A1
Constants and Units
Reference material used across every module: the constants of nature, and the scale words attached to their units.
A1.1Fundamental Constants
The fundamental constants of nature, gathered here for reference — each has already appeared in its own module.
Fundamental constants
| c | speed of light in vacuum | 2.998×10⁸ m/s | SI (exact) |
| G | gravitational constant | 6.674×10⁻¹¹ N·m²/kg² | CODATA 2022 |
| h | Planck constant | 6.626×10⁻³⁴ J·s | SI (exact) |
| ħ | reduced Planck constant (h/2π) | 1.055×10⁻³⁴ J·s | SI (exact) |
| e | elementary charge | 1.602×10⁻¹⁹ C | SI (exact) |
| ε₀ | vacuum permittivity | 8.854×10⁻¹² C²/(N·m²) | CODATA 2022 |
| k_e | Coulomb constant (1/4πε₀) | 8.99×10⁹ N·m²/C² | CODATA 2022 |
| k_B | Boltzmann constant | 1.381×10⁻²³ J/K | SI (exact) |
| N_A | Avogadro constant | 6.022×10²³ mol⁻¹ | SI (exact) |
| R | molar gas constant | 8.314 J/(mol·K) | SI (exact) |
| m_e | electron mass | 9.109×10⁻³¹ kg | CODATA 2022 |
| m_p | proton mass | 1.673×10⁻²⁷ kg | CODATA 2022 |
| σ | Stefan-Boltzmann constant | 5.670×10⁻⁸ W/(m²·K⁴) | SI (exact) |
A1.2Unit Conversions
Converting between unit systems means multiplying by a conversion factor equal to one — for example, multiplying by (1 m / 3.281 ft) to convert feet to metres. Chaining several such factors converts through several units at once, and any unit left over that shouldn't be there is an immediate signal that a conversion factor was inverted or omitted.
A1.3Prefixes and Orders of Magnitude
SI prefixes attach a power-of-ten multiplier to any unit, keeping numbers a manageable size across vastly different scales.
Common SI prefixes
| tera | T | 10¹² |
| giga | G | 10⁹ |
| mega | M | 10⁶ |
| kilo | k | 10³ |
| centi | c | 10⁻² |
| milli | m | 10⁻³ |
| micro | µ | 10⁻⁶ |
| nano | n | 10⁻⁹ |
| pico | p | 10⁻¹² |
| femto | f | 10⁻¹⁵ |
A1.4Imperial / US Customary to SI
Common non-SI units still seen in engineering and everyday measurement. Every factor below is exact — fixed either by international definition or by combining other exact factors — except the one marked †, which rests on a reference condition rather than a fixed definition.
Length
| Inch (in) | Meter (m) | 0.0254 |
| Foot (ft) | Meter (m) | 0.3048 |
| Yard (yd) | Meter (m) | 0.9144 |
| Mile (mi) | Kilometer (km) | 1.609344 |
Mass
| Ounce (oz) | Kilogram (kg) | 0.028349523125 |
| Pound (lb) | Kilogram (kg) | 0.45359237 |
Pressure
| PSI (lbf/in²) | Pascal (Pa) | 6894.757293168 |
| inHg (0 °C) | Pascal (Pa) | 3386.389† |
Force & Energy
| Pound-force (lbf) | Newton (N) | 4.4482216152605 |
| Foot-pound (ft·lbf) | Joule (J) | 1.3558179483314 |
| Horsepower (hp) | Watt (W) | 745.69987158727 |
Volume
| US Gallon (gal) | Liter (L) | 3.785411784 |
| UK Gallon (gal) | Liter (L) | 4.54609 |
| US Fluid Ounce (fl oz) | Milliliter (mL) | 29.5735295625 |