Retaining Wall Pressure Calculator
Computes the Rankine active lateral earth pressure resultant acting on a retaining wall based on soil height, unit weight, and internal friction angle. Essential for structural design of basement walls, highway cuts, and embankments.
About this calculator
This calculator uses Rankine's active earth pressure theory to find the total horizontal force per unit length of wall. The active earth pressure coefficient is Ka = tan²(45° − φ/2), where φ is the soil's internal friction angle. The pressure increases linearly with depth, so the resultant force on the wall is Pa = 0.5 × γ × H² × Ka. Here γ is the soil unit weight (kN/m³), H is the wall height (m), and Ka is dimensionless. The resultant acts at one-third of the wall height from the base. Rankine's theory assumes a cohesionless, homogeneous, dry backfill with no wall friction — conservative assumptions suitable for preliminary design. For walls with surcharge loads, inclined backfill, or cohesive soils, more advanced methods such as Coulomb's theory or the log-spiral approach should be used.
How to use
Assume a wall retaining 4 m of sand with a unit weight of 18 kN/m³ and a friction angle of 30°. Step 1: Ka = tan²(45° − 30°/2) = tan²(30°) = 0.577² ≈ 0.333. Step 2: Pa = 0.5 × 18 × 4² × 0.333 = 0.5 × 18 × 16 × 0.333 = 47.95 kN/m. Enter Height = 4, Unit Weight = 18, Friction Angle = 30 and the calculator returns approximately 47.95 kN per metre of wall, acting at 4/3 ≈ 1.33 m above the base.
Frequently asked questions
What is the difference between active and passive earth pressure on a retaining wall?
Active pressure develops when the wall moves slightly away from the soil, allowing the soil to expand and reach its minimum stable state — this is the force trying to push the wall over. Passive pressure develops when the wall is pushed into the soil, mobilising maximum resistance. Active pressure is much smaller than passive pressure for the same soil. Retaining wall design uses active pressure as the destabilising load and passive pressure (at the toe) as part of the resisting force.
How does the soil friction angle affect the lateral earth pressure result?
A higher friction angle produces a lower Ka value, meaning the soil exerts less lateral pressure on the wall. For example, dense gravel (φ ≈ 38°) gives Ka ≈ 0.24, while loose sand (φ ≈ 28°) gives Ka ≈ 0.36 — a 50% increase in pressure. This is why compacting backfill and choosing granular, free-draining material behind a retaining wall significantly reduces structural demand. Poorly drained or saturated soils introduce additional hydrostatic pressure that can dominate the design.
When should I use Rankine's theory versus Coulomb's theory for retaining wall design?
Rankine's theory is simpler and conservative: it ignores wall friction and assumes the failure plane is planar, making it suitable for preliminary design and smooth or frictionless walls. Coulomb's theory accounts for wall friction (δ) and inclined backfill surfaces, giving lower (less conservative) pressures that are more realistic for rough concrete or timber walls. Most codes allow either method, but Coulomb's theory is preferred for final design of walls with significant wall friction or sloped backfill. Always apply appropriate factors of safety regardless of which theory is used.