Slope Stability Calculator
Compute the factor of safety against sliding failure on an infinite slope using soil strength and groundwater parameters. Used by geotechnical engineers assessing embankments, hillside cuts, and natural slopes.
Last updated: September 2026
Formula below · 2 sources (asce.org, Wikipedia) · Updated Sep 2026
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About this calculator
The infinite slope model is the simplest analytical method for evaluating slope stability where the failure surface runs parallel to the ground surface at shallow depth. With seepage parallel to the slope, the factor of safety is: FS = c′ / (γ·z·sin α·cos α) + [(γ − m·γw) / γ] · tan φ′ / tan α, where c′ is effective cohesion (kN/m²), γ is soil unit weight (kN/m³), z is the depth to the failure plane (m), α is the slope angle (°), φ′ is the internal friction angle (°), γw = 9.81 kN/m³ is the unit weight of water, and m is the height of the water table above the failure plane as a fraction of z (0 = dry, 1 = water table at the surface). A FS above 1.5 is generally considered safe, 1.0–1.5 is marginal, and below 1.0 indicates failure. Pore-water pressure from a high water table reduces effective stress and so the frictional resistance; with the water table at the surface, the friction term is roughly halved.
How to use
Given: slope angle α = 30°, cohesion c′ = 5 kN/m², friction angle φ′ = 25°, unit weight γ = 18 kN/m³, failure depth z = 3 m, dry (m = 0). Step 1 — Cohesion term: 5 / (18 × 3 × sin 30° × cos 30°) = 5 / (54 × 0.5 × 0.866) = 5 / 23.38 = 0.214. Step 2 — Friction term: tan 25° / tan 30° = 0.4663 / 0.5774 = 0.808. Step 3 — FS = 0.214 + 0.808 ≈ 1.02, at the verge of failure. With the water table at the surface (m = 1) the friction term falls to 0.808 × (18 − 9.81) / 18 = 0.368 and FS ≈ 0.58, so saturation would trigger sliding. The defaults (25°, 15 kPa, 28°, 19 kN/m³, 3 m, dry) give FS ≈ 1.83.
Frequently asked questions
What factor of safety is considered acceptable for slope stability in geotechnical engineering?
Most geotechnical codes and standards require a minimum factor of safety of 1.5 for permanent slopes under static loading. For temporary construction slopes a FS of 1.25 is sometimes accepted. Critical infrastructure such as dams or highway embankments may demand FS ≥ 2.0. When dynamic loads such as earthquakes are included in the analysis, lower values around 1.1–1.2 may be tolerated because seismic events are transient. Always consult local building codes and a licensed geotechnical engineer for site-specific decisions.
How does a rising water table affect slope stability and factor of safety?
A rising water table increases pore-water pressure within the soil, which reduces effective normal stress on the failure plane. Since frictional shear strength depends on effective stress, higher pore pressure directly lowers the factor of safety. In the infinite-slope formula the friction term is multiplied by (γ − m·γw) / γ: with the water table at the surface (m = 1) and γ ≈ 19 kN/m³, roughly half of the frictional resistance is lost. This is why many slope failures occur during or immediately after heavy rainfall events that raise the water table.
When is the infinite slope method appropriate versus more advanced stability analyses?
The infinite slope method is appropriate when the failure surface is long relative to the depth — typically a depth-to-length ratio less than about 0.1 — and runs parallel to the slope surface. It works well for shallow translational failures in uniform soils, such as debris slides or shallow cut slopes. For deeper rotational failures, irregular geometry, layered soils, or complex pore-pressure distributions, methods such as Bishop's Simplified, Janbu, or Spencer's method — or finite-element analysis — are more appropriate and accurate.