Quantitels

Quantitels are systematic names for coherent units of measure derived directly from the names of the physical quantities they measure, plus the ending -el, which signifies "element", as in the familiar word "pixel" = "picture element". For example, lengthel is the quantitel for a coherent unit of length. When a quantity has multiple synonyms (e.g. "work" and "energy"), it can have multiple synonymous quantitels (e.g. workel and energiel); such synonyms can be used interchangeably.

Quantitels are generic and can be used across potentially many metrologies. When unmarked, a quantitel can be used to speak abstractly about the notion of coherent units. For instance, one may ask the question, "What is the lengthel for SI?" The answer, of course, is the meter. One can say, "The centimeter is an auxiliary unit in SI, but it was the lengthel for CGS."  But if a quantitel is marked, or "branded", with some disambiguating adjective or prefix, it can be used to name the coherent unit of a particular metrology.

This metrology is named "Primel" because it is the first (i.e., prime) system to use quantitels for its coherent unit names. "Primel" can be used as its brand-marker (e.g. Primel lengthel). The die-face-1 character (⚀) serves as an abbreviation for this prefix, marking every Primel unit as such (e.g. ⚀lengthel). It may be pronounced "prime" or "Primel" as needed, or optionally left silent in a context where Primel is the only metrology being discussed that uses quantitels.

Table of Quantitels

MECHANICS
Physical Quantity

Quantitel

Abbr

Derivation/Decomposition

SI Analog

Abbr

MECHANICS
Physical Quantity

Quantitel

Abbr

Derivation/Decomposition

SI Analog

Abbr

time
duration
period 

timel
durationel
periodel 

tm
drnℓ
prdℓ 

timel

second

s

frequency
inverse time

frequenciel
timelic
durationelic
periodelic

fq
tmℓ\
drnℓ\
prdℓ\

timel1

hertz
second1

Hz
1/s 

acceleration

accelerel

acc

lengthel × timel−2

meter × second2

m/s2

velocity
speed 

velocitel
speedel

vc
sp

lengthel × timel−1
accelerel × timel

meter × second1

m/s

length
width
breadth
height
depth 

lengthel
widthel
breadthel
heightel
depthel

lg
wdℓ
brdℓ
hgtℓ
dptℓ

lengthel
velocitel × timel

meter

m

reciprocal length
lineic density

lengthelic
widthelic
breadthelic
heightelic
depthelic


lgℓ\
wdℓ\
brdℓ\
hgtℓ\
dptℓ\

lengthel−1

meter1

1/m

area

areanel

ar

lengthel2

meter2

m2

reciprocal area
areic density 

areanelic

arℓ\

areanel−1
lengthel−2

meter2

1/m2

volume

volumel

vm

lengthel3

meter3

m3

reciprocal volume
volumic density 

volumelic

vmℓ\

volumel−1
lengthel−3

meter3

1/m3

density
volumic mass

densitel
volumelic·massel 

ds

massel × volumel−1
massel × lengthel−3 

kilogram × meter2

kg/m3

mass

massel

ms

massel
densitel × volumel

kilogram

kg

reciprocal mass
specific- = massic-

masselic

msℓ\

massel−1

kilogram1

1/kg

momentum

momentumel (or momel)

