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Two-Body Reduced Mass & Missing Mass

Calculate the reduced mass for two positive masses or infer one mass from the other and a valid reduced mass.

Calculator inputs

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Enter the known values in the units shown. Results update as you type.
Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
Use the worked example to check the method. Reset restores the starting fields.

Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

Masses of 3 kg and 6 kg have reduced mass 2 kg. Two equal masses have reduced mass equal to half either mass.

μ = m₁m₂ / (m₁ + m₂); 1/μ = 1/m₁ + 1/m₂

Enter these known values and leave the other values blank.

Both body masses and reduced mass must be positive and finite. Reduced mass must be smaller than either body mass.
For an inverse calculation, a reduced mass equal to a known body mass would require the other mass to diverge. A larger reduced mass is incompatible with positive masses.
This is the classical two-body reduced-mass parameter, not the sum of the masses or the mass of either body.

For two masses m, the reduced mass is m/2.

The reduced mass approaches the smaller mass from below; it remains less than that mass for a finite positive partner.

Bookify requires positive masses and a reduced mass strictly below each known body mass, rejecting undefined inverse limits.