Jeans Mass Calculator
A cloud of interstellar gas sits in a tug of war between its own gravity, which pulls it inward, and thermal pressure, which pushes it outward. The Jeans mass is the tipping point: a cloud heavier than its Jeans mass cannot support itself and collapses to form stars, while a lighter one stays diffuse. It depends on temperature, density, and the mean molecular weight of the gas. This calculator applies the classic Jeans criterion to return the threshold mass in both kilograms and solar masses, using user-editable physical constants so you can match any convention.
Jeans mass formula
M_J = (5 k T / (G mu m_H))^(3/2) * (3 / (4 pi rho))^(1/2)
Solar masses = M_J / 1.989e30
This expression comes from setting the thermal kinetic energy of a uniform gas sphere equal to its gravitational binding energy. A cloud whose mass exceeds M_J is gravitationally unstable. The solar mass conversion uses 1.989e30 kg per solar mass.
Jeans mass facts
- Colder clouds have lower Jeans masses because thermal pressure is weaker.
- Denser clouds have lower Jeans masses because self-gravity is stronger.
- Cold molecular hydrogen clouds use a mean molecular weight near 2.3.
- Star formation occurs in cloud cores that exceed their local Jeans mass.
- Physical constants are user-editable so you can match a specific textbook convention.
Jeans mass: frequently asked questions
What is the Jeans mass?
The Jeans mass is the critical mass above which a gas cloud collapses under its own gravity to form stars. Below it, thermal pressure wins and the cloud is stable. It is named for Sir James Jeans, who derived the instability criterion. A cloud exceeding its Jeans mass is gravitationally unstable and begins to contract.
What is the Jeans mass formula used here?
This calculator uses M_J = (5 k T / (G mu m_H))^(3/2) * (3 / (4 pi rho))^(1/2), where k is Boltzmann's constant, T the temperature, G the gravitational constant, mu the mean molecular weight, m_H the hydrogen mass, and rho the mass density. It follows from balancing thermal and gravitational energy for a uniform sphere.
What inputs do I need and in what units?
Temperature in kelvin, mass density in kilograms per cubic meter, and the dimensionless mean molecular weight mu (about 2.3 for cold molecular hydrogen clouds). The physical constants k, G, and m_H are user-editable inputs set to their CODATA values. The output Jeans mass is given in kilograms and in solar masses.
Why does a colder, denser cloud collapse more easily?
Lower temperature means less thermal pressure to resist gravity, and higher density means stronger self-gravity, so both lower the Jeans mass. That is why star formation happens in cold dense molecular cloud cores, where even modest masses exceed the collapse threshold.
What is a typical Jeans mass for a star-forming cloud?
For a cold molecular cloud core at about 10 K with mu near 2.3 and densities of order 1e-18 kilograms per cubic meter, the Jeans mass is roughly one to a few solar masses, consistent with forming Sun-like stars. Different prefactor conventions exist, so compare like with like when checking values.
Official sources
Reviewed by the CalculatorHub team, edited by James Graham, 16 June 2026. See our methodology.