Planck mass, the fundamental mass scale in quantum gravityThe Planck mass is a fundamental scale in physics where quantum effects and gravitational effects become equally important. It is defined as the mass of a particle whose reduced Compton wavelength equals its Schwarzschild radius, making it the natural unit of mass in quantum gravity. Its value is about 2.18×10^-8 kg, which is roughly the mass of a grain of dust, but it corresponds to an enormous energy of about 10^19 GeV.
The concept was introduced by Max Planck in 1899, who proposed natural units based on these constants, though he did not explicitly discuss its role in quantum gravity. The modern interpretation as the scale of quantum gravity developed in the mid-20th century.
The Planck mass emerges from combining three fundamental constants: the speed of light (c), the reduced Planck constant (ħ), and Newton's gravitational constant (G). It is given by m_P = sqrt(ħc/G). At this mass scale, the gravitational attraction between two such particles would be so strong that quantum fluctuations of spacetime itself become significant, requiring a full theory of quantum gravity to describe.
It is not directly used in everyday technology, but it sets the energy scale for hypothetical particles like the graviton and for theories of quantum gravity, such as string theory and loop quantum gravity.
The Planck mass is about 2.18×10^-8 kg, which is roughly the mass of a flea egg, yet it packs the energy of a large lightning bolt into a single particle.
| μ | variable | mass per unit length of cosmic string — linear mass density kilogram per metre |
| G | constant | Newton's constant of universal gravitation — gravitational constant = 6.67430e-11 cubic metre per kilogram per second squared |
| m_Pl | constant | Planck mass, the fundamental mass scale in quantum gravity — planck mass = 2.176434e-8 kilogram |









