic drag, air resistance N newton
C, CD drag coefficient, coefficient of drag unitless
η viscosity, dynamic viscosity Pa s pascal second
ν kinematic viscosity m2/s square meter per second
Ma mach number unitless
Re reynolds number unitless
Fr froude number unitless
E young's modulus, modulus of elasticity Pa pascal
G shear modulus, modulus of rigidity Pa pascal
K bulk modulus, modulus of compression Pa pascal
ε linear strain unitless
γ shear strain unitless
θ volume strain unitless
γ surface tension N/m newton per meter
Thermal Physics
symbol quantity symbol unit
T temperature K kelvin
α linear expansivity, coefficient of linear thermal expansion K−1 inverse kelvin
β volume expansivity, coefficient of volume thermal expansion K−1 inverse kelvin
Q heat J joule
c specific heat, specific heat capacity J/kg K joule per kilogram kelvin
L latent heat, specific latent heat J/kg joule per kilogram
n amount of substance mole
N number of particles unitless
P heat flow rate W watt
k thermal conductivity W/m K watt per meter kelvin
ε emissivity unitless
U internal energy J joule
S entropy J/K joule per kelvin
w ways, number of identical microstates unitless
COP coefficient of performance unitless
Waves & Optics
symbol quantity symbol unit
λ wavelength m meter
v, c wave speed m/s meter per second
I intensity W/m2 watt per square meter
L level dB, dNp decibel, decineper
n index of refraction, absolute index of refraction unitless
f focal length m meter
M magnification unitless
Electricity & Magnetism
symbol quantity symbol unit
q, Q charge, electric charge C coulomb
ρ charge density, volume charge density kg/m3 kilogram per cubic meter
σ area charge density, superficial charge density kg/m2 kilogram per square meter
λ linear charge density kg/m kilogram per meter
FE, FE electric force, electrostatic force N newton
E, E electric field N/C, V/m newton per coulomb, volt per meter
ΦE electric flux N m2/C, V m newton meter squared per coulomb, volt meter
U, UE potential energy, electric potential energy J joule
V, VE voltage, potential, electric potential V volt
electromotive force, emf V volt
C capacitance F farad
κ dielectric constant unitless
I current, electric current A ampère
R, r resistance, electrical resistance, internal resistance Ω ohm
ρ resistivity Ω m ohm meter
G conductance S siemens
σ conductivity S/m siemens per meter
FB, FB magnetic force N newton
B, B magnetic field T tesla
ΦB magnetic flux Wb weber
N number of turns   unitless
n turns per unit length, turns density m−1 inverse meter
η energy density J/m3 joule per cubic meter
S, S poynting vector, intensity W/m2 watt per square meter
Modern Physics
symbol quantity symbol unit
γ lorentz factor, lorentz gamma unitless
φ work function J joule
ψ(r,t), ψ(r)φ(t) wave function   unitless
T½ half life s second
D dose, absorbed dose Gy gray
H effective dose Sv sievert

Miscellaneous symbols

Mathematical symbols and notation
symbol description
+ plus, add, positive
minus, subtract, negative
± uncertainty, error, plus-minus
· multiply, dot, dot product, scalar product
× multiply, cross, cross product, vector product
÷, / divide
x2 square
x3 cube
square root, root, radical
cube root
1x, x−1 invert, reciprocal
= equal to, equality
approximately equal to
proportional to
not equal to, inequality
~ on the order of, tilde
< less than
> greater than
less than or equal to
greater than or equal to
⇒, ⇐ logical implication
logical equivalence
and so on, ellipsis
f(x) function
sin sine
cos cosine
tan tangent
sinh hyperbolic sine
cosh hyperbolic cosine
tanh hyperbolic tangent
unit vector, hat, circumflex
mean, average, antiparticle, bar, macron, overline
median, supersymetric particle, tilde
⟨⟩ time average, ensemble average, bracket
p(x) probability distribution, probability density function
Δ increment, change, delta
d differential, d
partial differential, d partial
gradient, del
∇· divergence, div, del dot
∇× curl, del cross
2 laplacian, del squared
summation, sigma
double integral
triple integral
contour integral
surface integral
volume integral
0 transfinite number, aleph null
Greek alphabet (with variants)
letter English name letter English name
Α, α alpha Ν, ν nu
Β, β, ϐ beta Ξ, ξ xi
Γ, γ gamma Ο, ο omicron
Δ, δ delta Π, π, ϖ pi
Ε, ε, ϵ epsilon Ρ, ρ, ϱ rho
Ζ, ζ zeta Σ, σ, ς sigma
Η, η eta Τ, τ tau
Θ, ϴ, θ, ϑ theta Υ, υ upsilon
Ι, ι iota Φ, φ, ϕ phi
Κ, κ, ϰ kappa Χ, χ chi
Λ, λ lambda Ψ, ψ psi
Μ, μ mu Ω, ω omega
Astronomical symbols
symbol celestial body symbol constellation
sun aries
mercury taurus
venus gemini
earth cancer
, moon leo
mars virgo
jupiter libra
saturn scorpius
, uranus sagittarius
neptune capricorn
, pluto aquarius
ceres pisces
Musical symbols
symbol name
flat, semitone lower
natural, no semitone adjustment
sharp, semitone higher