Slope Stability Factor of Safety Calculator
Determine whether a soil slope is safe against sliding by computing the Factor of Safety (FS) using the simplified Bishop method. Use this when designing embankments, road cuts, or evaluating landslide risk.
Last updated: September 2026
Formula below · 2 sources (asce.org, Wikipedia) · Updated Sep 2026
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About this calculator
The Factor of Safety (FS) for a slope is the ratio of the shear strength available along a potential failure plane to the shear stress acting on it. This calculator uses the infinite-slope model for a dry slope with a planar failure surface parallel to the ground at vertical depth H: the normal stress on the plane is σ = γ·H·cos²α and the shear stress is τ = γ·H·sin α·cos α, so FS = (c + γ·H·cos²α·tan φ) / (γ·H·sin α·cos α) = c / (γ·H·sin α·cos α) + tan φ / tan α, where c is soil cohesion (psf), γ is unit weight (pcf), H is the depth of the failure plane (ft), α is the slope angle and φ is the internal friction angle. A FS greater than 1.5 is generally considered safe for permanent slopes; 1.0 to 1.5 is marginal; below 1.0 the slope is expected to fail. The infinite-slope model suits shallow, translational slides; it does not model deep rotational (circular) failures, which need the simplified Bishop or Spencer methods, and it assumes no groundwater (seepage lowers FS substantially).
How to use
Suppose you have a slope with: angle α = 30°, failure-plane depth H = 20 ft, cohesion c = 200 psf, friction angle φ = 25°, and unit weight γ = 110 pcf. Step 1 — Cohesion term: c / (γ·H·sin α·cos α) = 200 / (110 × 20 × 0.5 × 0.866) = 200 / 952.6 ≈ 0.210. Step 2 — Friction term: tan φ / tan α = 0.4663 / 0.5774 ≈ 0.808. Step 3 — FS = 0.210 + 0.808 ≈ 1.02. This slope is at the verge of failure and would require flattening, drainage or reinforcement. The defaults (25°, 20 ft, 200 psf, 25°, 115 pcf) give FS ≈ 1.23.
Frequently asked questions
What is a safe Factor of Safety for slope stability in geotechnical engineering?
A Factor of Safety (FS) of 1.5 or higher is the standard minimum for permanent engineered slopes such as highway embankments and dam sides. Temporary construction slopes may be accepted at FS ≥ 1.25. Values below 1.0 indicate imminent failure, while values between 1.0 and 1.5 signal marginal stability that may require regrading, drainage improvement, or soil reinforcement. Regulatory agencies and codes such as AASHTO and local building departments often specify minimum FS requirements for specific project types.
How does soil cohesion affect slope stability calculations?
Cohesion is the component of shear strength that exists independently of normal stress, arising from particle bonding in fine-grained soils like clay. Higher cohesion directly increases the resisting force in the FS numerator, making a slope more stable. Cohesionless soils such as clean sand (c = 0) rely entirely on friction angle for stability, making slope angle relative to friction angle the critical design parameter. Seasonal changes, saturation, and weathering can reduce cohesion significantly, which is why long-term stability analysis often uses lower, conservative cohesion values.
When should I use the simplified Bishop method versus other slope stability methods?
This calculator uses the infinite-slope method, which is appropriate for shallow, translational failures parallel to the slope surface in fairly uniform soil. The simplified Bishop method is better for circular (rotational) slip surfaces, which are common in homogeneous clay slopes, and Janbu or Spencer methods handle non-circular surfaces and layered soils. Software such as SLOPE/W implements these; use it, with a geotechnical engineer, for any slope where failure would matter.