Dimensional-units

Reality can be described (or defined) in terms of dimension units. There are several ways to do this. The most common method (used on this page) is to define a set of base (fundamental) units, and then describe everything else in terms of derived units.

Farther below is a large table of units (both derived and fundamental), but lets start with the Table of Fundamental Units:

Dimension		Unit		Description
Symbol	Name	Symbol	Name
T	Time	s	second	9192631770 cycles of caesium-133 (¹³³Ce) groundstate hyperfine splitting frequency (at 0 K)
				[1/86400 = 1/(246060)] of an Earth day
L	Length	m	meter	Distance traveled by light (in vacuum) in 1/299792458 of a second
M	Mass	kg	kilogram	1 liter (1 cubic decimeter = 1000 cubic centimeters) of pure water (H₂O) at sea-level-pressure and at 4°C
Q	Electric Charge	C	coulomb	charge of 6.24150913 • 10¹⁸ protons
				negative charge of 6.24150913 • 10¹⁸ electrons
Θ	Temperature	Kelvin	K	1/273.16 of the triple-point of water

This page considers electric charge (Q) as a fundamental unit, in contrast to the SI (a.k.a, "metric system") which considers electric current (I) as the fundamental unit. In other words, the SI considers electric charge to be a derived unit, while this page makes it a fundamental unit.

The SI considers the candella (cd) as the fundamental unit of luminous intensity. It is really just radiant intensity at a specific frequency (540 THz). Since all known light sources, except lasers, produce multiple frequencies, some form of weighting function, specific to human vision, should be employed. The SI doesn't define one, and several methods have been published, so this unit is quite murky and not considered as fundamental on this page.

The SI also considers the mole (mol) to be a dimensional unit. However, it is a pure (dimensionless) number, like a dozen or a hundred; it is a rather large number, approximately 6.0221408×10²³. You may find it listed occasionally in the table below under the column of SI Units, but if you look at the corresponding Dimension Symbol, you should see the mole has no effect on the physical dimension.

Similarly, both plane angles and solid angles have no real physical dimension, but for a different reason. The way these are defined, the dimension of length (L) gets cancelled out. Thus a plane angle is listed with a length dimension of L^1-1 because it is a length (L¹) divided by a length, and a solid angle is listed as L^2-2 because it is an area (L²) divided by an area.

In case you didn't already know and the above didn't make it clear, negative exponents in the dimensional symbol refers to division by that dimension. For example, meters per second (or miles per hour, etc.) has dimensional symbol L¹T^-1 because it is length divided by time (notice length has a positive exponent, while time has a negative exponent).

Usually, dimensions which do not appear in a unit of measurement are simply omitted. For consistency, I have included all the base dimensions described above for each unit in the table below. Those dimensions which are not present have an exponent of zero. For example, length is listed as L¹T⁰M⁰Q⁰Θ⁰.

3 Types of Symbols

One thing that confuses many beginning students of algebra and physics is that the same symbol can have very different meanings in different contexts. Even professionals sometimes misunderstand the meaning of a symbol. The main reason for this is there are many more concepts than there are letters of the Roman and Greek alphabets. To prevent confusion (as much as possible), I will tell you this page has three (3) different types of symbols:

Dimensional Symbols (1st column below) are described in the table above; briefly: L=Length, T=Time, M=Mass, Q=Charge, Θ=Temperature
SI Unit Symbols (3rd column below) are defined by international standard; examples include: L=liter, T=Tesla or Tera, M=Mega, m=meter or milli, s = second, and many more!
Math Symbols (5th column below) are commonly used in engineering and mathematical formulas (there is no official standard for all, but a few are defined by SI or ISO)

In general, all symbols should be considered case-sensitive. In particular, the second type (SI Unit Symbols) can be confusing because the same symbol (for example m) could mean two different things in the same (SI Unit) context. Fortunately for you, I have included the corresponding name of the SI Symbol in the 4th column; this should resolve any ambiguity.

The final Description column (in the table below) describes a dimensional unit in English text and often with SI Unit Symbols. For example, a Watt-Hour may be described as "3600 J" which means "3600 joules" because J is the SI symbol for joule. However, it is often informative to have a description in terms of engineering/math symbols. When math symbols appear in the Description column, they will be enclosed in square brackets; for example, heat capacity (entropy) may be described as energy / temperature [E/T]. Note the E and T shown in square brackets are math symbols (not dimensional symbols nor SI symbols). In summary, the description column uses English text with SI symbols in general, but also includes math symbols in square brackets for extra information.

Colored Units

Under "SI Units" (columns 3 and 4 in the table below), most entries are "official" (explicitly listed or implicitly endorsed) by the SI system; these have a normal (white) background color. Some of them are "recognized" or considered "acceptable" with the SI system; these have a yellow background (the most popular is the liter). A few are not recognized (perhaps even forbidden) by the SI system, but are shown here because they are used by people anyway (for example kilowatt-hour, kW•hr), and some of these have no official SI unit; these have a light-red background.

To keep this page relatively short, I have included only SI Units (as much as possible). There are other metric but non-SI units in use (such as currie, dyne, and cubic centimeter), and many other non-metric units in common use (such as miles and pounds). These would also be shown with a light-red background if included (but that would greatly multiply the size of this page).

Extra Subscripts

Several of the "Math Symbols" (5th column below) may include a subscript letter(s) to be consistent and precise. Some of these will rarely be seen in other documentation, because of their limited scope; few papers span all possible dimensional units! A good example is Einstein's famous equation, which is most often written: E = mc². The context of most documents which use that form implies that E is mass-energy (and not kinetic energy or something else), and c is light-speed (and not some other speed, like the speed of sound). On this page, the same equation would be written with subscripts: E_M = mc₀². The symbol E_M is for mass-energy, and c₀ is for light-speed.

Some subscripts are generic (often "i" and "n"). For example, the math symbol for molar concentration is c_i when referring to an unknown, but might written as c_H when referring to Hydrogen or c_Ar when referring to Argon.

