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CGS System of Units Converter

The CGS (centimeter-gram-second) system remains essential in scientific fields like electromagnetism, atomic physics, and astrophysics, despite SI dominance. This converter handles conversions across mechanics—acceleration, force, energy, pressure, viscosity—and electromagnetism, where the mathematical frameworks differ significantly between CGS and SI. Researchers and engineers working with older literature or specialized domains frequently need rapid, accurate conversions.

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Creators Filip Derma, MA
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CGS Mechanics: Scaling from Metric Roots

The CGS and SI (meter-kilogram-second) systems diverge only in scale for mechanical quantities. While SI uses m, kg, and s, CGS uses cm, g, and s. Because 1 cm = 0.01 m and 1 g = 0.001 kg, conversion factors are straightforward powers of 10.

  • Acceleration: 1 cm/s² = 0.01 m/s² (multiply CGS by 0.01)
  • Force: 1 dyne = 10⁻⁵ N (multiply CGS by 0.00001)
  • Energy: 1 erg = 10⁻⁷ J (multiply CGS by 0.0000001)
  • Pressure: 1 barye = 0.1 Pa (multiply CGS by 0.1)
  • Viscosity: 1 poise = 0.1 Pa·s (multiply CGS by 0.1)

This proportional relationship makes mechanical conversions predictable—no surprise factors emerge once you understand the base unit ratios.

Electromagnetic Conversion: Where Systems Diverge

Electromagnetism exposes fundamental differences between CGS and SI. The two systems encode Maxwell's equations differently, leading to dimensionally dissimilar unit definitions. Three major CGS subsystems exist—Gaussian, electrostatic (ESU), and electromagnetic (EMU)—each with distinct constants.

The most consequential difference: the Coulomb constant k_e. In SI, k_e ≈ 9×10⁹ N·m²/C². In Gaussian CGS, it equals 1 by definition, simplifying some theoretical expressions. Consequently:

  • Electric charge: Requires a factor of approximately 3×10⁹ due to speed-of-light coupling
  • Voltage: Statvolt conversions involve factors of ~300, reflecting the electrostatic/magnetic unit asymmetry
  • Magnetic field: Gauss and Oersted units relate to Tesla and A/m via factors tied to permeability of free space

Electromagnetic conversions demand careful attention—they are not simple scaling exercises.

Core Conversion Equations

The following relationships translate CGS measurements into SI equivalents:

F_SI = F_CGS × (1 ÷ 100000)

E_SI = E_CGS × (1 ÷ 10000000)

a_SI = a_CGS × (1 ÷ 100)

P_SI = P_CGS × (1 ÷ 10)

μ_SI = μ_CGS × (1 ÷ 10)

ν_SI = ν_CGS × (1 ÷ 1000)

q_SI = q_CGS × (1 ÷ 2997924580)

V_SI = V_CGS × 299.8

B_SI = B_CGS × (1 ÷ 1000)

H_SI = H_CGS × (1 ÷ (4π × 0.001))

  • F_SI / F_CGS — Force in SI (newtons) / CGS (dynes)
  • E_SI / E_CGS — Energy in SI (joules) / CGS (ergs)
  • a_SI / a_CGS — Acceleration in SI (m/s²) / CGS (cm/s²)
  • P_SI / P_CGS — Pressure in SI (pascals) / CGS (baryes)
  • μ_SI / μ_CGS — Dynamic viscosity in SI (Pa·s) / CGS (poise)
  • ν_SI / ν_CGS — Kinematic viscosity in SI (m²/s) / CGS (stokes)
  • q_SI / q_CGS — Electric charge in SI (coulombs) / CGS (franklin)
  • V_SI / V_CGS — Electric potential in SI (volts) / CGS (statvolt)
  • B_SI / B_CGS — Magnetic flux density in SI (tesla) / CGS (gauss)
  • H_SI / H_CGS — Magnetic field strength in SI (A/m) / CGS (oersted)

Physical Constants: Values Across Systems

Because dimensional definitions differ, physical constants take on different numerical values in CGS versus SI. A constant's numerical form depends on which units express it. This is not a flaw—it reflects how each system encodes nature—but it requires awareness when switching between literature sources.

