Airy Isostasy Calculator (Mountain Roots)
How deep the crust extends into the mantle under a mountain, and how thick it is in total, if the mountain floats in balance like an iceberg.
Results
The dashed line marks the value you entered.
What this tool does
Isostasy is the idea that mountains float on the denser mantle the way an iceberg floats in water, and in Airy's version every mountain has a root: depth = height × ρ_crust ÷ (ρ_mantle − ρ_crust). With typical densities the root is about five or six times as deep as the mountain is high, so a 3 km range has a root some 17 km deep. It explains why the crust is 60–70 km thick under the Himalaya and about 35 km elsewhere on the continents. Real mountains are partly supported by the stiffness of the plate, so this is a first estimate.
Formula
root r = h × ρ_crust ÷ (ρ_mantle − ρ_crust) (Airy isostasy)
Variables
| Symbol | Meaning | Unit |
|---|---|---|
hh | Height of the mountain above sea level | m |
rc | Density of the crust | kg/m³ |
rm | Density of the mantle | kg/m³ |
t0 | Crust thickness at sea level | km |
R | Depth of the crustal root | km |
TT | Total crust thickness under the mountain | km |
RT | Root depth per metre of height | — |
Worked example
- Height of the mountain above sea level3000 m
- Density of the crust2800 kg/m³
- Density of the mantle3300 kg/m³
- Crust thickness at sea level35 km
- Depth of the crustal root16.80 km
- Total crust thickness under the mountain54.8 km
- Root depth per metre of height5.60
Limitations
- The result is an estimate based only on the values you type. Real situations often include factors this calculator does not know about.
- The default values are typical reference figures, not measurements of your situation. Replace them with your own data whenever you have it.