Before we dive into the details, it is important to note that other dimensional units are possible. Here are three good examples:

Time could be defined in terms of length (or vice versa), according to Einstein/Lorentz relativity
Mass could be defined in terms of length, according to Schwartzchild radius
Electric charge could be defined in terms of the square root of mass times length (√M•L)

Anyway, below is a list of dimensional units, sorted in the order of (first) Length, Time, Mass, Charge, and (finally) Temperature...

Dimension		SI Unit		Math Symbol(s)	Description
Symbol	Name(s)	Symbol	Name	Math Symbol(s)	Description
L^-3T^-1M⁰Q⁰Θ⁰	Catalytic Concentration	kat/m³	katals per cubic meter	?	catalytic activity / unit volume [z/V]; 1 mkat/L
L^-3T⁰M⁰Q⁰Θ⁰	Molarity, [Molar] Concentration	mol/m³	moles per cubic meter	c_i	moles / unit volume [n_m/V]; 1 mmol/L
	Molarity, [Molar] Concentration	mol/L, M	moles per liter	c_i	moles / liter [n_m/V]; reciprocal of molar volume [1/V_m]; 1 kmol/m³
	Number Concentration	m^-3	per cubic meter	C_i	number of particles per unit volume [n/V]
	Acidity,Basicity	*	power of Hydrogen	pH, P_H	approximately, negative decimal logarithm of hydrogen molar concentration [-log₁₀ c_H]; pure H₂O has pH = 7.0; acids are less (lemon pH ≈ 2.2), bases are more (bleach pH ≈ 13.0)
L^-3T⁰M⁰Q¹Θ⁰	Charge Density	C/m³	coulombs per cubic meter	ρ_q	electric charge / volume [Q/V]
L^-3T⁰M¹Q⁰Θ⁰	[Mass] Density	kg/m³	kilograms per cubic meter	ρ	mass / unit volume [m/V]; 1 kg/m³ = 0.0010 kg/L = 1 g/L
L^-3T¹M¹Q⁰Θ⁰	Toxic Exposure	s kg/m³	second-kilograms per cubic meter	E	mass density * time period [ρ•t]; may be multiplied by "toxicity factor" for the type of toxin
L^-2-1T¹M^-1Q²Θ⁰	Conductivity, Admittivity, Susceptivity	S/m	siemans per meter	κ, ?, ?	conductance * distance / area [C•r/A] = reciprocal of resistivity [1/ρ]; 1 S/m = 1 A/(V m)
L^-3T²M^-1Q²Θ⁰	[Electric] Permittivity	F/m	ferads per meter	ε	capacitance / distance [C/r]
L^-3T²M^-1Q²Θ⁰	[Electric] Permittivity	F/m	vacuum permittivity	ε₀	[1/c₀²μ₀]; ≈ 8.854187817 pF/m
L^-2T^-2M^1-1Q⁰Θ^-1	Specific Heat Capacity	J/(K kg)	joules per kelvin per kilogram	h	heat capacity / mass [H/m] = energy / temperature / mass [E/(T•m)]
L^-2T^-2M¹Q⁰Θ⁰	Force Density, Specific Weight	N/m³	newtons per cubic meter	f	force / volume [F/V] = acceleration * density [a•ρ] = standard gravity * density [g•ρ]
L^-2T^-1M⁰Q¹Θ⁰	Current Density	A/m²	amperes per square meter	J	current / directed area [I/S] = charge density * velocity [ρ_q•v]; electric field * conductivity [E•κ]
L^-2T^-1M¹Q⁰Θ⁰	Momentum Density	N s/m³	newton seconds per cubic meter	g	momentum / volume [p/V]; permittivity * electric field * magnetic field (ε•E×B
	Advective Flux	N s/m³	newton seconds per cubic meter	?	volumetric flux * density [q•ρ] = velocity * density [v•ρ]
	Mass Flux	kg Hz/m²	kilogram hertz per square meter	J_m	mass flow rate / directed area [ṁ/S] = momentum / volume [p/V]
L^-2T⁰M^-1Q²Θ⁰	Reluctance	H^-1	per Henry	R	current / magnetic flux [I/Φ_B] = reciprocal of permeance [1/P]
L^-2T⁰M⁰Q¹Θ⁰	Polarization Density	C/m²	coulombs per square meter	P_e	electric dipole / volume [δp/V]; vacuum permittivity * electric susceptibility * electric field [ε₀χ_eE]
L^-2T⁰M⁰Q¹Θ⁰	Electric Displacement	C/m²	coulombs per square meter	D	vacuum permittivity * electric field + polarization density [ε₀E+P_e = ε(1+χ_e)E]
L^-2T¹M^-1Q²Θ⁰	Conductance, Admittance, Subsceptance	S	Sieman	G, Y, B	reciprocal ohm [1/R] = 1/Ω; current / voltage [I/V]
L^-2T¹M^-1Q²Θ⁰	Magnetic Capacitance	Ω^-1	per ohms	x_C	reciprocal of (angular frequency * magnetic capacity) [1/(ω•C_M)]
L^-2T²M^-1Q⁰Θ⁰	Coldness	nat/J	natural entropy per joule	β_T	thermodynamic beta = change in (entropy / energy) / Boltzman's constant [δH/(δE•k_B)]; 1 nat/J ≈ 1.442969504089 Sh/J
L^-2T²M^-1Q¹Θ⁰	Charge Affinity	C/J	coulombs per joule	ε_p	reciprocal voltage [1/V] = charge / energy [Q/E] = current / power [I/P]
L^-2T²M^-1Q²Θ⁰	Capacitance	F	ferad	C	charge / electric potential [Q/V]; reciprocal of elastance [1/P]; 1 F = 1 J/V²
L^-2T²M^-1Q²Θ⁰	Capacitance	C²/J	square coulombs per joule	C	square charge / energy [Q²/E]; 1 C²/J = 1 F
