What Is a Roche Limit Calculator?
The Roche limit is the distance from a planet, star, or other massive body inside which tidal forces would overpower a satellite's self-gravity and pull it apart. This calculator uses the classic rigid-body version of the formula, derived from the primary body's radius and the densities of both objects, to estimate that distance.
Named for French astronomer Édouard Roche, who worked it out in 1848, the concept explains why some moons survive close orbits while others get shredded into rings, and it sets a hard lower limit on how close an intact moon can orbit its planet.
How to Read Your Results
Roche Limit Distance
The primary result: the distance, measured from the primary body's center, inside which a satellite of the density you entered would be tidally disrupted.
In Primary Radii
The same distance expressed as a multiple of the primary body's own radius — a quick way to see how close that is relative to the primary's surface.
Density Ratio
The ratio of the primary's density to the satellite's density, the single number (besides the primary's radius) that determines the Roche limit.
Real-World Example
Consider Earth (radius 6,371 km, average density 5.51 g/cm³) and a rigid body with the Moon's density (3.34 g/cm³):
| Input | Value |
|---|---|
| Primary radius | 6,371 km |
| Primary density | 5.51 g/cm³ |
| Satellite density | 3.34 g/cm³ |
| Roche limit | ≈ 9,485 km from Earth's center (≈ 1.49× Earth's radius) |
The Moon's actual orbit, at about 384,400 km, is more than 40 times farther out than this rigid-body Roche limit — comfortably safe from tidal disruption.
Tips for Using This Calculator
- Only the density ratio matters, not the absolute units — g/cm³, kg/m³, or any consistent unit works as long as both densities use the same one.
- The rigid-body formula is a conservative estimate — real, weakly-bound "rubble pile" satellites (like many comets and small moons) can break apart farther out, closer to the fluid-body Roche limit, which is roughly 2.44× the primary's radius times the density-ratio cube root.
- A denser satellite (like a solid metal or rocky moon) can survive much closer to its primary than a loose icy one.
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Last updated: August 2026 · Reviewed by: Simple Calculator Tools Editorial Team