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Free CGS System of Units Converter

Quick Reference

1 cm = 0.01 m • 1 g = 0.001 kg
1 dyn = 10⁻⁵ N • 1 erg = 10⁻⁷ J
1 Ba = 0.1 Pa • 1 P = 0.1 Pa·s
1 G = 10⁻⁴ T • 1 Mx = 10⁻⁸ Wb
1 Oe ≈ 79.58 A/m • 1 statV ≈ 299.79 V

CGS → SI Converter

1 dyn = 10⁻⁵ N • 1 erg = 10⁻⁷ J

Enter a value and select a CGS unit - conversion is automatic

Understanding the CGS System of Units

The CGS (centimeter-gram-second) system of measurement remains widely used in certain scientific fields, despite the dominance of the SI (International System of Units). This free CGS to SI unit conversion calculator allows for quick and accurate conversion between CGS and SI units, covering mechanics and electromagnetism alike. Whether you need to convert dyne to newton, erg to joule, or gauss to tesla, this centimeter-gram-second system converter provides the necessary conversion factors at your fingertips.

CGS vs. SI: Base Units

The two systems differ primarily in their fundamental units of length and mass. The CGS system defines:

  • Length: centimeter (1 cm=10−2 m1\,\text{cm} = 10^{-2}\,\text{m})
  • Mass: gram (1 g=10−3 kg1\,\text{g} = 10^{-3}\,\text{kg})
  • Time: second (1 s1\,\text{s})

The SI (or MKS) system uses the meter, kilogram, and second as base units. As a result, derived units in CGS are scaled by powers of ten relative to SI, making conversions straightforward for many mechanical quantities.

Mechanical CGS Units

In mechanics, several CGS units have special names that are still encountered in physics literature. The table below lists these units along with their conversion to SI.

Quantity (symbol)CGS unit (symbol)Equivalent in SI
Acceleration (a)gal (Gal)10−2 m/s210^{-2}\,\text{m/s}^2
Force (F)dyne (dyn)10−5 N10^{-5}\,\text{N}
Energy (E)erg (erg)10−7 J10^{-7}\,\text{J}
Pressure (p)barye (Ba)10−1 Pa10^{-1}\,\text{Pa}
Dynamic viscosity (μ)poise (P)10−1 Pa⋅s10^{-1}\,\text{Pa·s}
Kinematic viscosity (ν)stokes (St)10−4 m2/s10^{-4}\,\text{m}^2/\text{s}

From these base relationships you can derive other CGS units. For example, power in SI is expressed in watts (W=J/s\text{W} = \text{J/s}). In CGS, power is given in ergs per second (erg/s\text{erg/s}), and 1 erg/s=10−7 W1\,\text{erg/s} = 10^{-7}\,\text{W}.

Electromagnetic CGS Units

Converting electromagnetic units between CGS and SI is more involved because the two systems express the fundamental laws of electromagnetism differently. Several CGS subsystems exist, including the electrostatic (ESU), electromagnetic (EMU), and Gaussian systems. This calculator focuses on the Gaussian CGS system, which is the most common variant in physics.

The following table provides Gaussian CGS units for key electromagnetic quantities and their SI equivalents.

Quantity (symbol)Gaussian CGS unit (symbol)Equivalent in SI
Electric charge (q)franklin (Fr)3.336×10−10 C3.336\times10^{-10}\,\text{C}
Voltage (V)statvolt (statV)299.8 V299.8\,\text{V}
Magnetic flux density (B)gauss (G)10−3 T10^{-3}\,\text{T}
Magnetic field strength (H)oersted (Oe)79.577 A/m79.577\,\text{A/m}

It is also useful to note the behavior of the Coulomb constant kek_e across systems: it equals 1/4πϵ0=9×109 N⋅m2/C21/4\pi\epsilon_0 = 9\times10^9\,\text{N·m}^2/\text{C}^2 in SI, 11 in ESU and Gaussian CGS, and c2c^2 in EMU CGS (where cc is the speed of light). These differences can simplify many theoretical formulas in the CGS framework.

