What is the Rankine active earth pressure coefficient?

Ka = tan²(45° − φ/2) is a dimensionless ratio derived from Rankine's theory for cohesionless soils. It relates vertical effective stress to the horizontal active pressure. A lower friction angle gives a higher Ka (more pressure).

What does "active" earth pressure mean?

Active pressure develops when the wall moves or tilts away from the soil, allowing the backfill to expand laterally. It is the minimum state of lateral earth pressure and is the design case for most retaining walls.

Does this calculator account for cohesion (c)?

No. The Rankine formula used here assumes c = 0 (cohesionless soil: sand, gravel). For c > 0 clays, a separate Rankine c-φ formula or Coulomb method is needed.

How is the resultant force calculated?

The resultant horizontal force per unit width is the area of the pressure diagram: a triangular component ½·Ka·γ·H² from soil weight plus a rectangular component Ka·q·H from uniform surcharge.

Where does the resultant act?

The triangular (soil) component acts at H/3 from the base; the rectangular (surcharge) component acts at H/2 from the base. The tool reports both.

Can I use imperial units (pcf, feet)?

Yes. Select "Imperial" in the unit toggle. Enter unit weight in pcf (lb/ft³) and height in feet; results will be in psf and lb/ft.

Active Earth Pressure Calculator

Compute the Rankine active earth pressure coefficient (Ka), total lateral pressure, and resultant force on a retaining wall from soil friction angle, unit weight, wall height, and surcharge.

Soil & Wall Parameters

Units:

Internal Friction Angle φ (degrees)

Typical range: 28° – 42° for granular soils.

Soil Unit Weight γ (kN/m³)

Typical: 17–21 kN/m³ (108–133 pcf).

Wall Height H (m)

Surcharge Load q (kN/m²) (optional)

Uniform load on the backfill surface (e.g. traffic, slabs).

Ka (Rankine)

—

dimensionless

Resultant Force / m

—

kN/m

Pressure Diagram

Lateral pressure (kPa)

Depth	Soil Pressure	Surcharge Press.	Total Pressure

Force Breakdown (per unit width)

Triangular soil force (P_soil = ½·Ka·γ·H²) —

Rectangular surcharge force (P_q = Ka·q·H) —

Total resultant P_h —

Soil component acts at — from base (H/3).

Surcharge component acts at — from base (H/2).

Combined resultant acts at — from base.

Enter soil parameters and click Calculate.

Ka and the lateral pressure diagram will appear here.

Summary

This tool applies Rankine's theory to compute the active earth pressure coefficient Ka = tan²(45° − φ/2), where φ is the effective friction angle of the cohesionless backfill. It then calculates the lateral pressure at any depth, the pressure due to surcharge, and the total resultant horizontal force acting on the retaining wall per unit length. Results include a pressure diagram with depth-by-depth values.

How it works

Enter the soil internal friction angle (φ) in degrees.
Enter the soil unit weight (γ) in kN/m³ or pcf.
Enter the wall height (H) in meters or feet.
Optionally enter a uniform surcharge load (q) acting on the backfill surface.
The calculator applies Ka = tan²(45° − φ/2) (Rankine active theory).
Results show Ka, the pressure diagram, and total horizontal resultant force per unit width.

Use cases

Preliminary design of concrete or masonry retaining walls.
Checking lateral earth pressure for basement walls.
Geotechnical coursework and exam practice.
Comparing Rankine Ka values across different soil types.
Estimating surcharge contribution to total wall pressure.
Quick sanity checks for structural analysis models.

Frequently Asked Questions

Last updated: 2026-05-23 · Reviewed by Nham Vu