Isostasy and Crustal Thickness Calculator
Find the crustal root depth and total crust thickness that isostatic balance requires beneath a mountain range or an ocean basin.
🏔️ What is Isostasy and Crustal Thickness?
Isostasy is the state of gravitational equilibrium between Earth's lithosphere and the weaker asthenosphere beneath it. The word comes from the Greek for "equal standing". Light continental crust floats on denser mantle in the same way an iceberg floats in seawater: the higher the topography above the surface, the deeper the buoyant block must extend below it. The extra crust hanging down into the mantle is called the crustal root, and the total distance from the surface to the Moho is the crustal thickness.
Geophysicists and geology students use isostatic calculations constantly. They estimate Moho depth beneath the Himalaya, Tibet, the Andes and the Alps before checking against seismic data. They explain why gravity anomalies over mountains are strongly negative, interpret ocean basin depths, model how land rebounds after an ice sheet melts, and test whether a region is in balance or still being pushed up or down by tectonic forces.
A common misconception is that mountains are simply piles of rock sitting on a flat base. They are not. Most of a mountain belt is hidden below sea level, and with typical densities the root is about 5.6 times as deep as the mountain is high. Another misconception is that Airy and Pratt describe competing facts. They are two idealised models: Airy varies the thickness of crust of constant density, while Pratt varies the density of columns that all reach the same compensation depth. Real lithosphere shows elements of both, and also has some elastic strength.
This calculator applies Airy isostasy to any elevation, from a 1 km foothill range to an ocean basin several kilometres deep, and returns the root, total crust thickness and Moho depth. It also gives the matching Pratt column density, and it plots root and thickness against elevation so you can see where your chosen value sits on the curve.
📐 Formula
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1: Appalachian Mountains
h = 1000 m, ρc = 2800, ρm = 3300 kg/m³, H0 = 35 km
Example 2: Alps With Lighter Crust
h = 2500 m, ρc = 2750, ρm = 3300 kg/m³, H0 = 32 km
Example 3: Tibetan Plateau
h = 5000 m, ρc = 2800, ρm = 3300 kg/m³, H0 = 35 km
Example 4: Ocean Basin, 4 km Deep
h = -4000 m (water depth 4 km), ρw = 1030 kg/m³, ρc = 2800, ρm = 3300, H0 = 35 km
❓ Frequently Asked Questions
🔗 Related Calculators
What is isostasy in geology?
Isostasy is the gravitational balance between the lithosphere and the denser, fluid-like asthenosphere beneath it. Just as a block of wood floats with most of its volume below the water line, continental crust floats on mantle, so high topography is supported by a deep crustal root or by lower density rock.
How do you calculate the Airy crustal root depth?
The root is r = h x rho_c / (rho_m - rho_c), where h is the elevation, rho_c the crust density and rho_m the mantle density. With 2800 and 3300 kg/m3 the ratio is 5.6, so a 3 km mountain needs a root of 16.8 km.
How thick is the crust under a mountain range?
Total thickness is the reference thickness plus the elevation plus the root. With a 35 km reference, a 3 km mountain gives 35 + 3 + 16.8 = 54.8 km. The Tibetan Plateau at 5 km elevation gives about 68 km, close to seismic measurements.
What is the difference between Airy and Pratt isostasy?
Airy isostasy assumes constant crust density and a root whose depth grows with elevation. Pratt isostasy assumes a constant compensation depth and lets density vary laterally, so high terrain is made of lighter rock. Airy fits mountain belts better, while Pratt describes thermal swells and oceanic ridges.
What density should I use for continental crust and mantle?
Standard textbook values are 2800 kg/m3 for crust and 3300 kg/m3 for upper mantle, and those are this calculator's defaults. Upper crust is nearer 2700, lower crust 2900 to 3000, and the lithospheric mantle 3250 to 3350 kg/m3.
What is a crustal anti-root?
An anti-root is the thinning of crust beneath an ocean basin. Because water is much lighter than rock, the Moho rises where the surface sits below sea level. In this calculator a negative root value means the Moho is shallower than the reference level.
How is the ocean basin case calculated?
Water depth d is balanced against crust and mantle in a column of the same weight as a reference column. The anti-root is d x (rho_c - rho_w) / (rho_m - rho_c). With 4 km of 1030 kg/m3 water it is 14.16 km, giving a crust 16.84 km thick.
Why is real oceanic crust thinner than the Airy ocean result?
Real oceanic crust is only about 7 km thick because it is denser (about 2900 kg/m3, being basalt and gabbro) and because cooling oceanic mantle lithosphere adds a thermal contribution. Using one crust density for both continents and oceans overestimates oceanic crust thickness.
What is the Moho discontinuity?
The Mohorovicic discontinuity, or Moho, is the boundary between crust and mantle, marked by a jump in seismic P-wave speed from about 6.5 to 8 km/s. Continental Moho depth ranges from roughly 25 km under rifts to 70 km under the Himalaya and Tibet.
Does isostasy explain post-glacial rebound?
Yes. When the Pleistocene ice sheets melted, the crust beneath Scandinavia and Canada began to rise to restore balance, and uplift of about 1 cm per year continues in places such as the Gulf of Bothnia. It is the same buoyancy balance, with ice mass in place of mountain mass.
How accurate is local isostasy for real mountains?
Local isostasy is a first-order guide. The Himalaya, Alps and Andes are within a few kilometres of Airy predictions, but the lithosphere has some flexural strength, so loads are spread over regions tens to hundreds of kilometres wide. Gravity anomalies are the usual test.