Important constants and conversion factors

= mol

electric current; SI base unit. one A = one C ˣ s⁻¹ = 6.241 509 744 607 ˣ 10¹⁸ e⁻ ˣ s⁻¹, based on the exact charge on the electron.

101.325 kPa (exactly) =1.013 25 bar (exactly) = 760 Torr (exactly)
= 1.033 23 kg_F ˣ cm⁻² = 760.001 mm Hg (0 °C) ≡ 10.3629 m H₂O (25 °C)

Standard pressure is now defined as 100 kPa exactly.

relates temperature to the kinetic energy of a gas; 1.380 649 ˣ 10⁻²³ J ˣ K⁻¹ (exactly, with the dimensions of entropy; an SI constant) [2395];

k_B ˣ T/e = 25.692 579 12 mV (at 25 °C)

heat energy; 1 Btu = 1.054 3503 kJ; one therm (thm)= 100,000 Btu

1 Btu ˣ hr⁻¹ = 0.292 875 W (power)

Celsius ( °C) (centigrade)

0ne °C = one kelvin by definition; T_K = T_°C + 273.15; T_°C = T_K - 273.15

273.15 K (exactly; one degree Celsius has the same size as one kelvin);

Standard temperature is now defined as 273.15 K exactly.

dynamic viscosity; one cP = mPa

1 C ˣ m⁻² = 6.241 5094 e⁻ ˣ nm⁻²

1 e⁻ ˣ nm⁻² = 0.1602177 C ˣ m⁻²

volume; = 10⁻⁶ m³

volume; = 0.028 316 846 592 m³ = 28.316 846 592 L (exactly)

1 m³ = 35.314 666 7215 cubic feet

energy, 1 eV = 1 ˣ e ˣ V = 1.602 176 634 ˣ 10⁻¹⁹ J (exactly) [934]

1 eV ≡ 96.485 332 12 kJ ˣ mol⁻¹

1 eV ≡  8,065.543 937  cm⁻¹ ≡ 241.798 924 208 492 THz (≡ 1,239.841 984 39 nm)

1 eV ≡ 11,604.518 121 5501 K

mass (m) to energy (E); E = m ˣ c²

frequency (ω) to energy (E); E = ħ ˣ ω

temperature (T) to energy (E); E = k_B ˣ T

(Fahrenheit temperature) = (Kelvin temperature) ˣ 9⁄5 − 459.67
(Kelvin temperature) = (Fahrenheit temperature + 459.67) ˣ 5⁄9

(Fahrenheit temperature) = (Celsius temperature) ˣ 9⁄5 + 32
(Celsius temperature) = (Fahrenheit temperature - 32) ˣ 5⁄9

One degree Fahrenheit has the same size as 5/9 kelvin and 5/9 °C

Relates energy to size; G = 6.674 30 ˣ 10⁻¹¹ m³ ˣ kg⁻¹ ˣ s⁻²; E = G ˣ m²/R

Imperial (UK) = 4.546 09 L (exactly)

US            = 3.785 411 784 L (exactly)

Gas constant, molar; R

(R = k_B ˣ N_A)

R = 8.314 462 618 153 24 Pa ˣ m³ ˣ mol⁻¹ ˣ K⁻¹ (exactly; J ˣ mol⁻¹ ˣ K⁻¹) [2395]

R = 8.314 462 618 153 24 kPa ˣ L ˣ mol⁻¹ ˣ K⁻¹ (exactly)

R = 0.082 057 46 L ˣ atm ˣ mol⁻¹ ˣ K⁻¹ = 1.987 21 cal ˣ K⁻¹ ˣ mol⁻¹

energy; E_h = atomic unit of energy = 4.359 744 722 2071 ˣ 10⁻¹⁸ J [934]

area, 1 ha = 1 hm² = 10⁴ m²

inductance; 1 H = 1 V ˣ s ˣ A⁻¹ = kg ˣ m² ˣ s⁻² ˣ A⁻²

length; One inch = 2.54 cm (exactly)

energy, work, amount of heat; one J = one kg ˣ m² ˣ s⁻²;

J = N ˣ m = Pa ˣ m³ = kPa ˣ L = C ˣ V

One joule ≡ 1.509 190 179 642 15 ˣ 10³³ Hz; ≡ 5.034 116 567 542 71 ˣ 10²² cm⁻¹;

≡ 6.241 509 074 460 76 ˣ 10¹⁸ eV; one J ˣ mol⁻¹ ≡ 0.120 272 355  K

catalytic activity; one kat = one mol ˣ s⁻¹

Thermodynamic temperature; SI base unit. It was defined as the fraction 1/273.16 of the thermodynamic temperature of the triple point of set isotopic composition water up until 20 May 2019; (Absolute zero, 0 K = −273.15 °C or −459.67 °F). Now it is defined in terms of the Boltzmann constant, the second, the meter, and the kilogram [934]. One kelvin is equal to a change in the thermodynamic temperature T resulting in a change of thermal energy k_BT by 1.380 649 ˣ 10^-23 J.

