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The soil's angle of internal friction.
In the infinite-slope model this one figure does nearly all the work: for a dry cohesionless slope the factor of safety reduces to the ratio of the friction angle's tangent to the slope angle's, so a slope standing at its friction angle is marginal by definition and no amount of length changes that. Two degrees of optimism moves a comfortable slope to a marginal one. Where the consequence of movement is a building, this comes from testing rather than judgement.
The slope's angle from horizontal.
Must be less than the friction angle for the formula to give a meaningful (>1) result in dry cohesionless soil.
Factor of safety
1.72 (FS)
Meets a common minimum target of FS ≥ 1.5 for long-term slope stability.
They open the calculator with your figures already in it
Infinite Slope Stability Factor of Safety Calculator: 1.72 (FS) — shown in imperial, US market. The link sets both, so the result they see is the one on your screen.
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How this was calculated
Formula source(s)
- Infinite slope stability, dry cohesionless soil: FS = tan(φ) / tan(β), where φ is the soil's friction angle and β is the slope angle — the classic simplified case where slope length is much greater than the failure depth
Inputs used
- Soil Friction Angle (φ, degrees)
- 32
- Slope Angle (β, degrees)
- 20
Confidence note: Meets a common minimum target of FS ≥ 1.5 for long-term slope stability.
What this calculation does not cover
- The formula is the dry case only. There is no pore-water pressure, no perched water table and no seepage term, and slope-parallel seepage through a fully saturated soil cuts the factor of safety to roughly half the dry value. A slope this page reports at 1.7 can sit near 0.85 after prolonged rain or snowmelt.
- Only friction is carried. Cohesion, cementation, root reinforcement and the apparent cohesion of a damp unsaturated soil are all left out, and so are the soil's unit weight and the depth of the failure surface — those drop out of the arithmetic only because the case is dry and cohesionless. The result therefore says nothing about how deep a slide would be, and it is the wrong model for a clay or residual soil held up by cohesion.
- One failure mode is covered: a shallow translational slide on a plane parallel to the ground surface, on a slope far longer than that plane is deep. Deep-seated rotational failure, sliding on a bedding plane or joint set, toe erosion and undercutting, and flow or liquefaction of loose saturated sand are outside the model and are not ruled out by a high number here.
- No load other than the soil's own weight is included. Surcharge from spoil heaps, stockpiles, plant, traffic or a structure near the crest, excavation or scour at the toe, and earthquake acceleration all change the driving force, and none of them appear in the calculation.
- This is a screening check, not a slope design, and it does not replace a site investigation with measured shear-strength parameters. The answer moves directly with the friction angle, so a value taken from a published table for "sand" rather than from a test on the actual soil sets the accuracy of everything above it. Cut and fill slopes, retaining structures and temporary excavations need design by a qualified geotechnical engineer.
Computed in your browser — nothing you enter is uploaded. Presented in US customary units and US trade terminology. Where a formula follows a published standard, that standard and its edition are cited beside it on this page; where none governs, the page says so. Local amendments override model codes — verify against the code in force where you build.
Sources checked 2026-09-03 · in the site-wide review of 2026-09-06 · v1.0.1
Regulatory standards & verification citations1
- Infinite slope stability, dry cohesionless soil: FS = tan(φ) / tan(β), where φ is the soil's friction angle and β is the slope angle — the classic simplified case where slope length is much greater than the failure depth
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