Retaining Wall Earth Pressure Calculator

How this retaining wall earth pressure calculator works

This calculator estimates the active lateral earth pressure acting on a retaining wall using classical Rankine theory. It is intended for quick, preliminary checks and for educational use, not as a substitute for a full geotechnical or structural design.

Given the wall height, soil unit weight, and friction angle of the retained soil, the tool computes:

• the active earth pressure coefficient, K_a,
• the maximum lateral pressure at the base of the wall,
• the total active force per metre length of wall, and
• the location of the resultant force above the base (for a triangular pressure distribution).

The calculation assumes granular backfill with a level surface behind the wall, no wall friction, no water pressure, and no surcharge loads at the ground surface. Under these conditions, Rankine active earth pressure theory gives a simple but useful approximation for many retaining wall problems at the concept or preliminary design stage.

Key formulas used in the calculator

The active condition is mobilised when the soil mass behind the wall is allowed to move enough for shear strength to be fully developed. Under the simplifying assumptions above, Rankine theory provides closed-form expressions for the active earth pressure coefficient and the resulting force.

Active earth pressure coefficient

For a cohesionless soil with internal friction angle φ (in degrees), the Rankine active earth pressure coefficient, K_a, is:

In conventional engineering notation, the same expression is usually written as:

K_a = tan^2(45° − φ/2)

Pressure distribution with depth

For a wall of height H (m) retaining a soil of unit weight γ (kN/m³), the lateral effective stress at depth z (measured from the ground surface, 0 ≤ z ≤ H) is:

σ_h(z) = K_a · γ · z

This pressure is zero at the top and increases linearly with depth, forming a triangular distribution with the maximum value at the base:

σ_h,base = K_a · γ · H

Total active force and its location

The total active force per metre run of wall is the area under the triangular pressure diagram:

P_a = (1/2) · K_a · γ · H²

This resultant force acts at a height H/3 above the base of the wall (i.e., one-third up from the bottom), measured along the back face of the wall.

Interpreting the calculator results

After entering the wall height, soil unit weight, and friction angle, the calculator returns:

• K_a: a dimensionless coefficient that links vertical effective stress to lateral earth pressure under active conditions.
• Pressure at base (kPa or kN/m²): σ_h,base = K_a · γ · H. This is the maximum lateral pressure at the bottom of the retained soil.
• Total active force, P_a (kN/m): the integrated lateral load per metre of wall height, suitable for use in sliding, overturning, and structural design checks.
• Resultant height (m): the distance of the force resultant above the base, taken as H/3 for a linear triangular distribution.

You can use the total active force value in simple stability checks:

• Sliding check: compare P_a to the available resisting force from base friction and any passive resistance in front of the toe.
• Overturning check: compute overturning moment about the toe of the wall as M_o = P_a · (H/3) and compare to stabilising moments from the wall self-weight and soil weight over the heel.
• Bearing pressure check: use the resultant vertical and horizontal forces and their eccentricity to estimate bearing pressures under the footing.

In all cases, these quick checks should be complemented by more detailed analysis and local code provisions before finalising a design.

Typical parameter values for retaining wall backfill

Choosing reasonable input values is important for meaningful results. The table below shows indicative friction angles and corresponding active earth pressure coefficients for common granular soils, computed from the Rankine formula above. Actual values depend on gradation, density, angularity, and moisture content, so refer to site investigation data wherever possible.

For cohesive or partially saturated soils, effective stress friction angles can vary widely; where possible, use values obtained from laboratory triaxial or direct shear tests, or from correlations to in-situ tests such as SPT or CPT.

Worked example

This example illustrates how the calculator applies the formulas step by step.

Problem: A 3.0 m high retaining wall supports level backfill consisting of medium dense sand. The soil unit weight is γ = 18 kN/m³ and the friction angle is φ = 35°. Estimate the active lateral earth pressure and total force per metre of wall.

