Scales

Scale meaning C or D= length (L)
C/D C C log(C)
A/B C2 sqrt(A) log(A)/2
K C3 cbrt(K) log(K)/3
CI 1/C 1/CI -log(CI)
L log(C) 10L L
LL1 e^(C/100) ln(LL1)*100 1+log(ln(LL1))
LL2 e^(C/10) ln(LL2)*10 2+log(ln(LL2))
LL3 eC ln(LL3) log(ln(LL3))
T arctan(C) tan(T) log(tan(T))
S arcsin(C) sin(S) log(sin(S))
ST inv arclen(C) sin=tan=arclen log(arclen
P sqrt(1-(C/10)2) sqrt(1-P2)*10 1+log(1-P2)/2
xxF Folded shifted(xx) xx + 0.5

Settings

a = b*c or b = a/c
            ---------------------
C          | 1        c          |
      ---------------------------
D    |       b        a    |
      ---------------------
a/b = c/d = e/f...
            ---------------------
C          |  a    c    e        |
      ---------------------------
D    |        b    d    f  |
      ---------------------
a = b^c
            ---------------------
C          | 1         c         |
      ---------------------------
LL   |       b         a   |
      ---------------------
a = b*c*d
a = b/c/d
a = b*c/d

            ---------------------
           |                     |
      ---------------------------
     |                     |
      ---------------------
            ---------------------
           |                     |
      ---------------------------
     |                     |
      ---------------------
           A
          /|
         / |
       c/  |b
       /   |
      /    |
     B-----C
        a
           A
          /\
         /  \
       c/    \b
       /      \
      /        \
     B----------C
           a

            ---------------------
C          |  a   b     c        |
      ---------------------------
S    |        A   B     C  |
      ---------------------

Ratios

The numerical values adopted by the CGPM[36] are identical to the published CODATA 2017 values.[37]

Following the successful 1983 redefinition of the metre in terms of an exact numerical value for the speed of light, the BIPM's Consultative Committee for Units (CCU) recommended and the BIPM proposed that four further constants of nature should be defined to have exact values. These are:[Note 5]

The Planck constant h is exactly 6.62607015e−34 joule-second (J⋅s).
The elementary charge e is exactly 1.602176634e−19 coulomb (C).
The Boltzmann constant k is exactly 1.380649e−23 joule per kelvin (J⋅K−1).
The Avogadro constant NA is exactly 6.02214076e23 reciprocal mole (mol−1).

The redefinition retains unchanged the numerical values associated with the following constants of nature:

The speed of light c is exactly 299792458 metres per second (m⋅s−1);
The ground state hyperfine structure transition frequency of the caesium-133 atom ΔνCs is exactly 9192631770 hertz (Hz);
The luminous efficacy of monochromatic radiation of frequency 5.40×1014 Hz (540 THz) – a frequency of green-colored light at approximately the peak sensitivity of the human eye – Kcd (where the subscript "cd" is the symbol for candela) is exactly 683 lumens per watt (lm⋅W−1).

The seven SI defining constants above, expressed in terms of derived units (joule, coulomb, hertz, lumen, and watt), are rewritten below in terms of the seven base units (second, metre, kilogram, ampere, kelvin, mole, and candela);[4] the dimensionless unit steradian (symbol sr) is also used:

ΔνCs = Δν(133Cs)hfs = 9192631770 s−1
c = 299792458 m⋅s−1
h = 6.62607015e−34 kg⋅m2⋅s−1
e = 1.602176634e−19 A⋅s
k = 1.380649e−23 kg⋅m2⋅K−1⋅s−2
NA = 6.02214076e23 mol−1
Kcd = 683 cd⋅sr⋅s3⋅kg−1⋅m−2

As part of the redefinition, the International Prototype of the Kilogram was retired and definitions of the kilogram, the ampere, and the kelvin were replaced. The definition of the mole was revised. These changes have the effect of redefining the SI base units, though the definitions of the SI derived units in terms of the base units remain the same.

