About

The Centimetre - Gram - Second system predates SI and remains embedded in astrophysics, plasma physics, and legacy engineering literature. Three incompatible electromagnetic sub-systems exist - Gaussian, ESU, and EMU - each defining charge, current, and magnetic flux differently. Mixing them produces dimensional errors that propagate silently through calculations. This converter maps every common CGS mechanical, thermal, and electromagnetic unit to its SI counterpart through exact multiplicative factors drawn from NIST SP 811 and the BIPM brochure, covering quantities from dyn (10⁻⁵ N) to Mx (10⁻⁸ Wb). Note: electromagnetic conversions assume free-space permittivity and permeability; results diverge inside material media.

Formulas

Every conversion passes through an SI intermediate. Given an input value x in source unit A with SI multiplier f_A, the result in target unit B with SI multiplier f_B is:

y = x ⋅ f_Af_B

where f_A = number of SI base units per one unit of A, and f_B likewise for B. For electromagnetic quantities the speed of light in vacuum enters the factor: c = 2.99792458 × 10⁸ m/s. ESU charge relates to SI via f_statC = 110 ⋅ c C, while EMU charge uses f_abC = 10 C. Gaussian magnetic field B in gauss converts as 1 G = 10⁻⁴ T.

Reference Data

Quantity	CGS Unit	Symbol	SI Equivalent	Factor
Length	centimetre	cm	m	10⁻²
Mass	gram	g	kg	10⁻³
Time	second	s	s	1
Force	dyne	dyn	N	10⁻⁵
Energy	erg	erg	J	10⁻⁷
Power	erg per second	erg/s	W	10⁻⁷
Pressure	barye	Ba	Pa	0.1
Dynamic Viscosity	poise	P	Pa⋅s	0.1
Kinematic Viscosity	stokes	St	m²/s	10⁻⁴
Acceleration	gal (galileo)	Gal	m/s²	10⁻²
Magnetic Flux	maxwell	Mx	Wb	10⁻⁸
Magnetic Field B	gauss	G	T	10⁻⁴
Magnetic Field H	oersted	Oe	A/m	79.5775
Magnetomotive Force	gilbert	Gb	A	0.795775
Electric Charge (ESU)	statcoulomb	statC	C	≈3.336×10⁻¹⁰
Electric Charge (EMU)	abcoulomb	abC	C	10
Electric Current (ESU)	statampere	statA	A	≈3.336×10⁻¹⁰
Electric Current (EMU)	abampere	abA	A	10
Voltage (ESU)	statvolt	statV	V	≈299.792
Voltage (EMU)	abvolt	abV	V	10⁻⁸
Capacitance (ESU)	statfarad (cm)	statF	F	≈1.113×10⁻¹²
Resistance (ESU)	statohm	statΩ	Ω	≈8.988×10¹¹
Resistance (EMU)	abohm	abΩ	Ω	10⁻⁹
Inductance (EMU)	abhenry	abH	H	10⁻⁹
Luminance	stilb	sb	cd/m²	10⁴
Illuminance	phot	ph	lx	10⁴
Wavenumber	kayser	cm⁻¹	m⁻¹	100

Frequently Asked Questions

All three share centimetre, gram, and second as base mechanical units. They diverge on how electric charge is defined. ESU (electrostatic) derives charge from Coulomb's law with the permittivity of free space set to unity (dimensionless). EMU (electromagnetic) instead sets the permeability of free space to unity. Gaussian mixes the two: electric quantities use ESU definitions while magnetic quantities use EMU. This means 1 statcoulomb ≈ 3.336 × 10⁻¹⁰ C but 1 abcoulomb = 10 C - a ratio of roughly 3 × 10¹⁰. Confusing the two produces errors of that magnitude.

In Gaussian and ESU systems, the factor 4πε₀ is absorbed into the unit definitions, making charge dimensionally equivalent to g^(1/2)·cm^(3/2)·s⁻¹. Converting to SI's independent ampere-based charge requires multiplying or dividing by c = 2.99792458 × 10⁸ m/s. For example, the statcoulomb-to-coulomb factor is 1/(10·c) ≈ 3.336 × 10⁻¹⁰, while the statvolt-to-volt factor is approximately 299.792.

Mechanical conversions (dyne → N, erg → J, barye → Pa) are exact powers of 10 by definition. Electromagnetic conversions involving the speed of light carry the full 9-digit NIST value c = 2.99792458 × 10⁸ m/s. The oersted-to-A/m factor (1000/4π ≈ 79.5775) is transcendental because π is irrational, so the tool uses 15-digit floating-point precision. For most engineering work, this exceeds measurement uncertainty by several orders.

Decompose them into base CGS dimensions. For instance, CGS surface tension is dyn/cm = 10⁻⁵ N / 10⁻² m = 10⁻³ N/m = 1 mN/m. The tool covers the most common named units; for exotic compounds, convert each factor individually and multiply the results.

CGS does not define a separate temperature unit; both CGS and SI use kelvin (or degree Celsius). The tool therefore omits temperature as a conversion category. If your source uses cgs-based thermal conductivity (cal·cm⁻¹·s⁻¹·K⁻¹), decompose it into energy and length factors manually.

Astrophysics and plasma physics journals (e.g., The Astrophysical Journal) still default to Gaussian CGS because Maxwell's equations simplify: the factors of 4πε₀ and μ₀ vanish, and E and B share the same dimension. Spectroscopy uses the kayser (cm⁻¹) as wavenumber. Geophysics retains the gal (cm/s²) for gravity surveys. Fluid dynamics literature often quotes viscosity in poise and stokes.