Metric Republic / Civil & structural engineering / Rankine Active Earth Pressure Calculator

Rankine Active Earth Pressure Calculator

Estimate active earth pressure for level cohesionless backfill with surcharge.

Updated September 2026

How it works

Estimate active earth pressure for level cohesionless backfill with surcharge.

Formula:
Ka = tan²(45°−φ/2); Pa,soil = 0.5·Ka·γ·H²; Pa,q = Ka·q·H.

Before you use the result: Simple Rankine case: level cohesionless backfill, no wall friction or groundwater.

Practical use

Use verified material data and project geometry. Treat results as planning estimates and compare them with the energy/thermal requirements that apply to the project.

Keep units consistent with the source information.
Use project-specific densities, pack sizes and coverage rates where provided.
Round purchasing quantities to supplier packaging and delivery rules.

How to use this calculator: Rankine Active Earth Pressure Calculator

Estimate active earth pressure for level cohesionless backfill with surcharge.

Quick workflow

Enter the project values from the latest drawing, specification or verified site measurement.
Check units, material properties, allowances and any code- or supplier-specific parameters before calculating.
Review the result together with the formula, assumptions and the related checks shown on this page.

Worked example

Example inputs: Retained height H [m]: 3; Soil friction angle φ [°]: 30; Soil unit weight γ [kN/m³]: 18; Uniform surcharge q [kPa]: 10.

Using the sample values built into the calculator, the calculation gives approximately: Active earth coefficient Ka: 0.333; Soil thrust: 27 kN/m; Surcharge thrust: 10 kN/m.

What the result means

Calculation method: Ka = tan²(45°−φ/2); Pa,soil = 0.5·Ka·γ·H²; Pa,q = Ka·q·H.

Before using the result: Simple Rankine case: level cohesionless backfill, no wall friction or groundwater.

Common questions

What does this calculator do?

Estimate active earth pressure for level cohesionless backfill with surcharge.

Which inputs should I verify?

Key inputs to verify include: Retained height H [m], Soil friction angle φ [°], Soil unit weight γ [kN/m³], Uniform surcharge q [kPa].

Can I use this result for final design or ordering?

Use the result as a transparent planning or checking aid. Final design, code compliance, supplier selection and project-specific decisions still need to be verified where applicable. Simple Rankine case: level cohesionless backfill, no wall friction or groundwater.

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