Counting

1728 units = 144 dozen = 12 gross = 1 great gross 20 units = 1 score 1 mol = N(A) = 6.02214076e23 ~ 1090/181e23

Metric/SI/IEC/JEDEC

Prefix Symbol Factor Number Name
quecto q 10^-30 = 1000^-10 nonillionth
ronto r 10^-27 = 1000^-9 octillionth
yocto y 10^-24 = 1000^-8 septillionth
zepto z 10^-21 = 1000^-7 sextillionth
atto a 10^-18 = 1000^-6 quintillionth
femto f 10^-15 = 1000^-5 quadrillionth
pico p 10^-12 = 1000^-4 trillionth
nano n 10^-9 = 1000^-3 billionth
micro μ 10^-6 = 1000^-2 millionth
milli m 10^-3 = 1000^-1 thousandth
centi c 10^-2 hundredth
deci d 10^-1 tenth
- - 100 = 10000 one/unit/whole
deka da 101 ten
hecto h 102 hundred
kilo k 103 = 10001 thousand
kibi/kilo Ki/K 210 = 10241 -
mega M 106 = 10002 million
mebi/mega Mi/M 220 = 10242 -
giga G 109 = 10003 billion
gibi/giga Gi/G 230 = 10243 -
tera T 1012 = 10004 trillion
tebi/tera Ti/T 240 = 10244 -
peta P 1015 = 10005 quadrillion
pebi Pi 250 = 10245 -
exa E 1018 = 10006 quintillion
exbi Ei 260 = 10246 -
zetta Z 1021 = 10007 sextillion
zebi Zi 270 = 10247 -
yotta Y 1024 = 10008 septillion
yobi Yi 280 = 10248 -
ronna R 1027 = 10009 octillion
quetta Q 1030 = 100010 nonillion

Time

1 day = 24 hours = 1440 minutes = 86400 seconds 400 Gregorian years = 146097 days = 20871 weeks = 4800 months = 4 centuries = 0.4 millennia 4 Julian years = 1461 days = 48 months 1 lunar sidereal month ~ 27.32 days 1 lunar synodic phase month ~ 29.53 days 1 solar year ~ 365.2422 days Hertz = cycles/second ~ radians/sec ~ degrees/sec

Geometry and Mathematics

pi = 710/226 tau = 1420/226 = 710/113 e = 685/252 phi = 466/288 180 degrees = pi radians = 200 grads = 0.5 turns 2120 degrees ~ 37 radians

Physical

G = gravitation = 6.674e-11 = 494/74e-11 m3/(kg s2) h = Plank = 6.62607015e-34 = 815/123 = 1630/246e-34 (J s) k = Boltzmann = 1.380649e-23 = 214/155e-23 J/K fine structure constant = 7.297e-3 = 270/37e-3 ~ 1/137 E0 = vacuum permittivity = 8.854e-12 = 850/96e-12 F/m μ0 = vacuum permeability = 4*pi e-7 H/m = 1.2566e-6 = 142/113e-6 N/A2 F = Faraday constant = 9.6485e4 = 1920/199e4 C/mol

ΔνCs = Δν(133Cs)hfs = 9192631770 s−1

Kcd = 683 cd⋅sr⋅s3⋅kg−1⋅m−2

Temperature

absolute zero = -273.15 C = 0 K = -495.69 F = 0 R triple point of water = 0.01 C = 273.16 K = 32.018 F = 527.708 R boiling water @ 1 atm = 100 C = 373.15 K = 212 F = 707.69 R F C K R

Mass

pound kilo ton atomic mass unit ~ 1.66e-27 ounces metric ton gram kilogram megagram

Distance

5 inches = 127 mm 12 inches = 1 feet inches meter foot mile nautical mile yard angstrom

Area

sq inches sq meter sq cm sq foot sq mile yard acre hectare

Volume

cb inches cb meter cb cm cb foot cb mile cb yard pint mL liter quart gallon cups tablespoon teaspoon oz barrels(oil) acre feet

Pressure

1 atm pounds/sq inch pascal N/m2 millibars pounds/sq foot mmHg feetH20

Speed

light = c = 299792458 m/s ~ 995/332e8 kph mph mps knots ft/min

Money

Energy

electron Volt BTU Joule foot pounds calorie Watt hour

Light

foot candels lux candelas

Force

Newton dynes

Power

Horsepower Watt BTU / hour V A

Charge

electron = 1.602176634e-19 C ~ 149/93e-19

New units

c = 161887940 staves/sec