How to use the mountain root depth calculator
Estimate how deep the crustal root of a mountain extends below sea level, from its elevation and rock densities. Enter mountain elevation, crust density, mantle density in the fields above; the root depth below sea level, root depth are computed instantly and plotted on the chart so you can see how the answer changes.
Common searches this calculator answers include “isostasy mountain root”, “crustal root depth”, “isostatic balance of mountains”, “calculate mountain root depth”, “find root depth below sea level”.
Formula
Variables
- h — Mountain elevation (m)
- rc — Crust density (kg/m³)
- rm — Mantle density (kg/m³)
Worked example
With mountain elevation = 4000 m, crust density = 2700 kg/m³, mantle density = 3300 kg/m³, the calculator gives root depth below sea level ≈ 18,000 m; root depth ≈ 18 km.
Frequently asked questions
What is the mountain root depth calculator used for?
Estimate how deep the crustal root of a mountain extends below sea level, from its elevation and rock densities. It helps with questions such as “isostasy mountain root”, “crustal root depth”, “isostatic balance of mountains”.
What is the formula for the mountain root depth calculation?
Root depth below sea level (m) = h × rc / (rm-rc). Root depth (km) = [Root depth below sea level] / 1000. Here h is mountain elevation (m), rc is crust density (kg/m³), rm is mantle density (kg/m³).
What inputs do I need for the mountain root depth (isostasy) calculator?
You need mountain elevation in m, crust density in kg/m³, mantle density in kg/m³. Each field is pre-filled with a typical example so you can see how the result responds as you edit the numbers.
How do I use the mountain root depth calculator?
Type values into the input fields. Results and the chart update instantly. Use Reset to restore the example values, Copy results to paste them elsewhere, or Share to copy a link that preserves your inputs.
Is the mountain root depth result exact?
Calculations use standard formulas and double-precision arithmetic, then display about seven significant figures. Real-world measurements carry uncertainty, so treat results as estimates unless your inputs are exact.