L^1-2T^-2M¹Q⁰Θ^-1	Volumetric Heat Capacity	J/(K m³)	joules per kelvin per cubic meter	VHC	heat capacity / volume [H/V] = molar heat capacity / molar volume [H_m/V_m] = energy / temperature / volume [E/(T•V)]
	Volumetric Heat Capacity	N/(m²K)	newtons per square meter per kelvin	VHC	force / area / temperature [\|F\|/(A•T)] = pressure / temperature [\|P\|/T]; 1 J/(Km³)
	Entropy Density	nat/m³	nats per cubic meter	s	entropy / volume [H/V]; 1 nat/m³ ≈ 13.80648 yJ/(Km³)
L^1-2T^-2M¹Q⁰Θ⁰	Pressure, Stress, Energy Density	Pa	Pascal	P	force / area [F/A]
		N/m²	newton per square meter	P	force / area [F/A]
		J/m³	joules per cubic meter	ρ_E	energy / volume [E/V]
L^1-2T^-1M⁰Q¹Θ⁰	Magnetic Field	N/Wb	newtons per weber	H	force / electric potential / time [F/(V•t)]; 1 A/m; 1 T•m/H
	Magnetic Field	T•m/H	tesla meters per second	H	magnetic flux density / permeability [B/μ]; 1 A/m; 1 N/Wb
	Magnetization	A/m	amperes per meter	M	magnetic dipole moment / volume [μ/V] = magnetic susceptibility * magnetic field [χ_mH]
L^-1T^-1M¹Q⁰Θ⁰	[Dynamic\|Shear] Viscosity	kg/(m s)	kilograms per meter per second	η, μ	mass / absition [m/\|A\|]; 1 Pa•s
L^1-2T^1-2M¹Q⁰Θ⁰		N s/m²	newton second per square meter		momentum / area [\|p\|/A]; 1 Pa•s
L^1-2T^1-2M¹Q⁰Θ⁰		PI	poiseuille		pressure * time [\|P\|•t] = reciprocal of fluidity [1/φ]; 1 Pa•s
L^1-2T⁰M^-1Q²Θ⁰	Reluctivity	m/H	meters per henry	?	reciprocal permeability [1/μ] = conductance * speed [G•\|v\|]; 1 S•m/s
L^-1T⁰M⁰Q⁰Θ⁰	Wavenumber	m^-1	per meter	ν	cycles / distance [n/r] = reciprocal wavelength [1/λ] = frequency / phase velocity [f/\|v_φ\| = ν/\|v_φ\|]
	Pixel Density	PPI, DPI	pixels [dots] per inch	?	Usually, a color pixel consists of 3 dots, so DPI and PPI are different for color images.
	Optical Power	diop, dpt	diopter	φ	reciprocal of focal-length [1/\|r\| = 1/f]; 1 m^-1
L^1-2T⁰M⁰Q⁰Θ⁰	Angular Wavenumber	rad/m	radians per meter	k	2π / wavelength [2π/λ] = angular velocity / phase velocity [ω/\|v_φ\|]; for a photon, k = 2πE/(hc₀)
L^-1T²M^-1Q⁰Θ⁰	Fuel Economy	m/J	meters per joule	FE	"energy efficiency in transportation"; distance / energy [r/E] = reciprocal force [1/\|F\|]; 1 N^-1; 1 m/J = 3600 m/(W•hr) ≈ 753.847530422 mi/gal_US
L^-1T²M^-1Q¹Θ⁰	Electric Strain	C/N	coulombs per newton	d	charge / force [Q/F] = reciprocal electric field [1/E]
L^-1T²M^-1Q¹Θ⁰	Electric Strain	m/V	meters per volt	d	distance / electric potential [r/V]; 1 m/V = 1 C/N
L^1-1T^-3M⁰Q⁰Θ⁰	Angular Jerk	rad/s³	radians per cubic second	ζ	angular acceleration / time period [α/t]
L^2-2T^-3M¹Q⁰Θ⁰	Luminance	W/m²	watts per square meter	?	radiant exposure / time [H_e/t]
	Luminance	cd/m²	candella per square meter	L_v	luminous flux / solid angle / directed area [Φ_v/(Ω•S)] = luminous intensity / directed area [I_v/S] = 1 W/m² @ 540 THz
	Illuminance	lx	lux	E_v	luminous flux / area [Φ_v/A]; 1 lm/m² ≈ 1.46413 mW/m² @ 540 THz
	Irradiance	W/m²	watts per square meter	E_e	radiant flux / area [Φ_e/A]
	Radiance	W/(sr m²)	watts per steradian per square meter	L_e	radiant flux / solid angle / directed area [Φ/Ω/S] = radiant intensity / directed area [I_e/S]
L^1-1T^-2M⁰Q⁰Θ⁰	Angular Acceleration	rad/s²	radians per square second	α	angular velocity / time period [ω/t]
L^2-2T^-2M^1-1Q⁰Θ⁰	Specific Radiant Exposure	J/(m²kg)	joules per square meter per kilogram	?	radiant exposure / mass [H_e/m] = force / leverage [\|F\|/\|Λ\|] = square frequency [f² = ν²]; 1 J/(m²kg) = 1 N/(m•kg) = 1 Hz²
L^2-2T^-2M¹Q⁰Θ⁰	Radiant Exposure	J/m²	joules per square meter	H_e	irradiance * time [E_et] = radiant energy / area [Q_e/A]
	Luminous Exposure	lx s	lux-second	H_v	illuminance * time [E_vt] = luminous energy / area [Q_v/A]; 1 lx•s ≈ 1.46413 mJ/m₂@ 540 THz
	Spectral Irradiance_ν	W/(m²Hz)	watts per square meter per hertz	E_e,v	irradiance / frequency [E_e/ν] = radiance * solid angle / frequency [L_e•Ω/ν]
	Spectral Radiance_ν	W/ (sr m²Hz)	watts per steradian per square meter per hertz	L_e,v	radiance / frequency [L_e/ν] = radiant flux / solid angle / area / frequency [Φ_e/(Ω•S•ν)]
L⁰T^-1M^-1Q⁰Θ⁰	Specific Activity	Bq/kg	bacquerel per kilogram	a	decay constant * Avagrado's number / molar mass [λ•N_A/m_m] = activity / mass [A/m]; natural log 2 / half-life * Avagrado's number / molar mass [(N_Aln 2)/(t_1/2m_m)]; 1 Hz/kg
