Ageometrized unit system^[1] orgeometrodynamic unit system is a system ofnatural units in which the basephysical units are chosen so that thespeed of light in vacuum,c, and thegravitational constant,G, are set equal to unity.

${\displaystyle c=1}$

${\displaystyle G=1}$

The geometrized unit system is not a completely defined system. Some systems are geometrized unit systems in the sense that they set these, in addition to otherconstants, to unity, for exampleStoney units andPlanck units.

This system is useful inphysics, especially in thespecial andgeneral theories of relativity. Allphysical quantities are identified with geometric quantities such as areas, lengths, dimensionless numbers, path curvatures, or sectional curvatures.

Many equations in relativistic physics appear simpler when expressed in geometric units, because all occurrences ofG and ofc drop out. For example, theSchwarzschild radius of a nonrotating unchargedblack hole with massm becomesr = 2m. For this reason, many books and papers on relativistic physics use geometric units. An alternative system of geometrized units is often used inparticle physics andcosmology, in which8πG = 1 instead. This introduces an additional factor of 8π into Newton'slaw of universal gravitation but simplifies theEinstein field equations, theEinstein–Hilbert action, theFriedmann equations and the NewtonianPoisson equation by removing the corresponding factor.

Geometrized units were defined in the bookGravitation byCharles W. Misner,Kip S. Thorne, andJohn Archibald Wheeler with thespeed of light,${\displaystyle c}$, thegravitational constant,${\displaystyle G}$, andBoltzmann constant,${\displaystyle k_b}$ all set to 1.^[1]: 36 Some authors refer to these units as geometrodynamic units.^[2]

In geometric units, every time interval is interpreted as the distance travelled by light during that given time interval. That is, onesecond is interpreted as onelight-second, so time has the geometric units oflength. This is dimensionally consistent with the notion that, according to thekinematical laws ofspecial relativity, time and distance are on an equal footing.

Energy andmomentum are interpreted as components of thefour-momentum vector, andmass is the magnitude of this vector, so in geometric units these must all have the dimension of length. We can convert a mass expressed in kilograms to the equivalent mass expressed in metres by multiplying by the conversion factorG/c². For example, theSun's mass of2.0×10³⁰ kg in SI units is equivalent to1.5 km. This is half theSchwarzschild radius of a one solar massblack hole. All other conversion factors can be worked out by combining these two.

The small numerical size of the few conversion factors reflects the fact that relativistic effects are only noticeable when large masses or high speeds are considered.

Listed below are all conversion factors that are useful to convert between all combinations of the SI base units, and if not possible, between them and their unique elements, because ampere is a dimensionless ratio of two lengths such as [C/s], and candela (1/683 [W/sr]) is a dimensionless ratio of two dimensionless ratios such as ratio of two volumes [kg⋅m²/s³] = [W] and ratio of two areas [m²/m²] = [sr], while mole is only a dimensionlessAvogadro number of entities such as atoms or particles. Thevacuum permittivity andBoltzmann constant areε₀ andk_B.

• Wald, Robert M. (1984).General Relativity. Chicago:University of Chicago Press.ISBN 0-226-87033-2.See Appendix F

• Conversion factors for energy equivalents

• General relativity
• Systems of units
• Natural units

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