Units of measurement

It is our responsibility as scientists, knowing the great progress which comes from a satisfactory philosophy of ignorance, the great progress which is the fruit of freedom of thought, to proclaim the value of this freedom; to teach how doubt is not to be feared but welcomed and discussed; and to demand this freedom as our duty to all coming generations.

(Richard Feynman. The Value of Science)

Here is a conversion table for the physical units of measurement. The unit names link to the dictionary.

You may also want to skip this table and see how to use these units in grammar.

Time and space
Dimension	Unit	Conversion (SI / European units)		Conversion (non-SI / Anglo-American units)
time	krà.	1 s = 0.7585 k	1 k = 1.318 s	—	—
length	xrà.	1 m = 10.87 x	1 x = 92.02 mm	1 ft = 3.312 x	1 x = 3.623 in
area	(see below)	1 m² = 118.1 ²x	1 ²x = 84.68 cm²	1 sq ft = 10.97 ²x	1 ²x = 13.13 sq in
volume	(see below)	1 m³ = 1,283 ³x	1 ³x = 779.3 cm³	1 cb ft = 36.34 ³x	1 ³x = 47.55 cb in
speed	kàx.	1 m⁄s = 14.33 kx 1 km⁄h = 3.980 kx	1 kx = 6.980 cm⁄s 1 kx = 0.2513 km⁄h	1 mph = 6.405 kx	1 kx = 0.1561 mph
		(valid up to ~3000 km⁄s*)		(valid up to ~1800 miles per second)
		ψ_Lem = 16⁸ artanh v⁄c	v = c tanh (16⁻⁸ ψ_Lem)	ψ_Lem = 16⁸ artanh v⁄c	v = c tanh (16⁻⁸ ψ_Lem)
		(c = 299,792,458 m⁄s)		(c = 670,616,629 mph)
angle	rà. [selà.]	1 rad = 1 r	1 r = 1 rad	1° = 2.13̅ s 360° = 768 s = 3 × 16² s	1 s = 28′ 7.5″
solid angle	(see below)	1 sr = 1 ²r	1 ²r = 1 sr	1 (°)² = 4.551̅ ²s	1 ²s = 791 (′)²
The official angle unit is of course the same as our radian, that is, a dimensionless unit with a value of one – and that is how it is named. This unit is used for compounding other units; but the alternative selà. is used for many practical purposes just like our degrees.

Mechanics (mass related units)
Dimension	Unit	Conversion (SI units)		Conversion (non-SI / Anglo-American)
mass	làq.	1 kg = 1.314 l	1 l = 761.1 g	1 lb = 0.5959 l	1 l = 1.678 lbs
energy	iotà.	1 J = 269.7 i	1 i = 3.708 mJ	1 cal = 1,128 i	1,000 i = 0.8863 cal 256 i = 0.2269 cal
energy per mass, ionising radiation dose	hàhs.	1 J⁄kg (Gy) = 205.2 h	1 h = 4.872 mJ⁄kg (mGy)	1 cal⁄lb = 1.893 h	1,000 h = 0.5282 cal⁄lb 256 h = 0.1352 cal⁄lb
energy per mass, ionising radiation dose	hàhs.	(but not sieverts)		1 cal⁄lb = 1.893 h	1,000 h = 0.5282 cal⁄lb 256 h = 0.1352 cal⁄lb
momentum	blàp.	1 N·s = 18.82 b	1 b = 53.13 mN·s	—	—
power	melàs.	1 W = 355.5 m	1 m = 2.813 mW	1 hp = 265,100 m	1,000,000 m = 3.772 hp 65,536 m = 0.2472 hp
angular power density	natlà.	1 W⁄sr = 355.5 n	1 n = 2.813 mW⁄sr	—	—
power density	gomàs.	1 W⁄m² = 3.010 g	1 g = 0.3322 W⁄m²	—	—
force	emblà.	1 N = 24.81 e	1 e = 40.30 mN	1 lbf = 110.4 e	1,000 e = 9.059 lbf 256 e = 2.319 lbf
pressure	aràc.	1 Pa = 0.2101 a	1 a = 4.759 Pa	1 atm = 21,290 a	1,000,000 a = 46.97 atm 65,536 a = 3.078 atm
pressure	aràc.	1 Pa = 0.2101 a	1 a = 4.759 Pa	1 mmHg = 28.02 a	1,000 a = 35.69 mmHg 256 a = 9.138 mmHg

