Roche Limit Calculator

Calculator

Fill the inputs, then press Calculate.

Advanced options included

Input method *

Choose how you want to describe each body.

Material model *

Use fluid for strengthless rubble, rigid for solid bodies.

Custom coefficient *

Typical values fall between 1 and 3.

Primary radius (Rp) *

The radius of the larger body.

Primary density (ρp) *

Average density of the primary body.

Satellite density (ρs) *

Average density of the smaller body.

Primary mass (Mp) *

Used to compute ρp from Mp and Rp.

Satellite mass (Ms) *

Used to compute ρs from Ms and Rs.

Satellite radius (Rs) *

Used to compute ρs from Ms and Rs.

Reset

Tip: For rocky moons, ρs is often 2500–3500 kg/m³. For icy bodies, it can be near 1000 kg/m³.

Example Data Table

Sample cases using densities and the fluid model.

Primary	Rp (km)	ρp (kg/m³)	Satellite ρs (kg/m³)	Model	Roche limit (km)
Earth	6371	5514	3340	Fluid (2.44)	~ 18,300
Jupiter (avg.)	69,911	1326	1000	Fluid (2.44)	~ 185,000
Sun (avg.)	695,700	1408	3000	Fluid (2.44)	~ 1,220,000

These are approximate, rounded values for demonstration.

Formula Used

The Roche limit estimates the minimum distance where tidal forces from a primary body can disrupt an orbiting body. A common density-based form is:

d = C · Rp · (ρp / ρs)^1/3

This calculator also lets you input masses and radii, then computes densities using ρ = M / (4/3 · π · R³) before applying the Roche limit equation.

How to Use This Calculator

Notes and Interpretation

The Roche limit is an idealized threshold; real outcomes depend on strength, rotation, and internal structure.
Ring systems often lie near or inside the fluid Roche limit for icy material.
For a stronger body, the rigid coefficient gives a smaller disruption distance.
Distances reported are from the primary center; subtract Rp to estimate altitude above the surface.