Examples:

  • Atomic mass unit: 1.66×10⁻²⁷ kg (SI) = 1.66×10⁻²⁴ g (CGS)
  • Bohr radius: 5.29×10⁻¹¹ m (SI) = 5.29×10⁻⁹ cm (CGS)
  • Boltzmann constant: 1.38×10⁻²³ J/K (SI) = 1.38×10⁻¹⁶ erg/K (CGS)
  • Electron mass: 9.11×10⁻³¹ kg (SI) = 9.11×10⁻²⁸ g (CGS)
  • Elementary charge: 1.6×10⁻¹⁹ C (SI) = 4.8×10⁻¹⁰ Fr (CGS)

The fine-structure constant remains invariant at 1/137 in both systems—a reminder that dimensionless ratios transcend unit choice.

Conversion Pitfalls and Best Practices

Avoid common errors when converting between these measurement systems.

  1. Verify your subsystem — Gaussian CGS is standard in physics texts, but older work may use electrostatic or electromagnetic subsystems. A voltage conversion factor of 300 applies only in Gaussian units. Always confirm which CGS variant you're using before applying formulas.
  2. Electromagnetic conversions are non-trivial — Unlike mechanical quantities—which scale predictably—electromagnetic conversions involve speed-of-light coupling and permeability constants. A charge of 1 coulomb does not simply divide by a round number; the factor is ~3×10⁹. Double-check results against reference tables.
  3. Watch compound units — Viscosity (poise = g/(cm·s)) converts by a factor of 0.1, but kinematic viscosity (stokes = cm²/s) uses 0.001. Compound units combining mass, length, and time scale differently. Identify each base component before calculating.
  4. SI dominates modern literature — Papers published after 1970 predominantly use SI. When bridging old and new sources, convert all values to SI for consistency. This minimizes unit-related algebra errors in calculations and comparisons.

Frequently Asked Questions

Why do some scientific fields still use CGS instead of SI?

Electromagnetism and astrophysics retain CGS (particularly Gaussian CGS) because the mathematical form of Maxwell's equations is simpler without factors of ε₀ and μ₀. Atomic physics also prefers CGS for historical reasons—many theoretical expressions date to the early 20th century. Conversion to SI is mechanical but adds notational clutter, so older scientists and legacy codebases continue using CGS. Younger researchers typically learn SI first and translate CGS as needed.

What is the difference between Gaussian CGS and electrostatic CGS?

Gaussian CGS treats electric and magnetic phenomena symmetrically by incorporating the speed of light into unit definitions. Electrostatic CGS (ESU) prioritizes electric units, making Coulomb's law dimensionally simple but leaving magnetic units awkward. Electromagnetic CGS (EMU) reverses this. Most physicists use Gaussian CGS because it balances both domains. The conversion factors differ depending on the subsystem, so always specify which variant you mean.

Can I convert directly from CGS to CGS subsystems, or must I go through SI?

You can convert directly if you know the appropriate factor. For instance, 1 Fr (franklin, ESU charge) = 1 statcoulomb = 1/(3×10⁹) esu in some notations. However, working through SI as an intermediate step reduces errors. Convert CGS to SI, then SI to the target CGS subsystem. This methodical approach is slower but more reliable when multiple systems are involved.

Why is the charge conversion factor so large (≈3×10⁹)?

The factor arises because CGS units embed the speed of light c ≈ 3×10¹⁰ cm/s into electromagnetic definitions. In SI, electric and magnetic constants ε₀ and μ₀ are defined independently; in CGS, they depend on c. When converting charge, this speed-of-light coupling produces the huge numerical factor. It is dimensionally correct and reflects genuine structural differences between the systems, not an error.

How do I convert magnetic field units like gauss to tesla?

One gauss equals 0.0001 tesla (or 10⁻⁴ T). This factor comes from the CGS-to-SI scaling in mechanical units (length and mass) combined with how magnetic field is defined in each system. For magnetic field strength (H), the conversion is more involved: 1 oersted ≈ 79.58 A/m, incorporating factors of permeability. Use the formula section or a reference table to avoid arithmetic errors.

Do I need to learn CGS if I only work in SI?

Not urgently, but familiarity is valuable. When reading papers from before 2000, especially in classical electromagnetism or atomic physics, CGS notation appears frequently. Even modern textbooks sometimes derive results in CGS for pedagogical clarity. Understanding the conversion factors and the conceptual differences—particularly in electromagnetism—deepens your grasp of unit systems and helps you communicate across generations of scientific literature.

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