Scales

Scale meaning(f(C)) 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    |       b        a    |
      ---------------------------
D          | 1        c          |
            ---------------------

a/b = c/d = e/f... or c = d*a/b

            ---------------------
C          |  a    c    e        |
      ---------------------------
D    |        b    d    f  |
      ---------------------

Use with the Ratios of Common Constants below to approximate a multiplication table. For Example pi720/226

            ---------------------
C          |  a*pi  720  b*pi    |
      ---------------------------
D    |        a     226  b |
      ---------------------

a = bc

            ---------------------
C          | 1         c         |
      ---------------------------
LL   |       b         a   |
      ---------------------

a = b2 or b = sqroot(a)

      ---------------------
A/B  |  1              a   |
      ---------------------
C/D  |  1              b   |
      ---------------------

a = f(b) or b = inverse(f)(a)

      ---------------------
Scale|  1              a   |
      ---------------------
C/D  |  1              b   |
      ---------------------

ab = cd or a = c*d/b

            ---------------------
CI         |  a    c             |
      ---------------------------
D    |        b    d       |
      ---------------------

a = bcd or b = a /c /d or b/a = c*d

            ---------------------
C          |  b                  |
CI         |       c             |
      ---------------------------
D    |        a    d       |
      ---------------------

Trigonometric Ratios

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

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

Ratios of Common Constants

Counting

1728 entity = 144 dozen = 12 gross = 1 great gross 20 entities = 1 score 1 mol = N(A) = 6.02214076e23 ~ 1090/181e23 entities 1 unit = 60 minutes = 3600 seconds = 216000 thirds

Metric/SI/IEC/JEDEC Decimalized prefixes

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

Geometry and Mathematics

pi ~ 710/226 tau ~ 1420/226 = 710/113 e ~ 685/252 ~ 87/32 phi ~ 466/288 180 degrees = pi radians = 200 grads = 0.5 turns = 500 milliturns 1 degree = 60 minutes = 3600 seconds 2120 degrees ~ 37 radians 106 degrees ~ 1.85 radians

Distance

1 meter = 100 cm = 1e3 mm = 4e3 Q(Web) = 1e6 microns = 1e6 μm 1 inch = 25.4 mm = 2.54 cm = 1 in = 6 pc = 72 pt = 96 px(Web) 5 inches = 127 mm = 12.7 cm = 5 in = 30 pc = 360 pt = 480 px(Web) 1.25 in = 127 Q 1 yard = 3 feet = 36 inches = 0.9144 m 5 yards = 15 feet = 180 inches 1 mile = 5280 feet = 1760 yards 5 miles = 26400 feet = 8800 yards 625 miles = 3.96e7 inches 1 nautical mile = 1852 meters 1 angstrom = 100 pm 1 mile = 1.609344 km 64 miles ~ 103km

Area

1 meter² = 1e4 cm² = 1e6 mm² = 1e-6 km² = 1e-4 hectares(ha) 1 inches² = 645.16 mm² = 6.4516 cm² 31 in² ~ 2e4 mm² = 200 cm² 1 foot² = 144 in² 1 yard² = 9 feet² 238 yard² ~ 199 m² 1 acre = 4840 yards² = 43560 feet² 1 mile² = 640 acre 855 acre ~ 346 ha

Volume

1 acre foot = 43560 feet³ 1 yard³ = 27 feet³ 1 foot³ = 1728 inches³ 1 gallon = 231 inches³ 1 foot³ = 1728/231 gallons ~ 1930/258 1 inches³ = 16.387064 mL ~ 2540/155 1 meter³ = 1 kiloliter, 1000 liters 1 litre = 1000 mL = 1000 cm³ 1 gallon ~ 3.785 L ~ 1870/494 1 gallon = 4 quarts = 8 pints = 16 cups = 128 oz = 256 tablespoons = 768 teaspoons 1 cup = 236.5882365 ml, 1 legal cup = 240 ml, 1 metric cup = 250 ml

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 1 Hertz = 1 cycles/second = 1 turns/sec = 2pi radians/sec = 360 degrees/sec 4 minutes = 1 degree rotation

Speed

light = c = 299792458 m/s ~ 995/332e8 64 miles/hour ~ 103km/hour 76 m/s ~ 170 mi/h 10 m/s = 36 k/h 1 mi/h = 88 ft/min 1 knot = 1.852 km/h 54 knots ~ 100 km/h 126 knots ~ 145 mi/h

Mass and Weight

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

Force

Newton dynes

Temperature

Point Celsius Kelvin Fahrenheit Rankine
absolute zero -273.15 C 0 K -459.67 F 0 R
-40 C 233.15 K -40 F 419.67 R
triple point of water 0.01 C 273.16 K 32.018 F 491.688 R
boiling water @ 1 atm 100 C 373.15 K 212 F 671.67 R

9 Rankine = 5 Kelvin 0 F = 459.67 R 0 C = 273.15 K F = 9C/5 + 32 = 9K/5 - 459.67 = R - 459.67 ~ 2C + 30 C = K - 273.15 = 5R/9 - 273.15 = 5(F - 32)/9 ~ F/2 - 15 C = 5(F+40)/9 - 40 F = 9(C+40)/5 - 40 K = C + 273.15 = 5R/9 = 5(F + 459.67)/9 R = F + 459.67 = 9K/5 = 9(C + 273.16)/5

Pressure

1 atm = 101325 Pascals = 760 torr ~ 1 bar = 1e5 Pascals pounds/sq inch pascal N/m2 millibars pounds/sq foot mmHg torr feetH20

Energy

electron Volt BTU Joule foot pounds calorie Watt hour

Power

Horsepower Watt BTU / hour V A

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 ~ 1700/192 = 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 = Cesium Hyperfine radiation rate = 9192631770 ~ 1480/161e9 s−1 Kcd = Candela constant = 683 ~ 36200/53 cd⋅sr⋅s3⋅kg−1⋅m−2

Light

foot candles lux candelas

Charge

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

Money

New units

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.

c = 161887940 staves/sec

Backup

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