Step 1 – Compute K_a

Using Rankine theory:

K_a = tan²(45° − φ/2)

First compute φ/2 = 35° / 2 = 17.5°, then:

45° − 17.5° = 27.5°

The tangent of 27.5° is approximately 0.52, so:

K_a ≈ (0.52)² ≈ 0.27

Step 2 – Pressure at the base

The maximum active pressure at the base is:

σ_h,base = K_a · γ · H

Substituting the numbers:

σ_h,base ≈ 0.27 · 18 · 3.0 ≈ 14.6 kN/m² (kPa)

Step 3 – Total active force

The total active force per metre of wall is:

P_a = (1/2) · K_a · γ · H²

With H² = (3.0)² = 9.0:

P_a ≈ 0.5 · 0.27 · 18 · 9.0

P_a ≈ 0.5 · 0.27 · 162 ≈ 0.5 · 43.7 ≈ 21.9 kN/m

Step 4 – Location of the resultant

For a triangular pressure distribution, the resultant acts at one-third of the height above the base:

z_R = H/3 = 3.0 / 3 ≈ 1.0 m

So the active force of about 21.9 kN/m acts 1.0 m above the base of the wall. These values can then be used in simplified sliding and overturning checks.

Comparison of active, at-rest, and passive conditions

Retaining wall problems can involve different lateral earth pressure states depending on how much the wall moves and how the soil is constrained. The calculator on this page focuses on the active condition, but it is helpful to understand how it compares to other states.

Using active pressure where at-rest conditions apply can underestimate loads; conversely, relying on full passive resistance in design may be unconservative if movements are insufficient to fully mobilise passive strength.

Assumptions and limitations of this calculator

The simplicity of the Rankine-based approach requires several idealisations. The calculator assumes:

• Level backfill surface: the ground surface behind the wall is horizontal with no slope.
• No surcharge loads: there are no additional surface loads (traffic, structures, storage, etc.) acting on the backfill.
• No wall friction: interaction between the wall and soil is neglected, which is consistent with the Rankine framework but differs from Coulomb theory.
• Homogeneous, cohesionless soil: a single layer of granular soil with constant unit weight and effective friction angle; layered or stratified profiles are not captured.
• No groundwater or pore pressure: the model uses total unit weight and does not explicitly account for hydrostatic or seepage effects. Saturated or partially submerged conditions require effective stress analysis.
• Drained, static loading: time-dependent effects, seismic loading, and undrained behaviour are not considered.
• Plane-strain conditions: the wall is assumed long enough in the out-of-plane direction that end effects can be ignored.

Because of these assumptions, the tool is best suited to:

• educational exploration of how H, γ, and φ influence active pressure,
• preliminary sizing of small gravity or cantilever walls in simple conditions, and
• quick order-of-magnitude checks against more detailed design calculations.

It should not be used as the sole basis for final design, for walls supporting buildings, for high-consequence structures, or where complex loading and soil conditions exist.

Practical design notes and safety disclaimer

Real retaining wall design involves more than computing active earth pressure. Engineers typically:

• check multiple load cases, including surcharges, water pressures, and in some regions seismic effects,
• consider at-rest conditions where wall movements are tightly restricted,
• evaluate global stability (e.g., sliding along deeper slip surfaces or overall slope stability), and
• account for constructability, drainage details, and long-term maintenance.

Drainage is especially critical. Poor drainage can allow water to build up behind the wall, generating hydrostatic pressure that may exceed the soil pressure and significantly increase total loads. Typical mitigation measures include free-draining granular backfill, perforated collector drains, and weep holes where appropriate.

Disclaimer: The calculations and explanations provided by this tool are simplified and are intended for informational and educational purposes only. They do not account for all factors required for safe retaining wall design and do not replace a full geotechnical and structural analysis. Local building codes, material specifications, construction methods, and site-specific soil data must be considered. Always consult a qualified engineer to review and approve any retaining wall design before construction.