The International System of Units or SI System: A Universal Standard for Measurements
The International System of Units or SI system, abbreviated from the French Système International d'Unités, is the globally accepted standard for measurement. It provides a coherent and precise framework for scientific, industrial, and everyday applications, ensuring consistency and accuracy across disciplines.
What Is the SI System?
The SI system is a modern iteration of the metric system, introduced in 1960 by the General Conference on Weights and Measures (CGPM). It is built on seven base units, which serve as the foundation for all other derived units. These base units are defined using fundamental physical constants, ensuring long-term stability and compatibility with emerging technologies like quantum measurements.
SI Base units
Below is an overview of the 7 essential base units in the SI system:
| Base Unit | Unit Symbol | Quantity | Quantity Symbol |
|---|---|---|---|
| second | s | time | t |
| meter | m | length | l, x, r, etc. |
| kilogram | kg | mass | m |
| ampere | A | electric current | I, i |
| kelvin | K | thermodynamic temperature | T |
| mole | mol | amount of substance | n |
| candela | cd | luminous intensity | Iν |
| Download this table as an image file | |||
Derived units with special names
The SI system also recognizes a set of 22 derived units with special names, which are widely used across scientific disciplines. These units simplify complex combinations of base units into memorable terms. Find a comprehensive overview below:
| Name | Symbol | Quantity | Equivalents | SI base unit Equivalents |
|---|---|---|---|---|
| hertz | Hz | frequency | 1/s | s−1 |
| radian | rad | angle | m/m | 1 |
| steradian | sr | solid angle | m2/m2 | 1 |
| newtons | N | force, weight | kg⋅m/s2 | kg⋅m⋅s−2 |
| pascals | Pa | pressure, stress | N/m2 | kg⋅m−1⋅s−2 |
| joules | J | energy, work, heat | m⋅N, C⋅V, W⋅s | kg⋅m2⋅s−2 |
| watt | W | power, radiant flux | J/s, V⋅A | kg⋅m2⋅s−3 |
| coulomb | C | electric charge | s⋅A, F⋅V | s⋅A |
| volt | V | voltage, electrical potential difference, electromotive force (EMF) | W/A, J/C | kg⋅m2⋅s−3⋅A−1 |
| farad | F | electrical capacitance | C/V, s/Ω | kg−1⋅m−2⋅s4⋅A2 |
| ohm | Ω | electrical resistance, impedance, reactance | 1/S, V/A | kg⋅m2⋅s−3⋅A−2 |
| siemens | S | electrical conductance | 1/Ω, A/V | kg−1⋅m−2⋅s3⋅A2 |
| weber | Wb | magnetic flux | J/A, T⋅m2, V⋅s | kg⋅m2⋅s−2⋅A−1 |
| tesla | T | magnetic induction, magnetic flux density | V⋅s/m2, Wb/m2, N/(A⋅m) | kg⋅s−2⋅A−1 |
| henry | H | electrical inductance | V⋅s/A, Ω⋅s, Wb/A | kg⋅m2⋅s−2⋅A−2 |
| degree Celsius | °C | temperature relative to 273.15 K | K | K |
| lumen | lm | luminous flux | cd⋅sr | cd |
| lux | lx | illuminance | lm/m2 | cd⋅m−2 |
| becquerel | Bq | radioactivity (decays per unit time) | 1/s | s−1 |
| gray | Gy | absorbed dose (of ionizing radiation) | J/kg | m2⋅s−2 |
| sievert | Sv | equivalent dose (of ionizing radiation) | J/kg | m2⋅s−2 |
| katal | kat | catalytic activity | mol/s | s−1⋅mol |
| Download this table as an image file | ||||
Unnamed derived units by field of application
Besides the 22 specially named derived units, many others are unnamed and simply expressed in terms of combinations of base units. Below is a breakdown of unnamed SI derived units categorized by their field of application:
Mechanics
Mechanics is a branch of physics that deals with the study of motion, forces, and their effects on physical objects. Besides several base and named derived units, a multitude of unnamed units play a key role in this field.