L⁰T^-1M^-1Q⁰Θ⁰	Specific Activity	(s kg)^-1	per second per kilogram	a	reciprocal of mass exposure [1/?]; 1 (s kg)^-1 = 1 Hz/kg = 1 Bq/kg
L⁰T^-1M⁰Q⁰Θ⁰	Frequency	Hz	hertz	f, ν	cycles per second [n/t]; 1 s^-1
	[Radio]Activity	Bq	becquerel	A	nuclear decays per time period [n/t]; 1 Hz
	Catalytic Activity	kat	katal	z	quantity of substance that converts another substance at 1 mole / second
L^2-2T^-1M^1-1Q⁰Θ⁰	Fluid Exchange Rate	Pa/PI	pascals per poiseuille	?	force / viscosity / area [\|F\|/(η•A)] = pressure / viscosity [\|P\|/η]; 1 Hz
L^2-2T^-1M^1-1Q⁰Θ⁰	Fluid Exchange Rate	ACH	air changes per hour	?	fluid flow rate / volume [Q/V]; 277.77 μHz
L^1-1T^-1M⁰Q⁰Θ⁰	Angular Speed	rad/s	radians per second	ω	2π * frequency [2πf = 2πν] = tangential speed / radius [\|v\|/r]; 1 rad/s ≈ 57.2957795 °/s
L^1-1T^-1M⁰Q⁰Θ⁰	Angular Velocity	rad/s	radians per second	ω	(r × v) / r²; the omega vector is perpendicular to both r and v; 1 rad/s ≈ 159.154943 mHz
L⁰T^-1M⁰Q¹Θ⁰	[Electric] Current	A	ampere	I	electric charge / time [Q/t] = voltage / resistance [V/R]; 1 A = 1 C/s = V/Ω
L^2-2T^-1M¹Q^-1Θ⁰	Magnetic Flux Density	T	tesla	B	magnetic flux / directed area [Φ_B/S]; 1 T = 1 Wb/m²
L^2-2T^-1M¹Q^-1Θ⁰	Magnetic Flux Density	Wb/m²	webers per square meter	B	magnetic flux / directed area [Φ_B/S]; 1 T = 1 Wb/m²
L⁰T^-1M¹Q⁰Θ⁰	Mass Flow Rate, Mass Current	kg/s	kilograms per second	ṁ	mass / time [m/t] = density * fluid flow rate [ρ•\|Q\|]; density * volumetric flux * directed area [ρ•q•S]; 1 kg/s = 1 kg•Hz
L⁰T⁰M^-1Q¹Θ⁰	Ionizing Exposure, Specific Charge	C/kg	coulombs per kilogram	γ	charge / mass [Q/m]
	Gyromagnetic Ratio	e^-/m_e	electron charge-to-mass ratio	γ_e	≈ -175.88200 GC/kg
	Gyromagnetic Ratio	p⁺/m_p	proton charge-to-mass ratio	γ_p	≈ +95.788332 MC/kg
L^3-3T⁰M⁰Q⁰Θ^-1	Coefficient of Thermal Expansion	m/(mK) m²/(m²K) m³/(m³K)	*dim* meters per *dim* meter per kelvin	α_L^_,α_A^_,α_V	change in (length / temperature) / length [(δr/δT)/r] change in (area / temperature) / area [(δA/δT)/A] change in (volume / temperature) / volume [(δV/δT)/V]
L^3-3T⁰M⁰Q⁰Θ^-1	Coldness	1/K	reciprocal kelvin	β_T	reciprocal temperature [1/T] = thermodynamic beta * Boltzman's constant [β•k_B]; 1/K ≈ 13.80648 ynat/J
L⁰T⁰M^1-1Q⁰Θ⁰	Mass Fraction	kg/kg	parts per million\|billion...	w_i	component mass / total mass[m_i/m]
L⁰T⁰M^1-1Q⁰Θ⁰	Mass Ratio	kg/kg	parts per million\|billion...	ζ_i	component mass / remaining mass [m_i/(m-m_i)]
L⁰T⁰M^1-1Q⁰Θ^1-1	Adiabatic Index	JK/(JK)	joule kelvins per joule-kelvin	γ	ratio of fixed-pressure to fixed-volume heat capacities [C_p/C_v]
L^1-1T⁰M⁰Q⁰Θ⁰	Plane Angle	rad	radian	θ, φ	2π radians per revolution; 1 rad ≈ 57.2957795131°
L^1-1T⁰M⁰Q⁰Θ⁰	?	π	pi		ratio of circumference of a circle to its diameter; π ≈ 3.14159265359
L^1-1T^1-1M⁰Q^1-1Θ⁰	Magnetic Susceptibility		magnetic susceptibility	χ_m	magnetization / magnetic field [M/H]; vacuum χ_m = 0
	Magnetic Susceptibility		relative permeability	μ_r	1 + magnetic susceptibility [1+χ_m] = permeability / vacuum permeability [μ/μ₀]
	Magnetic Modulus?			M_m?	reciprocal relative permeability [1/μ_r]
L^2-2T⁰M⁰Q⁰Θ⁰	Solid Angle	sr	steradian	Ω	4π steradians per sphere; 2π/3 sr per cube face measured from cube center
L^2-2T⁰M⁰Q^1-1Θ⁰	Electric Susceptibility		electric susceptibility	χ_e	polarization density / electric field / vacuum permittivity [P_e/(E•ε₀)]; polarization density / (electric displacement - polarization density) [P_e/(D-P_e)]; vacuum χ_e = 0
	Electric Susceptibility		relative permeability	ε_r	1 + electric susceptibility [1+χ_e] = permittivity / vacuum permittivity [ε/ε₀]
	Electric Modulus			M_e	reciprocal relative permittivity [1/ε_r]
L^2-2T^2-2M^1-1Q⁰Θ⁰	Energy Effeciency, Energy Intensity	J/J	joules per joule	?	energy efficiency = output energy / input energy [E_o/E_i]; energy intensity = input energy / output energy [E_i/E_o]
L^2-2T^3-3M^1-1Q⁰Θ⁰	Power Ratio, Power Effeciency, Power Intensity	W/W	watts per watt	?	power efficiency = output power / input power [P_o/P_i]; power intensity = input power / output power [P_i/P_o]
		dB	decibel	L_p	10 log₁₀ (measured power / reference power) [10 log₁₀ (P/P₀) = 10 log₁₀ (V²/V₀²)]