Physical Constants in CGS and SI Units

Because CGS and SI units differ in their base scales, fundamental constants take on different numerical values. The following table lists several important constants in both systems.

Constant (symbol)SI valueGaussian CGS value
Atomic mass unit (u)1.66×10−27 kg1.66\times10^{-27}\,\text{kg}1.66×10−24 g1.66\times10^{-24}\,\text{g}
Bohr magneton (μ_B)9.27×10−24 J/T9.27\times10^{-24}\,\text{J/T}9.27×10−21 erg/G9.27\times10^{-21}\,\text{erg/G}
Bohr radius (a_0)5.29×10−11 m5.29\times10^{-11}\,\text{m}5.29×10−9 cm5.29\times10^{-9}\,\text{cm}
Boltzmann constant (k_B)1.38×10−23 J/K1.38\times10^{-23}\,\text{J/K}1.38×10−16 erg/K1.38\times10^{-16}\,\text{erg/K}
Electron mass (m_e)9.11×10−31 kg9.11\times10^{-31}\,\text{kg}9.11×10−28 g9.11\times10^{-28}\,\text{g}
Elementary charge (e)1.6×10−19 C1.6\times10^{-19}\,\text{C}4.8×10−10 Fr4.8\times10^{-10}\,\text{Fr}
Fine-structure constant (α)1/1371/1371/1371/137
Gravitational constant (G)6.67×10−11 N⋅m2/kg26.67\times10^{-11}\,\text{N·m}^2/\text{kg}^26.67×10−8 dyn⋅cm2/g26.67\times10^{-8}\,\text{dyn·cm}^2/\text{g}^2
Planck constant (h)6.626×10−34 J⋅s6.626\times10^{-34}\,\text{J·s}6.626×10−27 erg⋅s6.626\times10^{-27}\,\text{erg·s}
Speed of light in vacuum (c)2.998×108 m/s2.998\times10^{8}\,\text{m/s}2.998×1010 cm/s2.998\times10^{10}\,\text{cm/s}

With this conversion calculator, you can instantly find relationships between any CGS unit and its SI counterpart, from dyne to newton, erg to joule, and gauss to tesla. The tool serves as both a practical reference and an educational resource for scientists, students, and engineers working across unit systems.

FAQ

1. How do I convert from dyne to newton using this tool?

Since 1 dyne equals 10⁻⁵ N, simply multiply the number of dynes by 10⁻⁵ to get newtons. The calculator automates this step for you.

2. What is the relationship between erg and joule?

One erg is equal to 10⁻⁷ J. Therefore, to convert ergs to joules, multiply the erg value by 10⁻⁷; to convert joules to ergs, multiply by 10⁷.

3. Why are electromagnetic unit conversions between CGS and SI more complex than mechanical ones?

The two systems define the laws of electromagnetism differently, leading to different scaling factors and multiple CGS subsystems (ESU, EMU, Gaussian). This converter uses the Gaussian CGS system, which is most common in physics.

4. What is the CGS unit for magnetic B field and how does it relate to tesla?

In the Gaussian CGS system, magnetic flux density B is measured in gauss (G). One gauss equals 10⁻³ tesla (T).

5. Can I convert physical constants like Planck's constant from SI to CGS with this calculator?

Yes, the calculator includes conversion factors for many fundamental constants, such as Planck's constant (h = 6.626×10⁻³⁴ J·s in SI; 6.626×10⁻²⁷ erg·s in Gaussian CGS). Simply input the SI value to obtain the CGS equivalent.

How to Use

  1. Enter a numeric value in the input field and select the CGS unit you want to convert from.
  2. All equivalent SI values for the selected CGS unit will be displayed instantly along with conversion factors.
  3. Use the results for your scientific calculations, physics problems, or engineering work.