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Active Earth Pressure (Rankine)

· Last updated：2026-07-18

Calculate the Rankine active earth pressure on a smooth vertical wall backfilled with cohesionless soil. K_a = tan²(45°−φ/2). Optional uniform surcharge q. Returns the base pressure p₀, the total force P, and the resultant height.

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Written by the Elysia Tools team
Math502
Civil Engineering16

Tool usage guide

Learn when to use this tool, what it supports, and how real users apply it.

Key facts

Category
Math & Numbers
Input types
number
Output type
json
Sample coverage
4
API ready
Yes

Overview

Calculate the Rankine active earth pressure on a smooth vertical retaining wall backfilled with cohesionless soil. This calculator computes the active earth pressure coefficient (Ka), base pressure, total lateral force, and the height of the resultant force, with optional support for uniform surcharge loads.

When to use

  • Designing smooth, vertical retaining walls backfilled with dry, cohesionless soil.
  • Estimating lateral earth pressures and resultant force locations for preliminary geotechnical design.
  • Evaluating the impact of uniform surcharge loads on the lateral pressure distribution of a retaining structure.

How it works

  1. 1Input the soil friction angle (φ) in degrees, the wall height (H) in meters, and the soil unit weight (γ) in kN/m³.
  2. 2Optionally enter a uniform surcharge load (q) in kPa acting on the backfill surface.
  3. 3The tool calculates the active earth pressure coefficient (Ka) using the formula Ka = tan²(45° − φ/2).
  4. 4It computes the base pressure, total lateral force, and the height of the resultant force above the wall base.

Use cases

  • Geotechnical engineers sizing gravity or cantilever retaining walls in granular soils.
  • Civil engineering students verifying homework calculations for lateral earth pressure distributions.
  • Structural designers calculating lateral load inputs for retaining wall stability checks against sliding and overturning.

Examples

1. Standard Retaining Wall with Cohesionless Backfill

Geotechnical Engineer

Background

Designing a 5-meter-high concrete retaining wall backfilled with clean sand.

Problem

Determine the lateral active earth pressure coefficient, total force per meter, and the resultant force location to perform stability checks.

How to use

Enter 30 for the friction angle, 5 for the wall height, and 18 for the soil unit weight. Leave the surcharge field blank.

Outcome

The tool calculates a Ka of 0.3333, a base pressure of 30.00 kPa, a total lateral force of 75.00 kN/m, and a resultant height of 1.67 meters above the base.

2. Retaining Wall with Surface Surcharge

Structural Designer

Background

A 5-meter retaining wall has a roadway nearby, imposing a uniform surcharge load of 10 kPa on the backfill surface.

Problem

Calculate the combined lateral force from both the soil and the surcharge, along with the new resultant height.

How to use

Enter 30 for the friction angle, 5 for the wall height, 18 for the soil unit weight, and 10 for the surcharge.

Outcome

FAQ

What is Rankine's active earth pressure theory?

It is a method that assumes a plastic equilibrium state in a soil mass behind a smooth, vertical retaining wall to calculate lateral earth pressure.

Can this calculator handle cohesive soils?

No, this calculator is designed specifically for cohesionless (granular) soils where cohesion (c) is zero.

How does a surcharge load affect the resultant height?

A uniform surcharge adds a rectangular pressure distribution, which shifts the resultant force height upward compared to soil pressure alone.

What units should I use for the inputs?

Use degrees for the friction angle, meters for wall height, kN/m³ for soil unit weight, and kPa for surcharge.

Does this tool account for wall friction or sloping backfills?

No, Rankine's basic theory assumes a smooth vertical wall and a horizontal backfill surface.

Hub

Preliminary Geotechnical Earth and Foundation Screening

Organize soil, groundwater, geometry, loading, and drainage assumptions before screening shallow-foundation capacity, infinite-slope stability, and Rankine active earth pressure. Calculator output is preliminary only.

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The tool outputs a total lateral force of 91.67 kN/m (75.00 kN/m from soil and 16.67 kN/m from surcharge) and a resultant height of 1.82 meters above the base.