Convert Planck Length (ℓₚ) to A.U. of Length (a.u.) instantly.
About these units
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.
A.U. of Length (a.u.)
The atomic unit of length, also known as the Bohr radius unit in atomic units, is approximately 5.29177 × 10⁻¹¹ meters. It is defined as the radius of the lowest-energy orbital of the hydrogen atom, providing a natural scale for describing atomic and quantum mechanical systems. Atomic units were devised to simplify equations in quantum chemistry and atomic physics by normalizing fundamental constants such as electron charge, Planck's constant, and electron mass to 1. In this system, many equations become dimensionless and far easier to manipulate mathematically. The atomic unit of length is essential in molecular orbital calculations, quantum simulations, and the study of electron behavior in atoms and molecules. Its use reflects an approach to physics in which units are chosen to match the natural scales of the systems being studied.