ONE FORMULA, ONE ANSWER
Jeans Mass Calculator
Calculate the mass of a critical-wavelength sphere in the linear Jeans instability model. Choose input units and calculate one value within the stated conditions.
Inputs
Calculations run in this browser. Scientific notation such as 1.2e-3 is supported. Do not group thousands.
Result
Jeans mass M_J
Enter values and select Calculate.
M_J = π^(5/2)c_s³ / (6G^(3/2)√ρ)
Assumptions
Required: ρ>0 and 0<c_s<c. The definition is the mass within a sphere of diameter λ_J=c_s√(π/(Gρ)): M_J=(4π/3)ρ(λ_J/2)³. This is linear perturbation theory for an infinite uniform nonrotating nonmagnetic nonrelativistic gas. Supply the derivative sound speed for the relevant pressure-density response. This differs from a finite-cloud virial mass or disk Toomre mass. Excluded: turbulence, magnetic fields, rotation, cooling history and cosmic expansion.
Displayed values are floating-point approximations. Design safety factors and unprovided error contributions are not calculated.
Formula references and credits
NaNa Lab created the code, descriptions, icons and preview images. Text, figures and code from the linked references have not been reproduced.
Physical constants: NIST / CODATA 2022. The values of μ₀ and ε₀ are measured recommendations, not exact defining constants. Values and precision notes are in the source record.
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