mm

massel × velocitel
massel × lengthel × timel−1

kilogram × meter × second1

kg·m/s

action

actionel

act

momentumel × lengthel
massel × lengthel2 × timel−1

kilogram × meter2 × second1

kg·m2/s

force
weight 

forcel
weightel 

fc
wtℓ 

massel × accelerel
massel × lengthel × timel−2

newton
kilogram × meter × second−2

N
kg·m/s2

energy
work
heat
potential 

energiel
workel
heatel
potentialel 

ng
wkℓ
htℓ
ptℓ 

forcel × lengthel
massel × velocitel2
massel × lengthel2 × timel−2

joule
kilogram × meter2 × second2

J
kg·m2/s2

influence

influencel

nf

forcel × areanel
massel × lengthel3 × timel−2

kilogram × meter3 × second2

kg·m3/s2

power

powerel

pw

energiel × timel−1
massel × lengthel2 × timel−3

watt
kilogram × meter2 × second3

W
kg·m2/s3

tension

tensionel
lengthelic·forcel

ts
lgℓ\fcℓ

forcel × lengthel−1
massel × timel−2

newton/meter
kilogram × second−2

N/m
kg/s2

pressure

pressurel
areanelic·forcel

ps
arℓ\fcℓ 

forcel × areanel−1
massel × lengthel−1 × timel−2

pascal
kilogram × meter1 × second−2

Pa
kg/m·s2

intensity

intensitel
areanelic·powerel

nt
arℓ\pwℓ 

powerel × areanel−1
massel × timel−3

watt/meter2
kilogram × second3

W/m2
kg/s3

ANGULAR MECHANICS
Physical Quantity

Quantitel

Abbr

Derivation/Decomposition

SI Analog

Abbr

ANGULAR MECHANICS
Physical Quantity

Quantitel

Abbr

Derivation/Decomposition

SI Analog

Abbr

plane angle

radian

rad

radian
lengthel × radiel−1

radian

rad

solid angle

steradian

sr

radian2
areanel × steradiel−1

steradian

sr

radiality 

radialitel (or radiel)
radianic·lengthel

rdℓ
rad\lgℓ

lengthel × radian−1

meter × radian−1

m/rad

curvature

curvaturel (or curvel)
lengthelic·radian

cvℓ
lgℓ\rad

radiel−1 
radian × lengthel−1

radian × meter−1

rad/m

steradiality
squaradiality

steradialitel (or steradiel)
steradianic·areanel

srdℓ
sr\arℓ

radiel2
areanel × steradian−1
lengthel2 × radian−2

meter2 × radian−2
meter2 × steradian−1

m2/sr

stercurvature
squarecurvature

stercurvaturel (or stercurvel)
areanelic·steradian

scvℓ
arℓ\sr

steradiel−1 
steradian × areanel−1
radian2 × lengthel−2

meter−2 × radian2

sr/m2

angular displacement

curvel·lengthel
angular·lengthel (or anglengthel)
radian

cvℓ·lgℓ
∡lgℓ
rad

lengthel × curvel
radian

radian

rad

angular velocity

curvel·velocitel
angular·velocitel (or angvelocitel)

cvℓ·veℓ
∡veℓ

velocitel × curvel
radian × timel−1

radian × second−1

rad/s

angular acceleration

curvel·accelerel
angular·accelerel (or angaccelerel)

cvℓ·accℓ
∡accℓ

accelerel × curvel
radian × timel−2

radian × second−2

rad/s2

angular mass
moment of inertia 

steradiel·massel
angular·massel (or angmassel)

srdℓ·msℓ
∡msℓ

massel × steradiel
massel × radiel2
massel × areanel × steradian−1
massel × lengthel2 × radian−2

kilogram × meter2 × radian−2
kilogram × meter2 × steradian−1 

kg·m2/rad2
kg·m2/sr

angular momentum

radiel·momentumel
angular·momentumel (or angmomel)

