What is the Jeans mass?

The Jeans mass (M_J) is the minimum mass a gas cloud must have to collapse under its own gravity. If the cloud is more massive than M_J, gravity overcomes thermal pressure and the cloud contracts, eventually forming stars. If it is less massive, thermal pressure disperses the gas.

What is the Jeans mass formula?

M_J = (5 k_B T / G m)^(3/2) × (3 / 4π ρ)^(1/2), where k_B is the Boltzmann constant, T is temperature, G is the gravitational constant, m is the mean particle mass, and ρ is the mass density. This simplifies to roughly 45 M☉ × (T/10 K)^(3/2) × (n/1000 cm⁻³)^(−1/2) for molecular hydrogen.

What is a typical Jeans mass in a molecular cloud?

In a typical cold molecular cloud (T ≈ 10 K, n ≈ 1000 H₂/cm³), the Jeans mass is roughly 1–10 solar masses, consistent with the formation of Sun-like stars. In warmer, diffuse HI clouds (T ≈ 100 K, n ≈ 1 cm⁻³), M_J can exceed 10,000 solar masses.

What is the Jeans length?

The Jeans length (λ_J) is the critical radius below which a cloud is stable against collapse. It is related to the Jeans mass: λ_J = (π k_B T / G m ρ)^(1/2). Gas structures larger than λ_J in a given medium are Jeans-unstable.

What is the free-fall time?

The free-fall time (t_ff) is the time it would take a pressure-free cloud to collapse under gravity: t_ff = (3π / 32 G ρ)^(1/2). It sets the timescale for star formation and typically ranges from tens of thousands to a few million years.

Why does lower temperature lead to a lower Jeans mass?

Lower temperature means less thermal kinetic energy to resist gravity. A cooler cloud needs less mass for gravity to win. This explains why star formation preferentially occurs in the coldest, densest regions of molecular clouds.

Jeans Mass Calculator

Name: Jeans Mass Calculator
Availability: InStock
Author: Nham Vu

Enter temperature and density of a gas cloud to compute the Jeans mass — the minimum mass required for gravitational collapse and star formation.

Gas Cloud Parameters

Temperature (K)

Cold molecular core: 10 K | Warm HI cloud: 100 K

Number Density (particles / cm³)

Dense core: 10⁴–10⁶ cm⁻³ | Diffuse ISM: 1 cm⁻³

Mean Molecular Weight (μ)

Mean mass per particle in units of the proton mass

Preset Cloud Types

Formula

M_J = (5k_BT / Gm)^3/2 × (3 / 4πρ)^1/2

Derived from virial equilibrium between thermal energy and gravitational potential energy (Jeans, 1902).

Enter cloud parameters and click Calculate

Results will include Jeans mass, Jeans length, and free-fall time.

Summary

Enter temperature and density of a gas cloud to compute the Jeans mass — the minimum mass required for gravitational collapse and star formation.

How it works

Enter the gas temperature in Kelvin (typical molecular clouds: 10–100 K).
Enter the number density of hydrogen molecules per cubic centimeter.
Select the mean molecular weight — use 2.0 for molecular hydrogen (H₂), 1.0 for atomic hydrogen.
Click Calculate to get the Jeans mass in solar masses, the Jeans length in parsecs, and the free-fall time.
Use the preset cloud types to explore typical star-forming environments.

Use cases

Astrophysics students studying stellar formation and gravitational instability.
Estimating whether a given molecular cloud can collapse to form stars.
Comparing Jeans masses across different interstellar environments.
Understanding why massive stars form in warm, diffuse regions and low-mass stars in cold, dense cores.
Science education and interactive demonstrations of gravitational collapse.
Verifying textbook Jeans mass calculations with live inputs.

Frequently Asked Questions

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Last updated: 2026-05-29 · Reviewed by Nham Vu