1 K = 0.086 173 332 621 4518 meV = 0.695 034 8004 cm¹ ( ≡ 8.314 4626 J ˣ mol⁻¹)

mass (m); SI base unit. Defined in terms of the Planck constant (h), meter, and second [2395] (E =h ˣ ν = m ˣ c²); kg = h / (6.626 070 15 ˣ 10⁻³⁴ ) ˣ m⁻² ˣ s

= (299,792,458)²/{(6.626 070 15 ˣ 10⁻³⁴) ˣ ( 9,192,631,770)} ˣ Δν_Cs ˣ h ˣ c⁻² (exactly)

Permeability

the degree of magnetization of a material in response to a magnetic field;

= H ˣ m⁻¹ = m ˣ kg ˣ s⁻² ˣ A⁻²

Permeability of a vacuum (µ₀) (Magnetic constant)

µ₀ = 4π ˣ 10⁻⁷ N ˣ A⁻² = 4π ˣ 10⁻⁷ T² ˣ m³ ˣ J⁻¹ (exactly)

µ₀ = 1.256 637 062 12 µH ˣ m⁻¹ (μN ˣ A⁻²) [934]

Permittivity (ε)

the ability of a substance to store electrical energy in an electric field;

ε = F ˣ m⁻¹ = m⁻³ ˣ kg⁻¹ ˣ s⁴ ˣ A²

Permittivity of a vacuum (ε₀) (Electric constant)

ε₀ = (μ₀ c²)⁻¹ in units C² ˣ J⁻¹ ˣ m⁻¹ (exactly)

ε₀ = 8.854 187 8128 pF ˣ m⁻¹

quantum of electromagnetic action, relates energy to frequency; a photon's energy (E) is equal to its frequency multiplied by the Planck constant (E = h ˣ ν; h = 6.626 070 150 ˣ 10⁻³⁴ kg ˣ m² ˣ s⁻¹ (J  ˣ  s, J ˣ Hz⁻¹, exactly; a SI constant) [2395]

relates frequency to energy; ħ = 1.054 571 817 ˣ 10⁻³⁴ J  ˣ  s (J ˣ Hz⁻¹);

energy (J) =ħ ˣ ω

Imperial (UK) = 0.568 261 25 L (exactly); may be divided into 20 fluid ounces (UK)

US                = 0.473 176 473 L (exactly); may be divided into 16 fluid ounces (US)

Pound (lb) (avoirdupois, US and UK) (not an SI unit)

Quadrillion

SI unit of angle, the units are m ˣ m⁻¹ but usually treated as dimensionless;

one rad = 360°/2π = 57.295 779 513 082 320 876 798 154 814 105 170 3°;

one revolution (cycle) = 360° = 2π ˣ rad °

relative density; for liquids, it is relative to water at 3.98 °C (~ 1000 kg ˣ m⁻³)

                         for gases, it is relative to air at 20 °C, 101.325 kPa (~ 1.205 kg ˣ m⁻³)

c = 299,792,458 m ˣ s⁻¹ (exactly; also defines the meter) [934]

= 670,616,629.3844 mph

101.325 kPa, 273.15 K, concentration 1 mol ˣ L⁻¹ (1000 mol ˣ m⁻³)

STP ≡ 100 kPa, 273.15 K (exactly) IUPAC

electrical charge; 1 statC = dyn^½ ˣ cm = cm^3/2 ˣ g^½ ˣ s⁻¹ ; not an SI unit; see esu

varies as stated, but often; pressure, 100 kPa; temperature, 25.00 °C (77 °F)

σ = π²k_B⁴/(60ħ³c²) = 5.670 374 419 ˣ 10⁻⁸ W ˣ m⁻² ˣ K⁻⁴

The solid angle of the sphere surface (area A, radius r) from the center, = (A/r² ) ˣ sr

4π  ˣ sr = entire surface of a sphere radius r. The units of sr are m² ˣ m⁻² but usually treated as dimensionless.

kibi, Ki, (2¹⁰)¹ ; mebi, Mi, (2¹⁰)² ; gibi, Gi, (2¹⁰)³ ; tebi, Ti, (2¹⁰)⁴ ; pebi, Pi, (2¹⁰)⁵ ; exbi, Ei (2¹⁰)⁶; zebi, Zi, (2¹⁰)⁷ ; yobi, Yi (2¹⁰)⁸ , NIST e.g.,

1 gibibyte = 1 GiB = 1,073,741,824 byte; 1 gigabyte = 1 GB = 1,000,000,000 byte

deci- d 10⁻¹;centi- c 10⁻²; milli- m 10⁻³; micro- µ 10⁻⁶; nano- n 10⁻⁹; pico- p 10⁻¹²; femto- f 10⁻¹⁵; atto- a 10⁻¹⁸; zepto- z 10⁻²¹; yocto- y 10⁻²⁴; ronto- r 10^{−27 a}; quecto- q 10^{−30 a}

deca- da 10¹; hecto- h 10²; kilo- k 10³; mega- M 10⁶; giga- G 10⁹; tera- T 10¹²; peta- P 10¹⁵; exa- E 10¹⁸; zetta- Z 10²¹; yotta- Y 10²⁴; ronna- R 10^{27 a}; quetta- Q 10^{30 a}