Centimetre–gram–second system of units
Metric system variant using centimetre, gram, and second.
The centimetre–gram–second system of units, often abbreviated as CGS or cgs, is a version of the metric system that uses the centimetre for length, the gram for mass, and the second for time. All mechanical units in CGS are directly derived from these three base units, though the system was expanded to include electromagnetism in several different ways. CGS has largely been replaced by the MKS system—based on the metre, kilogram, and second—which later evolved into the International System of Units (SI). While SI is now the standard in most scientific and engineering fields, CGS remains common in certain specialized areas.
For purely mechanical measurements—such as length, mass, force, energy, and pressure—the differences between CGS and SI are simple, involving only powers of ten (since 100 cm equals 1 m and 1000 g equals 1 kg). For instance, the CGS unit of force, the dyne, is defined as 1 g·cm/s², making the SI newton (1 kg·m/s²) equal to 100,000 dynes.
Converting electromagnetic quantities like electric charge, fields, and voltage between CGS and SI is much more complex. This is because the equations governing electromagnetism, including Maxwell's equations, take different forms depending on the unit system used, and electromagnetic quantities are defined differently in each. Furthermore, several distinct versions of CGS exist for electromagnetism, including electrostatic (ESU), electromagnetic (EMU), Gaussian, and Heaviside–Lorentz units. Gaussian units are the most common in modern scientific literature, and the term "CGS units" often refers specifically to the CGS–Gaussian system.
**History**
The CGS system traces back to an 1832 proposal by mathematician Carl Friedrich Gauss to create a system of absolute units based on length, mass, and time. Gauss initially chose the millimetre, milligram, and second. In 1873, a committee of the British Association for the Advancement of Science, which included physicists James Clerk Maxwell and William Thomson (Lord Kelvin), recommended adopting the centimetre, gram, and second as fundamental units and naming derived electromagnetic units with the prefix "C.G.S. unit of ...".
Many CGS units proved impractical for everyday use—for example, common objects like humans and rooms measure hundreds or thousands of centimetres. As a result, CGS never saw widespread use outside science. Starting in the 1880s and accelerating by the mid-20th century, CGS was gradually replaced internationally by the MKS system, which later became the modern SI standard.
Following the adoption of MKS in the 1940s and SI in the 1960s, technical use of CGS has steadily declined. Organizations such as NIST, the American Physical Society, and the International Astronomical Union now deprecate CGS in favor of SI. SI units dominate engineering and physics education, while Gaussian CGS units remain common in theoretical physics, particularly for microscopic systems, relativistic electrodynamics, and astrophysics. The gram and centimetre still serve as noncoherent units within the SI system, like any other prefixed SI units.
**Definition of CGS units in mechanics**
In mechanics, the quantities in CGS and SI are defined identically; the systems differ only in the scale of the base units (centimetre versus metre, gram versus kilogram), with the second being the same in both. Because the laws of mechanics are expressed by the same formulas in both systems, and both are coherent, the definitions of all derived mechanical units in terms of base units are identical. This leads to an unambiguous relationship between derived units, such as velocity (v = dx/dt), force (F = m d²x/dt²), energy (E = ∫ F·dx), pressure (p = F/L²), and viscosity (η = τ / (dv/dx)).
- field
- Systems of measurement
- known_for
- Base units of centimetre, gram, and second; multiple electromagnetic variants including Gaussian units
Lore & Background
The centimetre–gram–second system of units (CGS or cgs) is a variant of the metric system that uses the centimetre for length, the gram for mass, and the second for time. All mechanical units in CGS are derived unambiguously from these three base units. In mechanics, the definitions of quantities are identical to those in the SI system; the two systems differ only in the scale of the base units, with the second being the same. For example, the CGS unit of force is the dyne, and the unit of pressure is the barye. Converting between CGS and SI mechanical units involves powers of ten, such as one barye equalling one-tenth of a pascal. However, converting electromagnetic quantities is far more complex because the form of equations like Maxwell’s equations depends on the unit system, and several distinct CGS versions exist for electromagnetism. These include electrostatic (ESU), electromagnetic (EMU), Gaussian, and Heaviside–Lorentz units. Gaussian units are the most common in modern scientific literature, and “CGS units” often refers specifically to the CGS–Gaussian system. The CGS system was proposed by Carl Friedrich Gauss in 1832, using millimetre, milligram, and second, and later recommended in 1873 by a British Association committee including James Clerk Maxwell and William Thomson. Many CGS units proved inconvenient for practical use—everyday objects are hundreds or thousands of centimetres long—so the system never gained wide use outside science. It was gradually superseded by the MKS system and later SI, though it remains prevalent in theoretical physics, relativistic electrodynamics, and astrophysics.
Reader's Guide
The CGS system was historically significant as the first coherent metric system for science, but its sizes proved inconvenient for practical use. Starting in the 1880s, and more significantly by the mid-20th century, CGS was gradually superseded internationally for scientific purposes by the MKS system, which in turn developed into the modern SI standard. Since the international adoption of the MKS standard in the 1940s and the SI standard in the 1960s, technical use of CGS units has gradually declined worldwide. CGS units have been deprecated in favour of SI units by NIST, as well as organisations such as the American Physical Society and the International Astronomical Union. SI units are predominantly used in engineering applications and physics education, while Gaussian CGS units are still commonly used in theoretical physics, describing microscopic systems, relativistic electrodynamics, and astrophysics. The units gram and centimetre remain useful as noncoherent units within the SI system.
Did You Know?
- Gaussian CGS units are the most widely used CGS variant in modern scientific literature.
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