Geometrized unit system

In physics, especially in the general theory of relativity, geometrized units or sometimes geometric units, is a physical unit system in which all physical quantities are expressed in the unit of length: meter. In this system, the speed of light c and the gravitational constant G are set to one, c = 1 and G = 1 (and sometimes also Boltzmann constant k = 1). In this system, formulas appear simpler because all constants drop out.

A time interval is in geometrical units expressed in meters, the distance travelled by light in that interval.

In exactly the same way as we can use light-seconds as a distance in meters, we can express a mass (kilogram) as "mass-meters". The Sun has a mass (in conventional units 2×10³⁰ kg) which is expressed in mass-meters as 1.5 km.

The conversion from conventional units (kg) is
mass [meters] = G/c² mass [kg] = 0.742 × 10^-27 (m/kg) mass [kg]

Other conversions are given in the table by expressing the number 1.0 in different ways.

{| bgcolor=#88ff88 |colspan=6 align=center| Converting geometrized units to conventional units |----------- | 1.0 || = || c || = || 2.997930 ×10⁸ || meter/sec |----------- | 1.0 || = || G/c² || = || 0.7425×10^-27 || meter/kg |----------- |1.0 || = || G/c⁴ || = || 0.826×10^-44 || meter/Newton |----------- |1.0 || = || Gk/c⁴ || = || 1.140×10^-67 || meter/K |----------- |}

See also

• Physical constants
• Natural units or Planck units, another system of units based on the fundamental physical constants.