Thermodynamics
Dimension	Unit	Conversion (SI units)		Conversion (non-SI / Anglo-American)
temperature	qàc.	1 K = 0.87908 q T_Lem = 0.87908 × (ϑ_°C + 273.15)	1 q = 1.1376 K ϑ_°C = 1.1376 T_Lem − 273.15	T_Lem = 0.48838 × (ϑ_°F + 459.67)	ϑ_°F = 2.0476 T_Lem − 459.67
temperature	qàc.
The temperature unit measures absolute or thermodynamic temperature, that is, the scale starts at zero Kelvin, −273.15 °C or −459.67 °F. Consequently, there are no negative temperatures.

Electromagnetism
Dimension	Unit	Conversion (SI units)
electric charge, dielectric flux	oàs.	1 C = 17.35 o	1 o = 57.64 mC
electric displacement (‘dielectric flux density’)	udreà.	1 C⁄m² = 0.1469 u	1 u = 6.807 C⁄m²
electric current; magnetic potential	potmàs.	1 A = 22.87 p	1 p = 43.72 mA
electric potential, voltage; magnetic current	disfàk.	1 V = 15.54 d	1 d = 64.34 mV
resistance	fragmà.	1 Ω = 0.6795 f	1 f = 1.472 Ω
capacitance	telmà.	1 F = 1.116 t	1 t = 0.8959 F

magnetic charge, magnetic flux	Oàs.	1 Wb = 11.79 O	1 O = 84.82 mWb
magnetic flux density	Udreà.	1 T = 0.09983 U	1 U = 10.02 T
inductance	ytàs.	1 H = 0.5154 y	1 y = 1.940 H

Light
These units are derived from mechanical ones by correcting for the sensitivity of the human eye (Koi ὀφθαλμός, whence the superscript o). At a wavelength of ~555 nm (lime green), where the eye is most sensitive, one unit of energy and one unit of luminous energy are equal. There are analogously defined acoustic units, which are written with a superscript u (Koi οὖς ‘ear’).
Dimension	Unit	Conversion (SI units)
luminous energy	(see below)	1 lm·s = 0.3948 i^o	1 i^o = 2.533 lm·s
luminous flux		1 lm = 0.5205 m^o	1 m^o = 1.921 lm
luminous intensity		1 cd = 0.5205 n^o	1 n^o = 1.921 cd
illuminance		1 klx = 4.408 g^o	1 g^o = 226.9 lx
Finance
Dimension	Unit	Conversion (European)		Conversion (British and American)
currency	nabà.	1 € = 0.69 Z	1 Z = 1.45 €	1 GB£ = 0.75 Z 1 US$ = 0.61 Z	1 Z = 1.33 GB£ 1 Z = 1.63 US$
The conversion factors are valid as of August 2019. The author is not responsible for any financial losses you might experience when investing in nabus or other currencies from the Lemizh world.

Rapidity goes to infinity as speed approaches c, the speed of light in vacuum.

* The speed unit is actually a unit of rapidity (ψ), which is a way of measuring motion alternative to the common concept of speed (v). ψ increases nearly proportionally to v as long as we are not approaching vacuum light speed (c), but then rises more and more quickly, reaching infinity at the speed of light. For everyday purposes, the conversion factors given above are usually more than accurate enough.