		dB	decibel	L_f	20 log₁₀ (measured field / reference field) [20 log₁₀ (V/V₀)]
L^3-3T⁰M⁰Q⁰Θ⁰	Volume Fraction	m³/m³	cubic meters per cubic meter	φ_i	component volume / total volume [V_i/V]
L⁰T⁰M⁰Q⁰Θ¹	Temperature	K	kelvin	T	0 K is 273.16 °C below triple point of water (which is defined as 0.01 °C)
L⁰T⁰M⁰Q¹Θ⁰	[Electric] Charge	C	coulomb	Q	electric current * time [I•t]; charge of approximately 6.24150913 Ee (quintillion protons)
L⁰T⁰M¹Q⁰Θ⁰	Mass, Inertia	kg	kilogram	m	originally, mass of one liter of water at 4°C at sea-level pressure
L⁰T⁰M¹Q⁰Θ⁰	Mass, Inertia	eV/c²	electron-volts per light-speed squared	?	1 eV/c² ≈ 160.217662 zJ ≈ 1.78266191•10^-36 g (per Einstein's mass/energy equivalence)
L⁰T¹M⁰Q⁰Θ⁰	Time	s	second	t	9192631770 cycles of caesium-133 (¹³³Ce) groundstate hyperfine splitting period (at 0 K)
L⁰T¹M⁰Q⁰Θ⁰	Time	F Ω	farad ohm	t	capacitance * resistance [C•R] = inductance / resistance [L/R]; 1 H/Ω = 1 s
L⁰T¹M⁰Q⁰Θ¹	???	K s	kelvin-second	k_DTS	Dam Thanh Son limit = viscosity / entropy density [η/s]; reduced plank constant / 4π / Boltzman's constant [ℏ/(4π•k_B] ≈ 607.8306 fKs
L⁰T¹M¹Q⁰Θ⁰	Mass Exposure	kg/Bq	kilogram per bacquerel	?	reciprocal specific activity [1/a] = mass / activity [m/A] = action / absorb dose [S/D]; 1 Js/Gy
L⁰T¹M¹Q⁰Θ⁰	Mass Exposure	s kg	second-kilogram	?	time * mass [t•m] = toxic exposure * volume [E•V] = payload distance / speed [Λ/v]; 1 kg/Hz
L⁰T²M⁰Q⁰Θ⁰	?	s²	square second	t²	time period / frequency [t/f = t/ν]; 1 s/Hz
L⁰T²M⁰Q⁰Θ⁰	?	F H	farad henry	t²	capacitance * inductance [C•L]; 1 s²
L¹T^-3M⁰Q⁰Θ⁰	Jerk	m/s³	meters per cubic second	j	acceleration / time period [a/t]
L¹T^-3M¹Q⁰Θ^-1	Thermal Conductivity	W/(m•K)	watts per meter-kelvin	?	spectral flux in wavelength / temperature [Φ_e,λ/T]
L¹T^-3M¹Q⁰Θ^-1	Thermal Conductivity	N/(s•K)	newtons per second-kelvin	?	yank / temperature [Y/T]; 1 W/(m•K)
L¹T^-3M¹Q⁰Θ⁰	Yank	N/s	newtons per second	Y	force / time period [F/t] = energy / absition [E/A]; 1 J/(m•s)
L¹T^-3M¹Q⁰Θ⁰	Spectral Flux_λ	W/m	watts per meter	Φ_e,λ	radiant flux / wavelength [Φ_e/λ] = power / distance [P/\|r\|]
L¹T^-2M⁰Q⁰Θ⁰	Acceleration	m/s²	meters per square second	a, g	velocity / time period [v/t]; standard (Earth surface) gravity [g_c]= 9.806650 m/s²
L¹T^-2M⁰Q⁰Θ⁰	Specific Force	N/kg	newtons per kilogram	\|a\|	force / mass [\|F\|/m]
L¹T^-2M¹Q^-1Θ⁰	Electric Field, Electric Flux Density	N/C	newtons per coulomb	E	force / charge [F/Q]
		V/m	volts per meter		electric potential / distance [V/r]; 1 N/C
		C/(F•m)	coulombs per ferad-meter		(electric displacement - polarization density) / vacuum permittivity [(D-P_e)/ε₀] electric displacement / permittivity [D/ε]; 1 N/C
		J/(C•m)	joules per coulomb-meter		energy / charge / distance [E/(Q•r)]; 1 N/C
		W/(A•m)	watts per ampere-meter		power / current / distance [P/(I•r)] = power / charge / velocity [P/(Q•v)]; 1 N/C
L¹T^-2M¹Q⁰Θ^-1	Thermic Force?	N/K	newtons per kelvin	?	force / temperature [\|F\|/T] = delta (entropy / distance) [δH/(δr)]
L¹T^-2M¹Q⁰Θ⁰	Force, Weight	N	newton	F	mass * acceleration [m•a] = momentum / time period [p/t]; 1 kg•m/s²; magnetic flux * magnetic field [Φ_BH] = charge * electric field [Q•E]; 1 N = Wb•A/m = 1 C•V/m
	Fuel Consumption	J/m	joules per meter	FC	"energy intensity in transportation"; energy / distance [E/r]; 1 N; 322 J/m ≈ 1 L_petrol/(100 km)
	Fuel Consumption	kW hr/km	kilowatt-hours per kilometer	FC	energy / distance [E/r]; 1 kW•hr/km = 3600 J/m = 3600 N
L¹T^-1M⁰Q⁰Θ⁰	Speed, Velocity	m/s	meters per second	c, v, v	distance / time period [r/t]; 1 m/s = 1 kL•Hz/m²
	Speed, Velocity		light-speed	c₀	speed of light in vacuum: 299792458 m/s (by definition)
	Volumetric Flux	L Hz/m²	liter hertz per square meter	q	fluid flow rate / directed area [Q/S]; 1 L•Hz/m² = 1 mm/s
L¹T^-1M^1-1Q⁰Θ⁰	Specific Momentum	N s/kg	newton-seconds per kilogram	v	momentum / mass [p/m]; 1 m/s
L¹T^-1M⁰Q¹Θ⁰	Magnetic Pole Strength	A m	ampere-meters	q_m	magnetization * directed area [M•S]
L¹T^-1M⁰Q¹Θ⁰	Magnetic Pole Strength	C m/s	coulomb-meters per second	q_m	charge * speed [Q•\|v\|]; 1 Am
L¹T^-1M¹Q^-1Θ⁰	Magnetic Potential	T•m	tesla-meters	A	curl of magnetic flux density [∇×B]
		N/A	newtons per ampere		force / current [F/I] = momentum / charge [q/Q]; 1 T•m