| Name | Symbol | Quantity | SI Base Unit Equivalent |
|---|---|---|---|
| square meter | m2 | area | m2 |
| cubic meter | m3 | volume | m3 |
| newton-second | N⋅s | momentum, impulse | m⋅kg⋅s−1 |
| newton meter second | N⋅m⋅s | angular momentum | m2⋅kg⋅s−1 |
| newton-meter | N⋅m = J/rad | torque, moment of force | m2⋅kg⋅s−2 |
| newton per second | N/s | yank | m⋅kg⋅s−3 |
| reciprocal meter | m−1 | wavenumber, optical power, curvature, spatial frequency | m−1 |
| kilogram per square meter | kg/m2 | area density | m−2⋅kg |
| kilogram per cubic meter | kg/m3 | density, mass density | m−3⋅kg |
| cubic meter per kilogram | m3/kg | specific volume | m3⋅kg−1 |
| joule-second | J⋅s | action | m2⋅kg⋅s−1 |
| joule per kilogram | J/kg | specific energy | m2⋅s−2 |
| joule per cubic meter | J/m3 | energy density | m−1⋅kg⋅s−2 |
| newton per meter | N/m = J/m2 | surface tension, stiffness | kg⋅s−2 |
| watt per square meter | W/m2 | heat flux density, irradiance | kg⋅s−3 |
| square meter per second | m2/s | kinematic viscosity, thermal diffusivity, diffusion coefficient | m2⋅s−1 |
| pascal-second | Pa⋅s = N⋅s/m2 | dynamic viscosity | m−1⋅kg⋅s−1 |
| kilogram per meter | kg/m | linear mass density | m−1⋅kg |
| kilogram per second | kg/s | mass flow rate | kg⋅s−1 |
| watt per steradian square meter | W/(sr⋅m2) | radiance | kg⋅s−3 |
| watt per steradian cubic meter | W/(sr⋅m3) | radiance | m−1⋅kg⋅s−3 |
| watt per meter | W/m | spectral power | m⋅kg⋅s−3 |
| gray per second | Gy/s | absorbed dose rate | m2⋅s−3 |
| meter per cubic meter | m/m3 | fuel efficiency | m−2 |
| watt per cubic meter | W/m3 | spectral irradiance, power density | m−1⋅kg⋅s−3 |
| joule per square meter second | J/(m2⋅s) | energy flux density | kg⋅s−3 |
| reciprocal pascal | Pa−1 | compressibility | m⋅kg−1⋅s2 |
| joule per square meter | J/m2 | radiant exposure | kg⋅s−2 |
| kilogram square meter | kg⋅m2 | moment of inertia | m2⋅kg |
| newton meter second per kilogram | N⋅m⋅s/kg | specific angular momentum | m2⋅s−1 |
| watt per steradian | W/sr | radiant intensity | m2⋅kg⋅s−3 |
| watt per steradian meter | W/(sr⋅m) | spectral intensity | m⋅kg⋅s−3 |
Kinematics
Kinematics is a branch of mechanics that focuses on the motion of objects without considering the forces that cause the motion. It deals with quantities such as displacement, velocity, acceleration, and time. While kinematics uses some named SI units (e.g., meter for displacement), many other quantities are represented using unnamed SI derived units:
| Name | Symbol | Quantity | SI Base Unit Equivalent |
|---|---|---|---|
| meter per second | m/s | speed, velocity | m⋅s−1 |
| meter per second squared | m/s2 | acceleration | m⋅s−2 |
| meter per second cubed | m/s3 | jerk, jolt | m⋅s−3 |
| meter per second to the fourth | m/s4 | snap, jounce | m⋅s−4 |
| kilogram meter per second to the third | kg⋅m/s3 | mass control | kg⋅m⋅s−3 |
| radian per second | rad/s | angular velocity | s−1 |
| radian per second squared | rad/s2 | angular acceleration | s−2 |
| hertz per second | Hz/s | frequency drift | s−2 |
| cubic meter per second | m3/s | volumetric flow | m3⋅s−1 |
Chemistry
Chemistry is the scientific study of matter, its properties, composition, and the changes it undergoes during chemical reactions. Precise measurements are essential in chemistry to quantify substances, analyze reactions, and communicate findings effectively. While the SI system provides named units for some quantities (e.g., mole as a base unit for the amount of substance), many other units used in chemistry are unnamed.