Large and small quantities

The planetary symbols we have already met on the previous page can be inserted between a numerical value and a unit, much like our metric prefixes k for ‘kilo-’, M for ‘mega-’, etc. Their values are listed in unit 9; they are powers of 65536 (including its square root, 256, which is denoted by É). Thus, 2Á x are 2 × 65536 length units or about 12 kilometres. Small quantities can be expressed with these symbols in the denominator: 6/Â x are 6⁄65536² length units or 129 picometres.

Amount of substance

Technically, the unit for the amount of substance is just the number of particles (atoms, molecules, ions, etc.), so that 1 mol = 0.4981 Å (i.e. 65536⁵) and 1 Å = 2.007 mol. However, chemists prefer to calculate in mass units per molar mass unit, giving a nonstandard unit corresponding to about 379.2 Å or 761.1 mol.

Expressing quantities

krà. means ‘make/become a time span of 1.318 seconds’. This and other units, including djàvf. ‘week’, Otà. ‘year’ etc., are basically definite numerals with a physical dimension: krÌ. timeunit-acc¹. means ‘a time span of 1.318 seconds’, krìl. timeunit-cons¹. ‘(the concept of) time units, time-unit-ness’. Units are usually multiplied with numbers; that is, we need an inner consecutive case and an accusative bracket. (See Multidigit numbers in unit 7; **dwÌ krÌy. two-acc¹ timeunit-acc-acc². would mean ‘two individuals, which are 1.318 seconds’.) The same applies if units need to be multiplied among themselves. Quotients of units work as fractions; powers of units work as described in the chapter on functions; and light related units are compounds with dmùt. ‘eye’ and an epenthetic benefactive.

É, the multiplier/divisor for 256, is pronounced as the exponential number of the same value (skmà.); Á the same as 65536 (mràj.); Â = 65536² and beyond are pronounced as in the weekdays’ modifiers (xsrà., xnà., etc.). They are part of the numeric value rather than the unit.

dwÌ xrìly. ⇒ xrildwÌ.	two consequences of making 9.2 cm; two 9.2 cm-nesses; 2 × 9.2 cm	18.4 cm (7¼ in)
two-acc¹ lengthunit-cons-acc². ⇒ lengthunit-cons-two-acc¹.
14Ì fragmìly xrìly. ⇒ 14Ì xrilfragmìly.	14_hex ≈ 20 resistance units times length units	2.71 Ω·m
20-acc¹ resistanceunit-cons-acc² lengthunit-cons-acc³. ⇒ 20-acc¹ lengthunit-cons-resistanceunit-cons-acc².
100Ì ligzkrìly.	100_hex = 256 per time unit	194 Hz or Bq
256-acc¹ little-dat-timeunit-cons-acc².
B9Ì kìlxy ligzkrìly.	B9_hex = 185 speed units per time unit	9.79 m⁄s²
185-acc¹ speedunit-cons-acc² little-dat-timeunit-cons-acc³.
lrÌ dwyè xrÌi. ⇔ ⇒ lredwÌ xrÌi.	a length unit squared	84.7 cm²
exponentiate-acc¹ two-acc-nom² lengthunit-acc-dat². ⇔ ⇒ exponentiate-nom-two-acc¹ lengthunit-acc-dat².
melÌs dmùtU. ⇔ ⇒ melUsdmÌt.	a power unit for the eye	1.92 lm
powerunit-acc¹ see-ins-ben². ⇔ ⇒ powerunit-ben-see-acc¹.
xsriltrÌ iotìly.	3×65536² energy units	47.8 MJ
Venus-cons-three-acc¹ energyunit-cons-acc².
dÌh ligzxsrìly lìlqy.	10⁄65536² mass units	1.77 µg
ten-acc¹ little-dat-Venus-cons-acc² massunit-cons-acc³.

Outside the context of measurements, the planetary names are used informally instead of the large exponential numbers discussed in unit 7.

The chapter Measuring in unit 12 of the tutorial shows the use of length, time and angle units in sentences. Here are some examples for the use of other units.

