Convert Electron Radius (re) to Planck Length (ℓₚ) instantly.
About these units
Electron Radius (re)
The classical electron radius, approximately 2.818 × 10⁻¹⁵ meters, is a theoretical value derived from classical electromagnetic theory rather than an actual measured size. It represents the radius a charged sphere would need to have in order for its electrostatic self-energy to equal the electron's rest energy. Although electrons are now understood to be point-like or extremely small compared to this radius, the classical electron radius remains useful in scattering theory, especially in calculations involving Thomson scattering — the elastic scattering of electromagnetic radiation by free electrons. Thus, while not a physical dimension of the electron, the classical radius serves as a meaningful parameter in specific areas of physics and retains importance in radiation modeling and plasma physics.
Planck Length (ℓₚ)
The Planck length, approximately 1.616 × 10⁻³⁵ meters, is perhaps the most conceptually profound unit in physics. It represents the scale at which classical notions of space and time cease to exist and quantum gravity effects dominate. Below this length, it is believed that spacetime becomes "foamy," subject to fluctuations predicted by quantum field theory and speculative models such as string theory. The Planck length is derived from fundamental constants: the speed of light, Planck's constant, and Newton's gravitational constant. These constants combine to yield a natural scale where both quantum mechanics and general relativity must merge into a unified theory. No experiment has ever probed distances anywhere near the Planck scale — it is many orders of magnitude smaller than even the size of protons — but it plays a crucial role in theoretical cosmology, black hole physics, and models of the early universe. The Planck length stands as a symbol of the limits of physical measurement and the frontier of fundamental physics.