Units, Symbols and Measurement Abbreviations
The International System of Units (SI, from the French Système international d’unités) is the metric system used universally in science, industry, and commerce. It is structured around seven base units, from which all other measurement units are derived.
SI Base Units
The seven foundational pillars of modern metrology are precisely defined by invariant constants of nature (such as the speed of light c and the Planck constant h).
| Quantity | Unit Name | Symbol | Dimension |
| Length | meter | m | mathsf{L} |
| Mass | kilogram | kg | mathsf{M} |
| Time | second | s | mathsf{T} |
| Electric Current | ampere | A | mathsf{I} |
| Thermodynamic Temperature | kelvin | K | Theta |
| Amount of Substance | mole | mol | mathsf{N} |
| Luminous Intensity | candela | cd | mathsf{J} |
SI Derived Units with Special Names
Derived units are algebraic combinations of the base units. Many of these combinations are given special names and symbols for ease of expression.
Mechanics and Thermodynamics
- Newton (N): Unit of force. text{N} = text{kg} cdot text{m/s}^2
- Joule (J): Unit of energy, work, or heat. text{J} = text{N} cdot text{m} = text{kg} cdot text{m}^2/text{s}^2
- Watt (W): Unit of power or radiant flux. text{W} = text{J/s} = text{kg} cdot text{m}^2/text{s}^3
- Pascal (Pa): Unit of pressure or stress. text{Pa} = text{N/m}^2 = text{kg}/(text{m} cdot text{s}^2)
- Hertz (Hz): Unit of frequency. text{Hz} = text{s}^{-1}
Electromagnetism
- Coulomb (C): Unit of electric charge. text{C} = text{A} cdot text{s}
- Volt (V): Unit of electric potential, potential difference, and electromotive force. text{V} = text{W/A} = text{kg} cdot text{m}^2/(text{A} cdot text{s}^3)
- Ohm (Ω): Unit of electrical resistance. Omega = text{V/A} = text{kg} cdot text{m}^2/(text{A}^2 cdot text{s}^3)
- Farad (F): Unit of electrical capacitance. text{F} = text{C/V}
- Tesla (T): Unit of magnetic flux density. text{T} = text{Wb/m}^2 = text{kg}/(text{A} cdot text{s}^2)
- Weber (Wb): Unit of magnetic flux. text{Wb} = text{V} cdot text{s}
- Henry (H): Unit of electrical inductance. text{H} = text{Wb/A}
SI Prefixes (Multiples and Submultiples)
Prefixes are scaling factors applied to SI units to express quantities across vast structural scales, from subatomic tracking to cosmological distances.
| Prefix | Symbol | Factor | Prefix | Symbol | Factor |
| quetta | Q | 1030 | deci | d | 10-1 |
| ronna | R | 1027 | centi | c | 10-2 |
| yotta | Y | 1024 | milli | m | 10-3 |
| zetta | Z | 1021 | micro | mu | 10-6 |
| exa | E | 1018 | nano | n | 10-9 |
| peta | P | 1015 | pico | p | 10-12 |
| tera | T | 1012 | femto | f | 10-15 |
| giga | G | 109 | atto | a | 10-18 |
| mega | M | 106 | zepto | z | 10-21 |
| kilo | k | 103 | yocto | y | 10-24 |
| hecto | h | 102 | ronto | r | 10-27 |
| deka | da | 101 | quecto | q | 10-30 |
Non-SI Units Accepted for Use with SI
These units do not strictly belong to the SI framework but are universally accepted due to historical baseline usage or structural convenience in specific fields.
- Minute (min): 1 min = 60 s
- Hour (h): 1 h = 60 min = 3600 s
- Day (d): 1 d = 24 h = 86400 s
- Liter (L or l): 1 L = 1 dm3 = 10^{-3 m3
- Tonne (t): Metric ton. 1 t = 103 kg
- Electronvolt (eV): Unit of energy typically deployed in particle physics. 1text{ eV} approx 1.602176634 times 10^{-19}text{ J}
- Astronomical Unit (au): Average distance from Earth to the Sun. 1 au = 149597870700 m
Imperial and US Customary Systems
Primarily utilized in the United States and historically across British Commonwealth systems, these systems are now structurally standardized relative to SI baselines.
Length and Area
- Inch (in): 1 in = 2.54 cm
- Foot (ft): 1 ft = 12 in = 0.3048 m
- Yard (yd): 1 yd = 3 ft = 0.9144 m
- Mile (mi): 1 mi = 1760 yd = 5280 ft ≈ 1.6093 km
- Acre (ac): Unit of land area. 1 ac = 43560 ft2 ≈ 4046.86 m^2
Mass and Weight
Note: In practical engineering and daily language, “weight” units double as mass or force depending on application.
- Ounce (oz): Avoirdupois mass fraction. 1 oz ≈ 28.35 g
- Pound (lb): Base mass baseline. 1 lb = 16 oz = 0.45359237 kg
- Stone (st): Primarily British shorthand. 1 st = 14 lb ≈ 6.35 kg
Fluid Volume
- Fluid Ounce (fl oz): US fl oz ≈ 29.57 mL | UK fl oz ≈ 28.41 mL
- Pint (pt): 1 pt = 16 US fl oz ≈ 473.18 mL
- Quart (qt): 1 qt = 2 pt ≈ 0.946 L
- Gallon (gal): 1 US gal = 4 qt = 3.785 L | 1 UK gal ≈ 4.546 L
Field-Specific Measurement Abbreviations
CGS (Centimeter-Gram-Second) / Specialized Physics Units
- Ångström (Å): Used in crystallography and structural chemistry. 1 Å = 10-10 m = 0.1 nm
- Barye (ba): CGS unit of pressure. 1 ba = 0.1 Pa
- Gal (Gal): Unit of acceleration used in geodesy and geophysics. 1 Gal = 1 cm/s2 = 10^{-2 m/s2
- Barn (b): Area unit used in nuclear physics to express cross-sections. 1 b = 10-28 m2
Data Science and Computing
Computer storage leverages binary scaling base-2 (210 = 1024) versus metric scaling base-10 (103 = 1000).
| Metric Binary Equivalent | Value | IEC Binary Standard | Value |
| Kilobyte (KB) | 103 bytes | Kibibyte (KiB) | 210 bytes |
| Megabyte (MB) | 106 bytes | Mebibyte (MiB) | 220 bytes |
| Gigabyte (GB) | 109 bytes | Gibibyte (GiB) | 230 bytes |
| Terabyte (TB) | 1012 bytes | Tebibyte (TiB) | 240 bytes |
Standard Notation Rules
- Capitalization: Symbols are lowercase (e.g., m, s) unless named after a person (e.g., N for Newton, K for Kelvin). The exception is Liter (L), to avoid confusion with the number 1.
- Plurals: Symbols are mathematical designators, not abbreviations. They never take an “s” (e.g., 50 kg, not 50 kgs).
- Punctuation: Never place a period after a unit symbol unless it falls at the end of a sentence.
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