| Name | Symbol | Quantity | SI Base Unit Equivalent |
|---|---|---|---|
| mole per cubic meter | mol/m3 | molarity, amount of substance concentration | m−3⋅mol |
| cubic meter per mole | m3/mol | molar volume | m3⋅mol−1 |
| joule per kelvin mole | J/(K⋅mol) | molar heat capacity, molar entropy | m2⋅kg⋅s−2⋅K−1⋅mol−1 |
| joule per mole | J/mol | molar energy | m2⋅kg⋅s−2⋅mol−1 |
| siemens square meter per mole | S⋅m2/mol | molar conductivity | kg−1⋅s3⋅A2⋅mol−1 |
| mole per kilogram | mol/kg | molality | kg−1⋅mol |
| kilogram per mole | kg/mol | molar mass | kg⋅mol−1 |
| cubic meter per mole second | m3/(mol⋅s) | catalytic efficiency | m3⋅s−1⋅mol−1 |
Electromagnetics
In electromagnetism, electric and magnetic fields are studied, how they interact, and how they effect matter. It encompasses phenomena such as electric currents, magnetic forces, electromagnetic waves, and more. While electromagnetism relies on several named SI derived units (e.g., volt, tesla), many other quantities are represented using unnamed SI derived units.
| Name | Symbol | Quantity | SI Base Unit Equivalent |
|---|---|---|---|
| coulomb per square meter | C/m2 | electric displacement field, polarization density | m−2⋅s⋅A |
| coulomb per cubic meter | C/m3 | electric charge density | m−3⋅s⋅A |
| ampere per square meter | A/m2 | electric current density | m−2⋅A |
| siemens per meter | S/m | electrical conductivity | m−3⋅kg−1⋅s3⋅A2 |
| farad per meter | F/m | permittivity | m−3⋅kg−1⋅s4⋅A2 |
| henry per meter | H/m | magnetic permeability | m⋅kg⋅s−2⋅A−2 |
| volt per meter | V/m | electric field strength | m⋅kg⋅s−3⋅A−1 |
| ampere per meter | A/m | magnetization, magnetic field strength | m−1⋅A |
| coulomb per kilogram | C/kg | exposure (X and gamma rays) | kg−1⋅s⋅A |
| ohm meter | Ω⋅m | resistivity | m3⋅kg⋅s−3⋅A−2 |
| coulomb per meter | C/m | linear charge density | m−1⋅s⋅A |
| joule per tesla | J/T | magnetic dipole moment | m2⋅A |
| square meter per volt second | m2/(V⋅s) | electron mobility | kg−1⋅s2⋅A |
| reciprocal henry | H−1 | magnetic reluctance | m−2⋅kg−1⋅s2⋅A2 |
| weber per meter | Wb/m | magnetic vector potential | m⋅kg⋅s−2⋅A−1 |
| weber meter | Wb⋅m | magnetic moment | m3⋅kg⋅s−2⋅A−1 |
| tesla meter | T⋅m | magnetic rigidity | m⋅kg⋅s−2⋅A−1 |
| ampere radian | A⋅rad | magnetomotive force | A |
| meter per henry | m/H | magnetic susceptibility | m−1⋅kg−1⋅s2⋅A2 |
Photometry
Photometry is the science of measuring light as perceived by the human visual system. It focuses on the visible portion of the electromagnetic spectrum and accounts for the sensitivity of the human eye to different wavelengths. While photometry uses several named SI units, such as candela (cd), lumen (lm), and lux (lx), many other quantities rely on unnamed units.
| Name | Symbol | Quantity | SI Base Unit Equivalent |
|---|---|---|---|
| lumen second | lm⋅s | luminous energy | s⋅cd |
| lux second | lx⋅s | luminous exposure | m−2⋅s⋅cd |
| candela per square meter | cd/m2 | luminance | m−2⋅cd |
| lumen per watt | lm/W | luminous efficacy | m−2⋅kg−1⋅s3⋅cd |
Thermodynamics
Thermodynamics studies the relationships between heat, energy, and work. It focuses on how energy is transferred and transformed in physical systems, as well as the properties of matter under various conditions. While thermodynamics uses named SI units like joule (J) for energy and watt (W) for power, many other quantities rely on unnamed SI units, as listed below.
