Calculadora de Massa Reduzida
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
Formula
μ = m₁·m₂/(m₁+m₂)
About this calculator
The Reduced Mass Calculator determines the effective mass of a two-body interacting system. The formula μ = m₁·m₂/(m₁+m₂) combines the two masses into a single value that simplifies calculations of relative motion, such as in orbits or collisions. This quantity is essential in classical and quantum mechanics to describe systems where two objects influence each other.
The operation is simple: enter the masses m₁ and m₂ (in any consistent unit, like kg or g) and the calculator applies the formula automatically. The result μ represents the mass of a single body that would have the same dynamic behavior as the original system. For example, in the orbital motion of a planet around the Sun, the reduced mass allows treating the problem as if the planet orbited a fixed body with a modified mass.
Use this calculator in physics problems involving binary systems, such as diatomic molecules (e.g., H₂), double star systems, or elastic collisions. It is also useful for calculating the center of mass and vibrational frequencies in chemistry. Caution: the formula assumes no external forces acting on the system. Also, masses must be positive and the unit must be the same for both inputs.
Common mistakes include confusing reduced mass with center of mass. Reduced mass is always less than or equal to the smaller mass, while center of mass depends on spatial distribution. Another error is using different units for m₁ and m₂ without converting. Always check that values are consistent before interpreting the result.
Frequently asked questions
What is reduced mass?
It is an effective mass that simplifies the study of relative motion between two bodies. It is calculated as the product of the masses divided by their sum.
Can I use different units for m₁ and m₂?
No. The masses must be in the same unit (kg, g, etc.). Otherwise, convert one of them before entering.
What is the difference between reduced mass and center of mass?
Reduced mass is a scalar used for relative motion, while center of mass is a geometric point that depends on the positions of the masses.
Can reduced mass be larger than the smaller mass?
No. It is always less than or equal to the smaller mass. For equal masses, μ = m/2.
What is reduced mass used for in chemistry?
It is used to calculate vibrational frequencies of diatomic molecules, such as in the quantum harmonic oscillator.