Special Symbols - The Physics Hypertextbook

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Reference

space & time, mechanics, thermal physics, waves & optics, electricity & magnetism, modern physics, mathematics, greek alphabet, astronomy, music

Style sheet

These are the conventions used in this book.

  • Vector quantities (F, g, v) are written in a bold, serif font — including vector quantities written with Greek symbols (α, τ, ω).
  • Scalar quantities (m, K, t) and the magnitudes of vector quantities (F, g, v) are written in an italic, serif font — except for Greek symbols (α, τ, ω), which use a roman serif font.
  • Mathematical symbols use a roman, serif font (½, +, √, cos) — except when they are applied to calculations with units.
  • Units are written with a roman, sans-serif font (m, N, ℃) as are mathematical operations with numbers and units (7 kg × 10 m/s ÷ 3 s = 23.3 N).

Symbols for physical quantities and their international units

Space & Time
symbol quantity symbol SI 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
î, ĵ, k̂ cartesian unit vectors unitless
r, θ, φ spherical coordinates m, rad meter, radian
r̂, θ̂, φ̂ spherical unit vectors unitless
ρ, φ, z cylindrical coordinates m, rad meter, radian
ρ̂, φ̂, ẑ cylindrical unit vectors unitless
n̂ normal unit vector unitless
t̂ 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
Mechanics
symbol quantity symbol SI 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 SI 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 SI 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 SI unit
q, Q charge, electric charge C coulomb
ρ charge density, volume charge density C/m3 coulomb per cubic meter
σ area charge density, superficial charge density C/m2 coulomb per square meter
λ linear charge density C/m coulomb 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
ℰ 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 SI 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 equivalent dose Sv sievert
E effective dose Sv sievert
wR radiation weighting factor unitless
wT tissue weighting factor unitless

Miscellaneous symbols

Mathematical symbols and notation
symbol description
+ plus, add, sum, positive
− minus, subtract, difference, 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
< less than
> greater than
≤ less than or equal to
≥ greater than or equal to
≪ much less than
≫ much greater than
⇒, ⇐ logical implication
⇔ logical equivalence
→ approaches
… and so on
∴ therefore
f(x) function
sin sine
cos cosine
tan tangent
sinh hyperbolic sine
cosh hyperbolic cosine
tanh hyperbolic tangent
x̂ unit vector, x hat
∥ parallel
⟂ perpendicular
x mean, average, antiparticle, x bar
x̃ median, supersymetric particle, x tilde
⟨⟩ time average, ensemble average, bracket
p(x) probability distribution, probability density function
∆ increment, change, delta
d differential, d
∂ partial differential, d partial, del
ẋ time rate of change, first derivative with respect to time, x dot
ẍ second derivative with respect to time, x double dot
x⃛ third derivative with respect to time, x triple dot
∇ gradient, grad, del, nabla
∇ · divergence, div, del dot
∇ × curl, del cross
∇2 laplacian, del squared
∑ summation, sigma
∫ integral
∬ double integral
∭ triple integral
∮ contour integral
∯ surface integral
∰ volume integral
∞ infinity
ℵ0 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, µ mu Ω, 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

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