Calculators
Reduced Mass Calculator
Calculate reduced mass, total mass, and their ratio for two positive masses in kilograms, privately in your browser.
Find the effective mass for two-body relative motion.
Reduced mass μ = m₁m₂/(m₁ + m₂) = 1/(1/m₁ + 1/m₂) describes the relative motion of two interacting bodies. Enter both masses in kilograms; μ and total mass are reported in kilograms, and μ/(m₁ + m₂) is dimensionless. For 3 kg and 6 kg, μ = 2 kg, total mass = 9 kg, and the ratio is about 0.222222. For equal masses m, μ = m/2. When one mass is much larger, μ approaches the smaller mass. The ratio is at most 0.25. This calculator evaluates the equivalent expression smaller mass / (1 + smaller mass / larger mass) to avoid unnecessary intermediate products. It supports positive inputs from 1e-12 to 1e40 and rounds results to 12 significant digits using browser floating-point arithmetic. Reduced mass is a mathematical parameter for ideal two-body relative motion, not the combined physical mass. No force law, orbit, or collision outcome is calculated. All inputs stay on your device.
Frequently Asked Questions
Everything you need to know about this tool, how it works, and privacy.
What is the reduced mass formula?
μ = m₁m₂/(m₁ + m₂). For masses of 3 kg and 6 kg, the reduced mass is 2 kg.
Is reduced mass the same as total mass?
No. Total mass is m₁ + m₂. Reduced mass is an effective parameter for relative motion in a two-body system, and is smaller than either positive input mass.
What happens when the masses are equal?
Two equal masses m have reduced mass m/2. The reduced-to-total mass ratio is then 0.25, its maximum value.
Which units and input values should I use?
Enter both masses in kilograms, from 1e-12 to 1e40. Scientific notation is accepted. Convert other mass units to kilograms first.
What if one mass is much heavier?
The reduced mass approaches the smaller mass as the mass difference grows. The calculator uses an equivalent ratio formula that avoids multiplying the two large masses.
Are my inputs uploaded?
No. Calculation and copying run in your browser. Reset restores the 3 kg and 6 kg example.