rdℓ·mmℓ
∡mmℓ

radiel × momentumel
actionel × radian−1
massel × lengthel2 × timel−1 × radian−1

kilogram × meter2 × second−1 × radian−1

kg·m2/s·rad

angular force
torque 

radiel·forcel
angular·forcel

rdℓ·fcℓ
∡fcℓ

radiel × forcel
workel × radian−1
massel × lengthel2 × timel−2 × radian−1

kilogram × meter2 × second−2 × radian−1
newton·meter/radian
joule/radian

kg·m2/s2·rad N·m/rad
J/rad

THERMODYNAMICS
Physical Quantity

Quantitel

Abbr

Derivation/Decomposition

SI Analog

Abbr

THERMODYNAMICS
Physical Quantity

Quantitel

Abbr

Derivation/Decomposition

SI Analog

Abbr

temperature

temperaturel

tmpℓ

heatel × heatabilitel−1

kelvin

K

heat capacity
heatability
entropy 

heatabilitel
entropiel 

htbℓ
ntpℓ 

heatel × temperaturel−1
massel × lengthel2 × timel−2 × temperaturel−1

joule/kelvin
kilogram × meter2 × second−2 × kelvin−1
 

J/K

massic heat capacity
massic·heatability
massic entropy

masselic·heatabilitel
masselic·entropiel

msℓ\htbℓ
msℓ\ntpℓ

heatabilitel × massel−1
lengthel2 × timel−2 × temperaturel−1

joule/kelvin/kilogram
meter2 × second−2 × kelvin−1

J/K/kg
m2/s2/K

temperature gradient
lineic·temperature

lengthelic·temperaturel

lgℓ\tmpℓ

temperaturel × lengthel−1 

kelvin × meter−1

K/m

ELECTROMAGNETISM
Physical Quantity

Quantitel

Abbr

Derivation/Decomposition

SI Analog

Abbr

ELECTROMAGNETISM
Physical Quantity

Quantitel

Abbr

Derivation/Decomposition

SI Analog

Abbr

quantity of electricity
electric charge

electrel

εtℓ

electrel
currentel × timel

coulomb

C

quantity of magnetism
magnetic pole strength 

magnetel

μtℓ

electrel × velocitel
electrel × lengthel × timel−1
currentel × lengthel

coulomb × meter × second−1
ampere × meter

C·m/s
A·m

electric current

currentel

ctℓ

electrel × timel−1
magnetel × lengthel−1

ampere
coulomb × second−1

A
C/s 

electric current change
electric alternation

alternationel

altℓ

currentel × timel−1
electrel × timel−2

ampere × second−1
coulomb × second−2

A/s
C/s2

reciprocal electricity

electrelic

εtℓ\

electrel−1

coulomb−1

1/C

reciprocal magnetism

magnetelic

μtℓ\

magnetel−1
electrel−1 × lengthel−1 × timel

ampere−1 × meter−1

1/A·m

electrization
electric displacement
polarization 

electrizel
areanelic·electrel 

εtzℓ
arℓ\εtℓ

electrel × areanel−1
electrel × lengthel−2

coulomb × meter−2

C/m2

magnetization
magnetizing field 

magnetizel
areanelic·magnetel

μtzℓ
arℓ\μtℓ

magnetel × areanel−1
magnetel × lengthel−2
currentel × lengthel−1
electrel × lengthel−1 × timel−1

ampere × meter−1

A/m

electric density

electrodensitel
volumelic·electrel 

εdsℓ
voℓ\εtℓ

electrel × volumel−1
electrel × lengthel−3 

coulomb × meter−3

C/m3

magnetic density
areic current density

magnetodensitel
volumelic·magnetel
areanelic·currentel 

μdsℓ
voℓ\μtℓ 
arℓ\ctℓ  

magnetel × volumel−1
currentel × areanel−1
electrel × lengthel−2 × timel−1

ampere × meter−2

A/m2

electric·force
electric field strength

electrelic·forcel

εtℓ\fcℓ

forcel × electrel−1
electric·potentilalel × lengthel−1
massel × lengthel × timel−2 × electrel−1

newton × coulomb−1
volt × meter−1

N/C
V/m 

magnetic·force
magnetic flux density

magnetelic·forcel

μtℓ\fcℓ

forcel × magnetel−1
massel × timel−1 × electrel−1
massel × timel−2 × currentel−1

tesla
weber × meter2

T
Wb·m2

electric·potential

electrelic·potentialel

εtℓ\ptℓ

potentialel × electrel−1
massel × lengthel2 × timel−2 × electrel−1

volt

V

magnetic·potential

magnetelic·potentialel

μtℓ\ptℓ

potential × magnetel−1
massel × lengthel × timel−1 × electrel−1
massel × lengthel × timel−2 × currentel−1

