Tectonic Stress Calculator
This calculator computes lithostatic (vertical) stress, minimum horizontal stress, and effective stress in the Earth's crust from depth, rock density, Poisson's ratio, and pore pressure. These are the fundamental quantities in crustal geomechanics, used for borehole stability analysis, fault reactivation assessment, hydraulic fracturing design, and CO2 storage site characterisation. The horizontal stress formula assumes uniaxial strain conditions (a relaxed sedimentary basin with no tectonic far-field stress).
Tectonic stress formulas
Sv = rho x g x z Sh = (nu / (1 - nu)) x Sv S'v = Sv - Pp
Where Sv = vertical (lithostatic) stress (Pa or MPa), rho = rock density (kg/m3), g = 9.81 m/s2, z = depth (m), nu = Poisson's ratio, Sh = minimum horizontal stress (uniaxial strain assumption), Pp = pore pressure (MPa), S'v = effective vertical stress. Source: Zoback, M.D. (2010). Reservoir Geomechanics. Cambridge University Press.
Typical crustal stress gradients
| Stress Type | Typical Gradient (MPa/km) | Notes |
|---|---|---|
| Vertical (Sv) | 23-27 | Depends on density |
| Horizontal (Sh) - relaxed | 7-13 | nu = 0.25 gives 0.33 x Sv |
| Hydrostatic pore pressure | 9.81 (freshwater) | 10.5 for saline formation water |
Tectonic stress calculator: frequently asked questions
What is lithostatic stress?
Lithostatic stress (also called overburden pressure or vertical stress Sv) is the pressure exerted by the weight of overlying rock and sediment. It is calculated as Sv = rho x g x z, where rho is average rock density, g is gravitational acceleration (9.81 m/s2), and z is depth. At 1 km depth in typical crustal rock (2,650 kg/m3), the lithostatic stress is approximately 26 MPa.
What is the difference between total stress and effective stress?
Total stress is the full overburden or tectonic stress at a point. Effective stress is the total stress minus pore fluid pressure: effective stress = total stress - pore pressure. Pore pressure reduces the stress carried by the rock matrix. Effective stress governs rock failure and fluid flow in porous media (Terzaghi's principle).
How are horizontal stresses related to vertical stress?
In a relaxed (uniaxial strain) sedimentary basin, the minimum horizontal stress (Sh) is approximately related to vertical stress by: Sh = (nu / (1 - nu)) x Sv, where nu is Poisson's ratio. Poisson's ratio for rock typically ranges from 0.1 (stiff, brittle rocks) to 0.45 (soft, plastic rocks). Active tectonic settings can produce horizontal stresses larger than Sv.
What is the Anderson fault classification system?
Anderson's faulting theory classifies tectonic regimes by the relative magnitudes of the three principal stresses: normal faulting (Sv is the largest, Sh(min) is smallest), strike-slip faulting (SH(max) largest, Sh(min) smallest, Sv intermediate), and reverse/thrust faulting (Sv is the smallest). USGS and academic geomechanics texts use this framework.
What is the typical Poisson's ratio for rock?
Poisson's ratio (nu) ranges from approximately 0.05 for very stiff rocks (quartzite) to 0.45 for soft, poorly consolidated sediments. Common values: granite 0.20-0.30, limestone 0.20-0.35, sandstone 0.15-0.35, shale 0.20-0.40, salt 0.30-0.45.
Official sources
- USGS Earthquake Hazards: USGS Stress Field Data.
- World Stress Map Project (WSM): World Stress Map (Heidbach et al., 2018).
Reviewed by the CalculatorHub team, edited by James Graham, 14 June 2026. See our methodology.