Calculate Rankine active pressure, soil and surcharge forces, overturning moment, and resultant location, or reverse-solve retaining height in metric or imperial units.

Dry cohesionless soil, level backfill, vertical smooth wall, and sufficient wall movement for active conditions. Excludes water, seismic and compaction loads; this is not a complete retaining-wall design.

Optional settings

Blank means zero surcharge.

Active Soil Pressure Formula

The active soil pressure calculation uses the active earth pressure coefficient, soil unit weight, and wall height or depth. If you enter the friction angle instead of Ka, the calculator first estimates Ka using the Rankine formula for level backfill and a vertical wall with no wall friction.

Kₐ = (1 - sin(phi)) / (1 + sin(phi))
pₐ = Kₐ × gamma × H
Pₐ = 0.5 × Kₐ × gamma × H² + Kₐ × q × H
M = Pₛoil × H / 3 + Pq × H / 2; y = M / Pₐ
  • Ka = active earth pressure coefficient
  • phi = soil internal friction angle, in degrees
  • gamma = soil unit weight, in kN/m³ or lb/ft³
  • H = depth or retaining wall height, in m or ft
  • q = uniform surface surcharge, in kPa or psf; blank means zero
  • pa = soil pressure at depth H; add Kaq for combined base pressure
  • Pa = total active force per unit length of wall, in kN/m or lb/ft
  • y = line of action of the resultant force above the base

If you choose the Ka input mode, the entered coefficient is used directly. If you choose the friction angle φ input mode, Ka is calculated first, then used in the pressure and force equations. The pressure result is the lateral pressure at the bottom of the entered depth. The soil-force component is the triangular pressure diagram and acts at H/3. Uniform surcharge adds KaqH at H/2. The combined resultant height is the sum of the component base moments divided by total force. Reverse solving gives the height for the target force; it does not determine safe wall height.

Illustrative Soil Input Ranges and Active Coefficients

These ranges are illustrative assumptions, not recommended design values or verified site properties. Moisture, grading and compaction affect soil parameters; use site-specific geotechnical data for design.

Soil type Illustrative unit weight, γ Illustrative friction angle, φ Approx. Ka
Loose sand 15 to 17 kN/m³, 95 to 110 lb/ft³ 28° to 30° 0.33 to 0.36
Medium dense sand 17 to 19 kN/m³, 105 to 120 lb/ft³ 32° to 35° 0.27 to 0.31
Dense sand or gravel 19 to 22 kN/m³, 120 to 140 lb/ft³ 36° to 40° 0.22 to 0.26
Silty sand 17 to 20 kN/m³, 105 to 125 lb/ft³ 28° to 34° 0.28 to 0.36

Result Interpretation

Result Meaning Common use
Ka Multiplier that converts vertical overburden pressure into active lateral pressure Checking assumed soil pressure conditions
Active pressure at depth H Maximum lateral pressure at the bottom of the wall or entered depth Pressure diagram and local wall checks
Total active force over H Resultant lateral force per unit length of wall Sliding, overturning, and bearing checks
Line of action Moment-weighted location of the soil-plus-surcharge resultant Moment calculations about the wall base

Example Problems

Example 1: Metric calculation using Ka

Suppose Ka = 0.3333, γ = 18 kN/m³, H = 3 m, and q = 0.

Active pressure at depth H:

pₐ = 0.3333 × 18 × 3 = 18.00 kPa

Total active force:

Pₐ = 0.5 × 0.3333 × 18 × 3² = 27.00 kN / m

Line of action:

y = 3 / 3 = 1.00 m above base

Example 2: Imperial calculation using friction angle

Suppose φ = 30°, γ = 120 lbf/ft³, H = 10 ft, and q = 0.

First calculate Ka:

Kₐ = (1 - sin(30)) / (1 + sin(30)) = 0.3333

Active pressure at depth H:

pₐ = 0.3333 × 120 × 10 = 400 psf

Total active force:

Pₐ = 0.5 × 0.3333 × 120 × 10² = 2000 lb / ft

Line of action:

y = 10 / 3 = 3.33 ft above base

FAQ

What assumptions are used for Ka from the friction angle?

When you enter φ, the calculator uses the Rankine active earth pressure equation. This assumes a simple active pressure case, usually treated as a vertical wall with level backfill, cohesionless soil, and no wall friction. Uniform surface surcharge is included when entered. Sloping backfill, wall friction, groundwater, compaction loads, seismic loads and cohesive soil behavior require separate models.

Why is the total active force one-half of KaγH²?

For dry cohesionless soil with no surcharge, lateral pressure increases linearly with depth. It is zero at the surface and reaches KaγH at the base. The pressure diagram is triangular, so the resultant force equals the area of that triangle: one-half times the base pressure times the wall height.

Where does the active force act on the wall?

For the triangular pressure distribution used here, the resultant active force acts at H/3 above the base of the wall. This location is used when calculating overturning moment. If the pressure diagram is not triangular, such as when surcharge or water pressure is included, the line of action may be different.