Article — CGS System of Units Converter
CGS System of Units: Conversion to SI
The CGS (centimeter-gram-second) system is a metric system of units that uses centimeter for length, gram for mass, and second for time as base units. It dominated physics from the 1870s until about 1960, when the SI (Système International d'Unités) replaced it almost everywhere except astronomy. CGS-to-SI conversions are usually clean powers of ten because the only difference is the choice of base unit size: 1 dyne = 10⁻⁵ N, 1 erg = 10⁻⁷ J, 1 gauss = 10⁻⁴ T, 1 g/cm³ = 1000 kg/m³.
This calculator covers the 11 most-used quantity types so you can move between CGS literature and modern SI references in either direction.
What is the CGS system of units?
CGS is a coherent metric system: every derived unit follows from the base units without conversion factors. A force of 1 dyne accelerates 1 gram by 1 cm/s². An energy of 1 erg is 1 dyne acting through 1 cm. A pressure of 1 barye is 1 dyne per square centimeter. Everything chains cleanly through the base units of centimeter, gram, and second.
The system was formally adopted by the British Association for the Advancement of Science in 1874 and remained the dominant system in physics journals until the International System of Units (SI) was promulgated in 1960. SI replaced cm with m and g with kg as base units, producing newton, joule, and pascal at sizes more useful for engineering and everyday science.
Astronomy still publishes in CGS in 2026. The Astrophysical Journal accepts both, but the de-facto standard for stellar luminosities is erg/s, for magnetic fields gauss, and for densities g/cm³. The reason is institutional inertia: a century of catalog data, simulation code, and textbooks would need conversion if the field switched.
CGS base units
The three CGS base units are the centimeter (1 cm = 0.01 m), the gram (1 g = 0.001 kg), and the second (identical to the SI second). The shorter length and lighter mass produce derived units smaller than their SI counterparts — usually by powers of 10 that compound.
- centimeter (cm) = 10⁻² m = base length
- gram (g) = 10⁻³ kg = base mass
- second (s) = same as SI = base time
- 1 cm² = 10⁻⁴ m² (area)
- 1 cm³ = 10⁻⁶ m³ = 1 mL (volume)
- 1 g/cm³ = 1000 kg/m³ (density of water)
- 1 cm/s² = 0.01 m/s² (acceleration)
Derived CGS units
Each CGS derived unit follows from F = ma, E = Fd, p = F/A, and similar definitions. The dyne is 1 g·cm/s², the erg is 1 dyne·cm = 1 g·cm²/s², the barye is 1 dyne/cm². The electromagnetic derived units — gauss, maxwell, oersted — come from Maxwell's equations expressed in CGS units, and they have a quirk: charge in CGS has units of mass × length per time, with no analog to the SI ampere.
dyne = g·cm/s² erg = g·cm²/s²barye = dyne/cm² poise = g/(cm·s)gauss = maxwell/cm² oersted = magnetic HCGS to SI conversion factors
For mechanical units the conversion is a clean power of 10. The dyne is 10⁻⁵ N (the factor 10⁵ comes from kg/g × m/cm = 1000 × 100). The erg is 10⁻⁷ J (the dyne factor × 100 for length). The barye is 0.1 Pa. The poise is 0.1 Pa·s. The stoke is 10⁻⁴ m²/s.
Magnetic units have similar power-of-10 factors when working in Gaussian CGS: 1 gauss = 10⁻⁴ tesla, 1 maxwell = 10⁻⁸ weber. The oersted-to-A/m conversion is not a clean power of 10 (1 Oe = 79.5775 A/m) because the SI introduces a 4π factor in the definition.
CGS variants: esu, emu, Gaussian
CGS has three electromagnetic flavors. CGS-esu (electrostatic units) puts the Coulomb constant equal to 1 in Coulomb's law, making charge derive from length and time. CGS-emu (electromagnetic units) does the same for the Biot-Savart constant. Gaussian CGS mixes the two: electric quantities in esu, magnetic quantities in emu, with explicit factors of c (speed of light) wherever they cross.
The SI sidesteps all this by introducing the ampere as a fourth base unit. The 4π factors that appear naturally in Gaussian CGS (and disappear from Maxwell's equations) move into the definitions of the permittivity ε₀ and permeability μ₀ in SI. Both choices have advantages; SI won because it scales better to engineering applications.
Why CGS was replaced by SI
The dyne is too small for everyday force. The erg is too small for everyday energy. A 1 kg apple falling from a tree releases about 10⁷ erg = 1 J — a routine number in SI, an awkward exponent in CGS. As physics moved from tabletop experiments to particle accelerators and bridge engineering, SI's larger base units became more practical.
The 11th General Conference on Weights and Measures formalized SI in 1960. Most national standards bodies adopted SI for engineering and education through the 1970s and 1980s. By 1990, undergraduate physics textbooks had switched, with CGS surviving only in graduate-level astrophysics courses.
CGS in modern astronomy
The Astrophysical Journal, Monthly Notices of the Royal Astronomical Society, and Astronomy & Astrophysics — the three flagship astronomy journals — all accept both CGS and SI but receive predominantly CGS submissions for theoretical and stellar work. Solar luminosity (3.828 × 10³³ erg/s), magnetic field strengths in stellar atmospheres (kilogauss), and densities of stellar interiors (g/cm³) are reported in CGS by default.
When reading an astrophysics paper, check the units before doing any arithmetic. The same paper may switch between CGS (for derived quantities) and SI (for cited engineering specs like detector sensitivity in watts). Mixing the two without converting produces errors that compound over multiple equations.
Common CGS conversion mistakes
The first mistake is forgetting that the factor for compound units compounds. The erg-to-joule factor is 10⁷, not 10⁵ (the dyne factor) or 10² (the centimeter factor) — it is the product. Always derive the conversion factor from the base units rather than memorizing per-unit factors.
Equations look different in Gaussian CGS — Maxwell's equations have no ε₀ or μ₀ but include factors of 4π and c (speed of light) in specific places. Copying a CGS formula into an SI calculation without rewriting these factors gives quantitatively wrong answers, sometimes by many orders of magnitude.
The second mistake is treating the centipoise as SI. It is not — the centipoise is CGS, but the numerical value happens to match millipascal-second (1 cP = 1 mPa·s exactly). Always check whether a viscosity table is in cP or mPa·s; the numbers are equal, but mixing the labels in scripts and databases produces unit-tracking bugs.