Reality → Base → Tools → Units
Scientific work is greatly facilitated by metric measuring and decimal numbering as prescribed by the Conférence Générale des Poids et Mesures (CGPM) for the modern international system of measurement (SI). The scheme rests on seven base units that, for maximum accuracy and reliability, are defined through fundamental physical constants set at fixed numerical values:
| quantity | name | symbol | SI units |
| force | newton | N | m kg s-2 |
| electric charge | coulomb | C | A s |
| energy | joule | J | m2 kg s-2 |
| power | watt | W | m2 kg s-3 |
| el. potential diff. | volt | V | m2 kg s-3 A-1 |
From the base units all other units used in physics and chemistry can be derived. The first table lists a few selected units (see Sheet for more). A beauty of the SI system is the easy transition between mechanical and electrical units (1 J = 1 N m = 1 W s). Prefixes are used to make very small or very large numbers more manageable.
| name | symbol | value in SI units | |
| hour | h | 3 600 s | |
| degree (angle) | ° | 0.017 rad | |
| lightyear | ly | 9.46 × 1015 m | |
| electronvolt | eV | 1.6 × 10-19 J |
Several important and commonly used non-SI units are also accepted for use with the SI. The second table lists a small selection. Hours and days are sexagesimal multiples of the SI second that require reconciliation with the calendar [8] . The degree and its sexagesimal subdivisions remain common measurements of angles [9] . The lightyear is a very popular unit for capturing astronomical distances, though astronomers (and SI) prefer other units [10] . The electronvolt is a standard unit for energy and mass in atomic and particle physics [11] .
SI defines the second as the duration of 9 192 631 770 periods of the radiation (9.19 GHz) emitted from the caesium-133 isotope as the resonant microwave frequency of the transition between two hyperfine energy levels. The latest caesium atomic clock is accurate to 1 second in 300 million years (see video).
The common astronomical definition of the second is based on Earth's rotation and the Babylonian sexagesimal system.
SI defines the meter as the distance light in vacuum travels in exactly 1/299 792 458 second, implying that the speed of light in vacuum is set at exactly 299 792 458 meters per second.
Originally the meter was defined as one ten-millionth of the distance between Earth’s equator and north pole (i.e. 40,000 km Earth's circumference) and physically represented in a prototype meter bar.
The Planck constant is set at exactly 6.626 070 15 x 10-34 J⋅s (dimension of action). The constituent joule is an energy unit defined by the kilogram and the SI base units meter (based on exactly set speed of light), and second (based on an exactly defined atomic oscillation). With these definitions, the kilogram is exactly and invariably defined by the Planck constant.
The kilogram was previously based on an artifact (a prototype created as a small platinum cylinder equaling the mass of one liter of water).
The Boltzmann constant is set at exactly 1.380 649×10 × 10-23 J⋅K-1. The constituent joule is an energy unit defined by the kilogram and the SI base units meter (based on exactly set speed of light), and second (based on an exactly defined atomic oscillation). With these definitions, the kelvin is exactly and invariably defined by the Boltzmann constant.
Previously the kelvin was defined as 1/273.16 of the triple point of water expressed in centigrade.
In parallel with the Avogadro constant, the mole is set at exactly 6.022 140 76 × 1023 particles (e.g., molecules, atoms, ions, protons, electrons).
Previously the mole was defined as the number of atoms in 12 grams of the carbon-12 isotope by setting its relative atomic mass at exactly 12.
The candela is defined as the luminous intensity produced by a light source that emits (green) light of 540 THz frequency and an intensity of 1/683 watt per steradian (this implies that the candela's luminous efficacy is set at exactly 683 lumen per watt).
The candela is roughly the luminous intensity of a common candle.
To reconcile the atom-based SI second (and related hour and day) with the astronomy-based calendar time, a leap second is occasionally (now about every 3 years) applied to UTC time for compatibility with mean solar time (see also Earth's rotation).
In normal daily use, the degree (1/360 of a full circle, equivalent to 2π/360 radian) with the subdivisions minute (1/60 degree) and second (1/3600 degree) is much preferred to the more abstract SI unit radian.
A lightyear (symbol ly) is the distance light in vacuum travels in one year (about 9 × 1015 m). Astronomers prefer the astronomical unit (symbol ua, from French unité astronomique, representing the mean earth-sun distance, about 150 million km or 150 × 109 m) or the parsec (symbol pc, distance at which one ua subtends an angle of one second, about 3 × 1016 m). The distances are related as follows: 1 pc equals about 3 ly or about 200 000 ua.
An electronvolt (symbol eV) is the kinetic energy (about 1.6 × 10-19 J) an electron gains (or looses) when passing through a potential difference of 1 volt. The use of the eV as a mass unit is based on Einstein’s famous equation E = m c2, which can also be written as m = E / c2 (the dimensions of the latter formula can be verified as follows: energy is force (m kg s-2) times length (m), divided by velocity squared (m2 s-2), i.e., mass (kg) remains).