What is the Ordinary (Fellenius) method?

The Ordinary method, also called the Fellenius or Swedish method, is a limit-equilibrium technique that assumes the interslice forces are parallel to the base of each slice. It satisfies moment equilibrium but not force equilibrium. It tends to give slightly conservative (lower) FS values compared to Bishop's simplified method.

How do I choose slice widths?

Divide the failure mass into equal-width slices, typically 8–15 for a hand calculation. More slices give a more accurate result. Each slice should be narrow enough that the base angle α is roughly constant within it.

What is the base angle α for a slice?

α is the angle between the horizontal and the tangent to the failure circle at the mid-base of each slice. Slices on the active (uphill) side typically have negative α (the base tilts toward the center), while slices on the passive (downhill) side have positive α.

How is pore water pressure included?

Enter the pore pressure u (in kPa) for each slice. It acts over the base length l = b/cosα, reducing effective normal stress. A common simplification uses a pore pressure ratio r_u = u/(γ·h).

What FS value is considered acceptable?

Most codes require FS ≥ 1.5 for permanent slopes, FS ≥ 1.3 for temporary cuts, and FS ≥ 1.2–1.4 for end-of-construction conditions. Values below 1.0 indicate predicted failure.

Does this tool account for tension cracks?

No. Tension crack effects, which reduce the effective arc length at the top of the slope, are not automatically applied. For slopes with tension cracks, reduce the number of slices at the crest accordingly or set c = 0 over the cracked zone.

Factor of Safety Slope Calculator

Name: Factor of Safety Slope Calculator
Availability: InStock
Author: Nham Vu

Compute the factor of safety for slope stability using the Ordinary (Fellenius) method of slices for a circular failure arc.

Soil Properties (Global)

Cohesion c (kPa)

0 for cohesionless soil.

Friction angle φ (°)

Unit weight γ (kN/m³)

Number of slices

Slice Parameters

α is positive for slices whose base dips toward the toe.

#	b (m)	h (m)	α (°)	u (kPa)

b = slice width, h = average height, α = base angle, u = pore pressure.

Fill in soil properties and slice data, then click Calculate.

Factor of Safety (Fellenius)

01.01.52.0+

Failure Marginal Safe

Force Totals

Total Resisting (Σ numerator)

kN/m

Total Driving (Σ W·sinα)

kN/m

Per-Slice Breakdown

#	W (kN/m)	l (m)	W·sinα	W·cosα	Resist.

W = slice weight, l = base arc length, Resist. = c·l + (W·cosα − u·l)·tanφ

Fellenius Formula

FS = Σ[c·l + (W·cosα − u·l)·tanφ] / Σ(W·sinα)

where l = b/cosα (arc length of each slice base)

Summary

Compute the factor of safety for slope stability using the Ordinary (Fellenius) method of slices for a circular failure arc.

How it works

Define the failure circle radius and its center coordinates relative to the slope crest.
Enter the number of slices (up to 10) and the global soil properties: cohesion and friction angle.
For each slice, specify the slice width, average height, and the angle of the base of the slice to the horizontal.
The calculator applies the Fellenius formula: FS = Σ[c·l + (W·cosα − u·l)·tanφ] / Σ(W·sinα) for each slice.
Results show the overall factor of safety and a per-slice breakdown of resisting and driving forces.

Use cases

Preliminary stability check for embankments and earth dams.
Evaluate cut slopes in cohesive soils before excavation.
Compare dry vs. seepage-affected conditions for natural hillsides.
Teaching and learning limit-equilibrium slope stability concepts.
Screen failure arc candidates before running full software analysis.
Back-calculate soil shear strength from a known failure.

Frequently Asked Questions

Last updated: 2026-07-23 · Reviewed by Nham Vu