1DÌ lilqÌ trÌxkU.	There are 1D_hex = 29 mass units of the beaver. The beaver has got 29 mass units. (see stative verbs in unit 10)	The beaver weighs 22 kg (three stone 7 pounds).
29-acc¹ massunit-cons-acc² beaver-acc-ben².
nená yhwÌ C8Ìa kìlxy.	The horse runs C8_hex = 200 speed units.	The horse is running 50 km⁄h (31 mph).
run-fact¹ horse-acc-acc^2a 200-acc-fact² speedunit-cons-acc³.
dwà melilsÌ xycgmyhrèe.	The laser makes 2 power units.	The laser emits 5.6 mW.
two-fact¹ powerunit-cons-acc² laser-nom-nom².

Notable constants

Several notable constants are approximately round numbers in the Lemizh system of units:

Einstein’s gravitational constant κ = 8πG⁄c² is ~3 × 16⁻²¹ (more accurately, 2.986) length units per mass unit.
One charge unit contains about 5 × 16¹⁴ (more accurately, 4.993) elementary charges.
The density of water is about one mass unit per volume unit (more accurately, 1.024).
Water freezes at ~F0_hex = 240 and boils at ~148_hex = 328 units; body temperature is about 110_hex = 272 units.
The Moon’s and Sun’s apparent diameters are just over one angle unit (between 1.04 and 1.21).
The Moon’s average distance from Earth is about 16⁸ length units, that is one ‘Lemizh light second’. (Its distance varies between 0.9017 and 1.0290, and the semi-major axis is 0.9726 × 16⁸ units long.)

Vacuum light speed, Planck’s constant, Boltzmann’s constant, and the electric and magnetic constants are exactly round numbers, as we will see in a moment.

Definitions

The earliest form of this system on which European consensus was achieved was devised by a group of physicists on the initiative of the Lemizh Scientific Society, which explains why the unit names and abbreviations are Lemizh. It was officially adopted in the year 1785 CE (CB0). Later additions (such as the electromagnetic units) stuck to this convention.

The time unit is of course 1⁄16⁴ of a day, but the definition has been changed and refined several times to increase accuracy.

The length unit is defined as the distance light travels in vacuum in 16⁻⁸ time units (about 307.0 ps). Conversely, vacuum light speed is 16⁸ length units (~ 395,200 km) per time unit. The units of area and volume are the square and cube of the length unit, respectively. Likewise, as in SI, all other units are derived as powers, products or quotients of the base units, so that all conversion factors are 1.

The mass unit is defined as the mass of 1⁄7 × 16⁴³ (~8.552 × 10⁵⁰) photons with an angular frequency of 1 per time unit (equalling a frequency of 1⁄2π per time unit and a wavelength of 2π × 16⁸ length units or 2.483 million kilometres). Consequently, the reduced Planck constant ħ = h⁄2π equals 7 × 16⁻²⁷ units of action (energy units × time units).

The temperature unit is defined as the absolute temperature at which an ideal particle has an average kinetic energy of 10 × 16⁻¹⁸ energy units (~7.853 × 10⁻²⁴ J = 49.01 µeV) per degree of freedom. So, the Boltzmann constant k_B is 20 × 16⁻¹⁸ = 1¼ × 16⁻¹⁷ energy units per temperature unit.

The unit of electric charge is defined as one of two equal charges in vacuum separated by one length unit that repel each other with 1⁄4π × 16¹⁰ force units (~3.526 GN). In other words, the electric constant ε₀ is 16⁻¹⁰ capacitance units per length unit, and the magnetic constant μ₀ is 16⁻⁶ inductance units per length unit.

Originally the definitions related more explicitly to the physical constants, e.g. ‘The mass unit is such that ħ = 7 × 16⁻²⁷ units of action’. Now that they have been revised to resemble the classical SI definitions, the International Committee for Weights and Measures has decided on new definitions of the SI base units that are more like the former Lemizh ones. Strange things happen.

Mathematics