		Wb/m	webers per meter		magnetic flux / distance [Φ_B/r]; 1 T•m
L¹T^-1M¹Q⁰Θ⁰	Momentum	kg m/s	kilogram-meters per second	p	mass * velocity [m•v] = √2 * mass * kinetic energy [√2m•E_k] = leverage / time [d/t] = density * volume * phase velocity [ρ•V•v]; 1 N•s
L¹T^-1M¹Q⁰Θ⁰	Impulse	N s	newton-second	p	delta momentum [δp] = force * time period [f•t] = charge * magnetic potential [Q•A]; 1 kg•m/s = 1 N•s = C•N/A
L¹T⁰M⁰Q⁰Θ⁰	Length	m	meter	r, d, x, y, z	1/299792458 of a light-second; approximately 1/40000000 of Earth's polar circumference
		m	Wavelength	λ	distance of 1 cycle in a wave; phase velocity / frequency [\|v_φ\|/f = \|v_φ\|/ν]; for a photon, λ = c₀/ν
		ly	light-year	?	distance traveled in 1 Julian year (365.25 Earth days) at light-speed; 9.46073047258080 Pm
L¹T⁰M⁰Q¹Θ⁰	Electric Dipole Moment	C m	coulomb-meters	Δp	(charge₊ - charge_-) / 2 / (position₊ - position_-) [δQ/(2r)]
L¹T⁰M¹Q^-2Θ⁰	[Magnetic] Permeability	H/m	henries per meter	μ	inductance / distance [L/r] = reciprocal of reluctivity [1/?]
		N/A²	newtons per square ampere	μ	force / square current [\|F\|/Q²]; 1 H/m; relative permeability * vacuum permeability [μ_rμ₀]
			vacuum permeability	μ₀	400 π nH/m ≈ 1.256637061 μH/m
L¹T⁰M¹Q⁰Θ⁰	Payload Distance	m kg	meter-kilogram	Λ ?	distance * mass [r•m] = momentum * time [p•t]
	Leverage	m kg	meter-kilogram		arm-length * mass [r•m] = rotational inertia / radius [I/r]
	Leverage	N/Hz²	newtons per square hertz		torque / acceleration [τ/a = (a × τ)/a²]; 1 m•kg
L¹T¹M^-1Q⁰Θ⁰	Fluidity	m•s/kg	meter-seconds per kilogram	φ	distance * time / mass [r•t/m] = absition / mass [\|A\|/m]
L¹T¹M^-1Q⁰Θ⁰	Fluidity	PI^-1	reciprocal poiseuille	φ	reciprocal viscosity [1/η]; 1 PI^-1 = 1 Hz/Pa
L¹T¹M⁰Q⁰Θ⁰	Absition, Absement	m s	meter second	A	distance * time period [r•t]
L^2-1T²M^-1Q⁰Θ⁰	Compressability	Pa^-1	reciprocal pascal	β	reciprocal pressure [1/\|P\|] = area / force [A/\|F\|]
		m²/N	square meters per newton		area / force [A/\|F\|] = 1 / density / square phase velocity [1/(ρv²)]
		m³/J	cubic meters per joule		volume / energy [V/E]; 1 m³/J = 1 kL/J
L²T^-3M^1-1Q⁰Θ⁰	Specific Power	W/kg	watts per kilogram	?	power / mass [P/m] = energy / mass exposure [E/(m•t)]; 1 J/(kg•s); 1 Gy/s
	Absorbtion Rate	Gy/s	grays per second		absorbed dose / time period [D/t] = absorbed dose * activity [D•A]; 1 Gy•Bq; 1 W/kg
	Dose Rate	rem/dy	rems per day		1/24 rem/hr = 1/86400 rem/s = 11.5740 μrem/s = 115.740 nSv/s
		MET	metabolic equivalent of task		energy / mass / time [E/(m•t)]; 1 kcal/(kg•hr) = 1.162 W/kg; 1 MET ≈ human sitting
L²T^-3M¹Q⁰Θ⁰	Rotatum	N m/s	newton-meters per second	R	delta torque / time period [δτ/t] = rotational inertia * angular jerk [I•ζ] = force * velocity [F×v]
	Power	W	watt	P	energy / time period [E/t]; 1 J/s; torque * angular velocity [τ•ω]; 1 JHz
		N m/s	newton-meters per second		force * velocity [F•v]; 1 W
		V A	volt amperes		electric potential * electric current [V•I]; 1 W
		A²Ω	square ampere ohm		square electric current * resistance [I²•R]; 1 W
		V²/Ω	square volts per ohm		square electric potential / resistance [V²/R]; 1 W
	Radiant Flux	W	watt	Φ_e	radiant intensity * solid angle [I_eΩ]
	Radiant Intensity	W/sr	watts per steradian	I_e	radiant flux / solid angle [Φ_e/Ω]
	Luminous Flux	lm	lumen	Φ_v	luminous intensity * solid angle [I_vΩ]; 1 cd•sr; 1/683 W @ 540 THz
	Luminous Flux	cd sr	candella-steradian	Φ_v	1 lm; 1 cd over full sphere = 4π cd•sr ≈ 12.56643706144 lm ≈ 18.3987856726 mW @ 540 THz
	Luminous Intensity	cd	candella	I_v	luminous flux / solid angle [Φ_v/Ω]; 1/683 W/sr (≈ 1.46412884334 mW/sr) @ 540 THz
L²T^-2M^1-1Q⁰Θ⁰	Specific Energy	J/kg	joules per kilogram	?	energy / mass [E/m] = work / mass [W/m] = torque / mass [\|τ\|/m]; 1 N•m/kg
	Absorbed Dose	Gy	gray	D	energy / mass [E/m]; 1 Gy = 1 J/kg = 100 RAD (radiation absorbed dose)
	Absorbed Dose	m²/s²	square meters per square second	D	area / square time [A/t²] = velocity squared [v•v]; 1 Gy
	Equivalent Dose	Sv	sievert	H	radiation weight * absorbed dose [W•D]; 1 Gy of "X-Rays" has 5.5% risk of 'eventual' cancer
	Equivalent Dose	rem	Roentgen equivalent man	H	10 mSv = 10 mGy of 'X-Rays' = 1 RAD of 'X-Rays'; has 0.055% risk of 'eventual' cancer
