Slope Stability Calculator
A Slope Angle Just a Few Degrees Steeper Can Cross the Line Into Failure
The infinite slope method models a shallow, translational slide along a failure plane running roughly parallel to the ground surface — the kind of failure common in thin soil layers over bedrock or a weak layer close to the surface. Because the driving force (gravity resolved along the slope) and the resisting force (friction and cohesion along the failure plane) both depend on the slope angle in different ways, the factor of safety can swing from comfortably stable to failing over a narrow band of angles.
The Formulas
Saturated slope (seepage parallel to face): FS = [c + (γ_sat − γ_w) × z × cos²(β) × tan(φ)] / [γ_sat × z × sin(β) × cos(β)]
c is cohesion, γ is soil unit weight, z is depth to the failure plane, β is the slope angle, φ is the friction angle, and γ_w is the unit weight of water (9.81 kN/m³ or 62.4 pcf).
How Slope Angle Alone Changes the Outcome
| Slope angle | Factor of safety | Assessment |
|---|---|---|
| 25° | 1.60 | Stable (FS ≥ 1.5) |
| 30° | 1.32 | Marginally stable |
| 35° | 1.12 | Marginally stable |
| 40° | 0.97 | Unstable (FS < 1.0) |
| 45° | 0.86 | Unstable (FS < 1.0) |
This example crosses from stable to unstable between 35° and 40° — a 5-degree change in slope angle, with every other parameter held fixed, is the difference between a marginal slope and a predicted failure.
Where This Gets Used
- Evaluating cut and fill slopes — roadway embankments and excavation slopes are commonly screened with this method before a more detailed circular or wedge failure analysis.
- Assessing saturation risk — comparing the dry and saturated cases for the same slope shows how much capacity is lost when seepage develops, which is a common trigger for slope failures after heavy rainfall.
- Site screening before detailed geotechnical analysis — a fast first check on whether a slope warrants closer engineering attention.
How to Use This Calculator
- Choose Unit system and Condition — Dry Slope or Saturated Slope.
- Enter Cohesion c, Unit Weight (or Saturated Unit Weight), Friction Angle phi, Slope Angle beta, and Depth to Failure Plane z.
- Select Calculate to see the factor of safety and a stability assessment.
Related Calculations
Check the bearing capacity of a foundation on similar soil with the Soil Bearing Capacity Calculator, or size a retaining structure with the Retaining Wall Design Calculator.