| Name | Symbol | Quantity | SI Base Unit Equivalent |
|---|---|---|---|
| joule per kelvin | J/K | heat capacity, entropy | m2⋅kg⋅s−2⋅K−1 |
| joule per kilogram kelvin | J/(K⋅kg) | specific heat capacity, specific entropy | m2⋅s−2⋅K−1 |
| watt per meter kelvin | W/(m⋅K) | thermal conductivity | m⋅kg⋅s−3⋅K−1 |
| kelvin per watt | K/W | thermal resistance | m−2⋅kg−1⋅s3⋅K |
| reciprocal kelvin | K−1 | thermal expansion coefficient | K−1 |
| kelvin per meter | K/m | temperature gradient | m−1⋅K |
SI unit prefixes
The SI system includes a comprehensive list of prefixes that can be combined with its units to express a wide range of quantities, from very large to very small. Until 2022, there were 20 prefixes available. However, with the rapid advancements in data science, four new prefixes were added: quetta, ronna, ronto, and quecto. These additions not only address the growing needs in data science but also enhance the symmetry of the prefix system, allowing for more precise and consistent communication.
| Prefix | Symbol | Power of 10 | Name | |
|---|---|---|---|---|
| quetta | Q | 1030 | nonillion | |
| ronna | R | 1027 | octillion | |
| yotta | Y | 1024 | septillion | |
| zetta | Z | 1021 | sextillion | |
| exa | E | 1018 | quintillion | |
| peta | P | 1015 | quadrillion | |
| tera | T | 1012 | trillion | |
| giga | G | 109 | billion | |
| mega | M | 106 | million | |
| kilo | k | 103 | thousand | |
| hecto | h | 102 | hundred | |
| deka | da | 101 | ten | |
| - | - | 100 | one | |
| deci | d | 10-1 | tenth | |
| centi | c | 10-2 | hundredth | |
| milli | m | 10-3 | thousandth | |
| micro | μ | 10-6 | millionth | |
| nano | n | 10-9 | billionth | |
| pico | p | 10-12 | trillionth | |
| femto | f | 10-15 | quadrillionth | |
| atto | a | 10-18 | quintillionth | |
| zepto | z | 10-21 | sextillionth | |
| yocto | y | 10-24 | septillionth | |
| ronto | r | 10-27 | octillionth | |
| quecto | q | 10-30 | nonillionth | |
| Download this table as an image file | ||||
Named units commonly used with SI units
Lastly there are some commonly known non-SI units, which are widely used in conjunction with SI units. Find below a non-exhaustive list. Most of these units are not prefixed, but there are exceptions. For example the liter, though not an official SI unit, may be used with SI prefixes. The most commonly used prefixed unit being the milliliter, which equals to one-thousandth of a liter.
| Name | Symbol | Quantity | SI Equivalent |
|---|---|---|---|
| Minute | min | Time | 1 min = 60 s |
| Hour | h | Time | 1 h = 3600 s |
| Day | d | Time | 1 d = 86,400 s |
| Degree (plane angle) | ° | Angle | 1° = π/180 rad |
| Minute of arc | ′ | Angle | 1′ = (1/60)° = π/10,800 rad |
| Second of arc | ″ | Angle | 1″ = (1/60)′ = π/648,000 rad |
| Astronomical Unit | au | Length | 1 au = 149,597,870,700 m |
| Hectare | ha | Area | 1 ha = 10,000 m² |
| Liter | L | Volume | 1 L = 1 dm³ = 0.001 m³ |
| Tonne (Metric Ton) | t | Mass | 1 t = 1,000 kg |
| Dalton (Unified Atomic Mass Unit) | Da | Mass | 1 Da ≈ 1.66053906660 × 10⁻²⁷ kg |
| Electronvolt | eV | Energy | 1 eV = 1.602176634 × 10⁻¹⁹ J |
| Atmosphere (Standard Atmosphere) | atm | Pressure | 1 atm ≈ 101,325 Pa |
| Calorie | cal | Energy | 1 cal = 4.184 J |
Free resources
We offer handy images of the base and derived unit tables above that are free to use. Please note that these images should not be modified. While a link back to our original resource is not required, it is greatly appreciated if you choose to use them on your personal website! Find the images below:
Conclusion
The SI system is more than just a tool for measurement; it is a universal language that bridges gaps between disciplines and nations. Whether you're converting units online or conducting cutting-edge research, understanding and using SI units ensures accuracy and consistency in all aspects of life. For quick conversions between SI units or non-SI units commonly used alongside them (like liters or minutes), explore our free unit converter tools today!