newton × ampere−1
weber × meter

N/A
Wb·m

electric·influence
electric flux 

electrelic·influencel

εtℓ\nfℓ

influencel × electrel−1
massel × lengthel3 × timel−2 × electrel−1

newton × meter2 × coulomb−1
volt × meter

N·m2/C
V·m

magnetic·influence
magnetic flux 

magnetelic·influencel

μtℓ\nfℓ

influencel × magnetel−1
massel × lengthel2 × timel−1 × electrel−1

weber

Wb

electric·tension

electrelic·tensionel

εtℓ\tsℓ

tensionel × electrel−1
massel × timel−2 × electrel−1

newton × meter−1 × coulomb−1
volt × meter−2

N/m/C
V/m2

magnetic·tension

magnetelic·tensionel

μtℓ\tsℓ

tensionel × electrel−1
massel × lengthel−1 × timel−1 × electrel−1

tesla × meter−1

T/m

electric·pressure

electrelic·pressurel

εtℓ\psℓ

pressurel × electrel−1
massel × lengthel−1 × timel−2 × electrel−1

pascal × coulomb−1
volt × meter−3

Pa/C
V/m3

magnetic·pressure

magnetelic·pressurel

μtℓ\psℓ

pressurel × magnetel−1
massel × lengthel−2 × timel−1 × electrel−1

tesla × meter−2

T/m2

resistance
reactance
impedance

resistancel
reactancel
impedancel

rstℓ
rctℓ
impℓ

electromagnetelic·influencel
influencel × electrel−1 × magnetel−1
massel × lengthel2 × timel−1 × electrel−2

ohm

Ω

conductance
susceptance
admittance

conductancel
susceptancel
admittancel

cdcℓ
scpℓ
admℓ

influencelic·electromagnetel
influencel−1 × electrel × magnetel
massel−1  × lengthel−2 × timel × electrel2

siemens

S

resistivity

resistivitel

rsvℓ 

resistancel × lengthel
massel × lengthel3 × timel−1 × electrel−2

ohm × meter

Ω·m

conductivity

conductivitel

cdvℓ

conductancel × lengthel−1
massel−1 × lengthel−3 × timel × electrel2

siemens × meter−1

S/m

elastance
reciprocal capacitance

elastancel

escℓ

squarelectrelic·potentialel
energel × electrel−2
massel × lengthel2 × timel−2 × electrel−2

farad−1

1/F

capacitance

capacitancel

cpcℓ

potentialelic·squarelectrel
energel−1 × electrel2
massel−1 × lengthel−2 × timel2 × electrel2

farad

F

elastivity
reciprocal permittivity

elastivitel

esvℓ

squarelectrelic·influencel
elastancel × lengthel
influencel × electrel−2
massel × lengthel3 × timel−2 × electrel−2

meter × farad−1

m/F

capacitivity
permittivity

capacitivitel

cpvℓ

influencelic·squarelectrel
capacitancel × lengthel−1
influencel−1 × electrel2
massel−1 × lengthel−3 × timel2 × electrel2

farad × meter−1

F/m

inductance

inductancel

ndcℓ

alternationelic·electrelic·potentialel
squarecurrentelic·potentialel
massel × lengthel2 × electrel−2
massel × lengthel2 × timel−2 × currentel−2

henry

H

reluctance
reciprocal inductance

reluctancel

rlcℓ

potentialelic·electrel·alternationel
potentialelic·squarecurrentel
massel−1 × lengthel−2 × electrel2
massel−1 × lengthel−2 × timel2 × currentel2

henry−1

1/H

inductivity
permeability

inductivitel

ndvℓ

squaremagnetelic·influencel
inductance × lengthel−1
massel × lengthel × electrel−2

henry × meter−1

H/m

reluctivity
reciprocal permeability

reluctivitel

rlvℓ

influencelic·squaremagnetel
reluctance × lengthel
massel−1 × lengthel−1 × electrel2

meter × henry−1

m/H