Isostatic Root Depth

This formula comes from isostasy: high topography is supported by a deeper, less-dense crustal root that displaces denser mantle until pressure at a compensation depth balances. A taller mountain needs a proportionally thicker root because the extra crustal thickness must offset the weight of the surface load using the density contrast between crust and mantle. The denominator ρ_m - ρ_c matters because the support depends on how much denser the mantle is than the crust, not just on mountain height alone.

Use this when estimating crustal root thickness beneath mountains, plateaus, or other elevated regions in simple Airy isostasy models. It is also useful for comparing how changes in crust and mantle density affect the subsurface support required for a landform.

• Using the mountain height in metres while the density values are in SI units but forgetting to convert the final root to the same distance unit
• Reversing the density difference and writing ρ_c - ρ_m, which gives a negative or nonsensical root depth
• Treating the formula as a full geologic reality check for every mountain, even though real crustal structure can deviate from ideal Airy isostasy