L²T^-2M¹Q^-2Θ⁰	Elastance	F^-1	per farad, daraf	P	reciprocal capacitance [1/C]
		V/C	volts per coulomb		electric potential / electric charge [V/Q]; 1 F^-1
		J/C²	joules per square coulomb		energy / square charge [E/Q²]; 1 F^-1
		Ω/s	ohms per second		resistance / time period [R/t]; 1 F^-1
L²T^-2M¹Q^-1Θ⁰	Electric Potential, Voltage	V	volt	V	reciprocal charge affinity [1/ε_p]; electric field * distance [E•r]
		J/C	joules per coulomb		energy / electric charge [E/Q]; 1 V
		W/A	watts per ampere		power / electric current [P/I]; 1 V
		Wb/s	webers per second		magnetic flux / time period [Φ_B/t] = magnetic potential * velocity [A•v]; 1 V
		C/F	coulombs per farad		electric charge / capacitance [Q/C]; 1 V
		A Ω	ampere-ohm		electric current * resistance [I•R]; 1 V
L²T^-2M¹Q⁰Θ^-1	Molar Heat Capacity	J/(K mol)	joules per kelvin-mole	H_m	energy / temperature / #moles [E/(T•n)] = entropy / #moles [H/n]
	Molar Heat Capacity	J/(K mol)	ideal gas constant	R	Boltzman's constant * Avogadro's number [k_B•N_A] ≈ 8.31446 J/(K•mol)
	Entropy, Heat Capacity	J/K	joules per kelvin	H, C_p, C_v	energy / temperature [E/T]
		W/(K Hz)	watts per kelvin-hertz	H, C_p, C_v	power / temperature / frequency [P/(T•f) = P/(T•ν)]; 1 J/K
			Boltzman's constant	k_B	≈ 13.80648 yJ/K ≈ 8.61733 μeV/K
		nat	natural unit of information	H, S	(1/log_e 2) Shannon ≈ 1.442695041 Sh ≈ 13.80648 yJ/K
	Information Capacity	bit, b	binary digit	?	binary (yes/no, on/off, etc.) information unit; 1 Sh (if both states equally likely) ≈ 693.14718056 mnat ≈ 9.569923 yJ/K
L²T^-2M¹Q⁰Θ⁰	Energy	J	joule	E	power * time period [P•t]; 1 J = 1 Ws (watt-second)
		kW•hr	kilowatt-hour		power * time period [P•t]; 3600 kJ = 3.60 MJ
		cal	(little) calorie		energy to raise 1 g (1 mL) of liquid water at 1 atm by 1°C ≈ 4.184 J; 1 kcal is a 'food Calorie'
		K nat	kelvin-nat		temperature * delta entropy [T•δH]; ≈ 13.80648 yJ
		Gy kg	gray-kilogram		absorbed-dose * mass [D•m]; 1 J
		Pa m³	pascal cubic meters		pressure * volume [\|P\|•V]; 1 Pa•m³ = 1 J = 4053/40 L•atm (liter-atmosphere)
		eV	electron-volt		charge * electric potential [Q•V]; 1 e•J/C ≈ 160.217662 zJ ≈ 1.78266191•10^-36 g
		C²/F	square coulombs per farad		square charge / capacitance [Q²/C]; 1 J
		H A²	henry square amperes		inductance * square current [L•I²]; 1 J
		kg m²Hz²	kilogram square meters square hertz		rotational inertia * half of square angular frequency [I•ω²/2]; 1 J
		kg m²/s²	kilogram square meters per square second		square momentum / mass [p²/m]; momentum * velocity [p•v]; leverage * acceleration [d•a]; 1 J
			potential energy	E_p	mass * height * gravity [m•r•g_c] = payload distance * gravity [d•g_c]
			kinetic energy	E_K	mass * half of square velocity [m•v²/2]
			(rest)mass energy	E_M	mass * square light-speed [m•c₀²]
			electromagnetic field energy	E_em	electric field energy + magnetic field energy [V•(E²ε+B²/μ)/2]
		F V²	farad square volts	E_e	electric field energy = volume * half of square electric field * permittivity [V•E²/2•ε]
		Wb²/H	square webers per henry	E_m	magnetic field energy = volume * half of square magnetic field / permeability [V•B²/2/μ]
		lm s	lumen second	Q_v	luminous energy = luminous flux * time period [Φ_vt] ≈ 1.46412884334 mJ of 540 THz light
		W s	watt second	Q_e	radiant energy = radiant flux * time period [Φ_et]; 1 J
	Spectral Flux_ν	W/Hz	watts per hertz	Φ_e,ν	spectral flux in frequency = radiant flux / frequency [Φ_e/ν = Φ_e/f]
	Work	N m	newton meter	W	force * distance [F•r]; 1 J
	Work	C V	coulomb volt	W	charge * electric potential [Q•V] = charge * electric field * distance [Q•E•r]; 1 N•m
	Torque	J/rad	joules per radian	\|τ\|	energy / plane angle [E/θ]
		kg m²Hz/s	kilogram square meter hertz per second	τ	delta (angular momentum / time) [δL/δt]; 1 J/rad
		kg m²/s²	kilogram square meters per square second		leverage * acceleration [Λ×a]; 1 J/rad; rotational inertia * angular acceleration [I•α]
		C V	coulomb volt		electric dipole moment * electric field [Δp×E]; 1 J/rad
L²T^-1M^1-1Q⁰Θ⁰	Kinematic Viscosity	m²/s	square meters per second	v	viscosity / density [μ/ρ] = area / time period [A/t]
	Specific Angular Momentum	m N s/kg	meter-newton-seconds per kilogram	h	angular momentum / mass [\|L\|/m]; 1 m²/s
