🏔️ Slope Stability

Written and maintained by the PhDino author · Last reviewed 21 September 2026 · A documented rule of thumb, pinned by automated tests · how PhDino checks its numbers

A simplified factor of safety against a slope sliding, comparing resisting shear strength to driving gravity forces.

A slope is stable as long as the soil's shear strength along any potential failure surface exceeds the shear stress gravity is trying to induce along that same surface. The factor of safety is the ratio of the two — below 1.0 means failure; typical design targets are 1.5 or higher for permanent slopes, with lower factors sometimes accepted for temporary excavations.

This calculator uses a simplified infinite-slope-type approach (treating the slope as effectively uniform and the failure surface as planar) rather than a full circular or non-circular slip-surface search, which real slope stability software performs across many trial surfaces to find the critical (lowest-FS) one.

Key formula

FS = [c + γH·cosβ·tanφ] / [γH·sinβ]

Variables

H

slope height

β

slope angle from horizontal

c, φ

soil cohesion and friction angle

Notes & limitations

• Groundwater dramatically reduces slope stability (it reduces effective stress and thus frictional resistance) — this simplified formula does not include a water table, which real analyses must.
• Real slope stability analysis (e.g. Bishop's method, or software search across many trial circular/non-circular surfaces) finds the critical failure surface rather than assuming a single planar one — this calculator is a rough screening tool, not a substitute for that.