Reduced Mass Calculator

Reduced mass is an effective inertial mass that turns a two-body problem into an equivalent one-body problem for relative motion. For masses m1 and m2, it is defined by mu = m1m2/(m1 + m2). The same relationship can be written 1/mu = 1/m1 + 1/m2. When both inputs use kilograms, the result is in kilograms; any consistent mass unit can be used mathematically, although the labels on this calculator specify SI units. The idea comes from separating the motion of the system's center of mass from the motion of one object relative to the other. The center of mass moves according to the total mass m1 + m2, while the relative coordinate behaves as though a single particle with mass mu experiences the interaction. This substitution greatly simplifies equations without discarding the mutual motion of either body. Reduced mass is always smaller than either individual positive mass. If the two masses are equal, mu equals half of either mass. If one mass is much larger than the other, mu approaches the smaller mass. That limiting behavior explains why a planet orbiting a much heavier star is often approximated as a small body around a fixed center, while comparable binary stars require both masses to be considered explicitly. Applications span classical and quantum physics. In orbital mechanics, gravitational two-body motion uses reduced mass in the relative equation. In molecular spectroscopy, the vibrational and rotational behavior of a diatomic molecule depends on the reduced mass of its atoms or isotopes. In atomic physics, replacing the electron mass with the electron-nucleus reduced mass improves hydrogen energy predictions. Collision and scattering calculations also use it to express center-of-mass kinetic energy. The formula assumes two point-like bodies whose relative motion can be isolated under an interaction depending on their separation. Extended bodies, changing mass, many-body systems, relativistic speeds, or strongly coupled environmental effects may need a more complete model. Reduced mass does not mean either object's physical mass has changed; it is a mathematical parameter associated with a chosen coordinate. Enter measured rather than nominal masses when precision matters, retain enough significant figures, and keep units consistent. Extremely different values can be entered in scientific notation. This calculator is useful for coursework, quick checks, isotope comparisons, orbital estimates, and preparing inputs for more detailed models. Always combine the result with the correct force law, potential, boundary conditions, and unit system for the physical problem being solved.