	Specific Action	J s/kg	joule-seconds per kilogram	?	action / mass [S/m]; 1 m²/s
L²T^-1M⁰Q¹Θ⁰	Magnetic Dipole Moment	A m²	ampere square meter	μ	electric current * directed area [I•S] = pole strength * distance [q_m•v]
		J/T	joules per tesla	μ	torque / magnetic flux density [τ/B = (B×τ)/B²]; 1 Am²
			magnetic moment of electron, proton, neutron	μ_e, μ_p, μ_n	≈ -9.284764 yJ/T, 0.014106067 yJ/T, -0.00966236 yJ/T
			Bohr magneton	μ_B	[ eh/(4π m_e) ] ≈ 9.274009 yJ/T
			nuclear magneton	μ_N	[ eh/(4π m_p) ] ≈ 0.005050783 yJ/T
L²T^-1M¹Q^-2Θ⁰	Resistance, Impedance, Reactance	Ω	ohm	R, Z, X	reciprocal of conductance\|admittance\|susceptance [1/(G\|Y\|B)]; 1 S^-1
		V/A	volts per ampere		electric potential / electric current [V/I]; 1 Ω
		V²/W	square volts per watt		square voltage / power [V²/P]; 1 Ω
		W/A²	watts per square ampere		power / square current [P/I²]; 1 Ω
		s/F	seconds per farad		time period / capacitance [t/C]; 1 Ω
		H/s	henries per second		inductance / time period [L/t]; 1 Ω
			vacuum impedance	Z₀	[ μ₀c₀ = 1/(ε₀c₀) = √μ₀/ε₀ = \|E\|/\|H\| ]; 119.91698320 π Ω ≈ 376.730313462 Ω
L²T^-1M¹Q^-1Θ⁰	Magnetic Flux	Wb	weber	Φ_B	magnetic flux density * directed area [B•S]; 1 T•m²(tesla square meter)
		J/A	joules per ampere		energy / electric current [E/I] = action / electric charge [S/Q]; 1 Wb
		H A	henry-ampere		inductance * electric current [L•I]; 1 Wb
		V s	volt-second		electric potential * time period [V•t]; 1 Wb
		C Ω	coulomb-ohm		electric charge * resistance [Q•R]; 1 Wb
L²T^-1M¹Q⁰Θ⁰	Angular Impulse	N m s	newton-meter-second	J	torque * time period [τ•t]
	Angular Momentum	m N s	meter-newton-second	L	momentum arm * tangential momentum [r×p]
	Angular Momentum	kg m²Hz	kilogram square meter hertz	L	rotational inertia * angular frequency [I•ω]
	Action	J s	joule-second	S	energy * time period [E•t] = energy / frequency [E/f = E/ν]; 1 J/Hz
		N s m	newton-second-meter		momentum * distance [p•r]; 1 Js
		kg m²/s	kilogram square meters per second		leverage * tangential velocity [Λ•v]; 1 Js
			Planck constant	h	charge * electric potential * time period [Q•V•t]; ≈ 4.1356676 feV•s ≈ 6.6260700•10^-34 Js
			reduced Planck constant	ℏ	charge * electric potential / angular speed [Q•V/ω = h/(2π)]; ≈ 658.211951 aeV/Hz ≈ 1.0545718•10^-34 Js/rad
L²T⁰M⁰Q⁰Θ⁰	Area	m²	square meter	A, S	an area equivalent to a square with each side 1 meter in length; [S = r_x × r_y]
L^4-2T⁰M⁰Q⁰Θ⁰	Étendue	m²sr	square meter steradian	G	area * solid angle [A•Ω]
L²T⁰M¹Q⁰Θ⁰	Rotational Inertia	kg m²	kilogram-square-meters	I	angular momentum / angular velocity [L/α] = mass * area [m•A]
L²T⁰M¹Q⁰Θ⁰	Rotational Inertia	N m/Hz²	newton-meters per square hertz	I	torque / angular acceleration [\|τ/α]; 1 kg•m²
L³T^-2M^1-2Q⁰T⁰	Gravitational Constant	N m²/kg²	newton-square meters per square kilogram	G_k	force * square distance / square mass [F•r²/m²]; G_k ≈ 66.74 pN•m²/kg²
L³T^-1M⁰Q⁰Θ⁰	Fluid Flow Rate	m³/s	cubic meters per second	Q	volumetric flux * directed area [q•S] = kinematic viscosity * distance [v•r] = volume / time [V/t]
L³T^-1M^1-1Q⁰Θ⁰	Fluid Flow Rate	N/PI	newtons per poiseuille	Q	force * fluidity [\|F\|•φ] = force / viscosity [\|F\|/η]; 1 N/PI = 1 m³/s = 1 kL/s = 1 kHzL
L³T⁰M^-1Q⁰T⁰	Specific Volume	m³/kg	cubic meters per kilogram	?	volume / mass [V/m]
L³T⁰M⁰Q⁰Θ⁰	Volume	m³	cubic meter	V	volume equivalent to a cube with each edge 1 meter in length; 1000 L
	Volume	L	liter	V	volume equivalent to a cube with each edge 10 centimeter in length; 1/1000 m³
	Molar Volume	m³/mol	cubic meter per mole	V_m	volume / #moles [V/n_m] = molar mass / density [M/ρ] = reciprocal molar density [1/c_i]

Notes

The unit for acidity/basicity (math symbol pH) is listed with units of "per cubic length" (L^-3). However, pH is actually the logarithm of that unit. Because the logarithm of a unit(s) is undefined, pH is truly dimensionless! Other "respectable" units which involve logarithms are unit-less; for example, the decibel (dB) is relative to the logarithm of power/power, or amplitude/amplitude. In either case, the decibel is based on a unit-less quantity (because the units cancel out). In other words, pH is a bastard unit (dimensionally incoherent).