CGS System of Units Converter

The CGS system is the centimeter-gram-second branch of metric measurement. It was widely used in physics and engineering before SI became the dominant international system, and it still appears in older textbooks, laboratory notes, data tables, and discipline-specific references. This converter handles the core mechanical relationships that are most often needed when reading a CGS source beside a modern SI calculation: length, mass, acceleration, force, energy, pressure, dynamic viscosity, and kinematic viscosity.

The calculator is not a general history lesson disguised as a form. It uses the exact fixed factor stored for the selected quantity. Choose a quantity, choose CGS → SI or SI → CGS, and enter the measurement. The output reports the converted value, the input unit, the quantity name, and the factor used. That factor row is important because CGS-to-SI conversion is not one universal multiplier; each derived unit inherits the centimeter and gram scale changes differently.

CGS versus SI in mechanics

Both systems share the second as the time unit. The difference starts with length and mass. CGS uses centimeters instead of meters, so one centimeter is 0.01 meter. CGS uses grams instead of kilograms, so one gram is 0.001 kilogram. Any unit built from length, mass, and time carries those scale changes into its definition.

For force, CGS uses the dyne. One dyne is the force needed to accelerate one gram by one centimeter per second squared. SI uses the newton, the force needed to accelerate one kilogram by one meter per second squared. The kilogram-to-gram factor and meter-to-centimeter factor combine to make one dyne equal 0.00001 newton. Energy adds distance to force, so one erg is one dyne centimeter and equals 0.0000001 joule.

Formula

For each quantity, the calculator stores the number of SI units represented by one CGS unit:

$\text{SI value} = \text{CGS value} \times \text{SI per CGS factor}$

For the reverse direction:

$\text{CGS value} = \frac{\text{SI value}}{\text{SI per CGS factor}}$

For force:

$1\ \text{dyn} = 10^{-5}\ \text{N}$

For energy:

$1\ \text{erg} = 10^{-7}\ \text{J}$

Worked example using the default values

The worked example selects Force, CGS → SI, and 100,000 as the value. Force uses the factor:

$1\ \text{dyn} = 0.00001\ \text{N}$

Therefore the converted value is:

$100{,}000\ \text{dyn} \times 0.00001\ \frac{\text{N}}{\text{dyn}} = 1\ \text{N}$

The result panel reports 1 N, keeps the input as 100,000 dyn, labels the quantity as force, and shows the same factor. If you reverse the direction and enter 1 N, the calculator divides by 0.00001 and returns 100,000 dyn. The same structure applies to every row, but the factor changes with the quantity.

Reference table

Domains and related calculators

CGS remains visible in physics history because many classic papers, constants tables, and teaching examples were written before SI practice settled into modern form. It also appears in material properties. Dynamic viscosity is often encountered as poise or centipoise, while kinematic viscosity is often encountered as stokes or centistokes. Pressure tables may use barye, and geophysics uses the gal for acceleration. Translating these values lets you compare older references with SI calculations without manually reconstructing the dimensions every time.

For broader conversions, use the length converter when centimeters and meters are only one step in a larger unit problem, the force converter when newtons must be compared with pounds-force or kilonewtons, and the energy converter when joules, calories, watt-hours, or ergs need to share a table. If your source number is written in powers of ten, the scientific notation calculator can make the scale easier to audit before conversion.

Pitfalls to avoid

Do not assume every CGS unit is just a centimeter or gram label. A derived unit may include length more than once, mass once, and time with a negative exponent. That is why energy and pressure do not share the same factor. Do not convert electromagnetic CGS units with this page unless the source is clearly using one of the mechanical quantities listed in the converter; electromagnetic CGS conventions are a separate topic. Also keep unit symbols attached in notes and spreadsheets. A bare value of 1 could mean 1 N, 1 dyn, 1 J, or 1 erg, and those are very different magnitudes.

Sources

• BIPM, SI measurement units — modern SI unit system context.
• NIST, SI Units — official SI definitions and unit guidance for U.S. users.
• NIST, Guide for the Use of the International System of Units — unit-symbol and conversion presentation guidance.