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Passive Earth Pressure Calculator

This calculator uses Rankine's theory for passive earth pressure on a smooth, vertical wall retaining a cohesionless soil with a level backfill.

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How to use this calculator

Enter Values

Enter your values and press Calculate to see results.

Before you rely on this: First-pass guide only. Verify safety-critical or regulated work against the relevant standards, your project requirements and a qualified professional.

How to use this calculator

  1. Enter the soil friction angle phi in degrees (typically 28-40° for granular soils), the soil unit weight gamma in kN/m³, and the retained/embedded height H in metres.
  2. Optionally add a uniform surcharge q (kPa) acting over the passive zone; leave it blank or 0 for none.
  3. Read Kp, the pressure at the base, the total passive thrust Pp per metre run, and the height of its resultant above the base.

How it works

This calculator uses Rankine's theory for passive earth pressure on a smooth, vertical wall retaining a cohesionless soil with a level backfill. The passive pressure coefficient is Kp = tan²(45 + phi/2), where phi is the soil's angle of internal friction. Passive pressure is the resistance the soil offers when the wall is pushed INTO the soil mass — the opposite of active pressure — so Kp is always greater than 1 and much larger than the active coefficient Ka.

The horizontal passive pressure at depth H is Kp·gamma·H, giving a triangular distribution whose resultant is the total passive thrust Pp = 0.5·Kp·gamma·H² per metre run, acting at H/3 above the base. A uniform surcharge q adds a rectangular pressure Kp·q over the height (thrust Kp·q·H acting at H/2), and the combined resultant height is the load-weighted average. Passive resistance requires substantial wall movement to develop fully, which is why geotechnical codes apply a large factor of safety (or a reduced mobilisation factor) before it is counted on in design.

Worked example

3 m wall, phi = 30°, gamma = 18 kN/m³, no surcharge. For a 3 m high wall retaining a dense sand with a friction angle of 30° and unit weight 18 kN/m³ (no surcharge): Kp = tan²(45 + 15) = tan²(60) = 3.000. The passive pressure at the base is Kp·gamma·H = 3.000 × 18 × 3 = 162.00 kPa. The total passive thrust is Pp = 0.5 × 3.000 × 18 × 3² = 243.00 kN per metre run, acting H/3 = 1.000 m above the base. This resisting thrust is what stabilises an embedded wall or footing against sliding — but it is only mobilised after appreciable wall movement, so designers apply a large factor of safety before relying on it.

Common mistakes

  • Confusing passive with active pressure — passive Kp = tan²(45 + phi/2) is large (>1) and resists movement; active Ka = tan²(45 - phi/2) is small (<1) and drives it. Swapping the sign inside the tangent gives a wildly wrong answer.
  • Relying on the full passive thrust without a safety factor. Passive resistance is only mobilised after significant wall deflection, so codes require a large factor of safety (often 2 or more) or a mobilisation reduction before it is used in a stability check.
  • Applying this cohesionless (c = 0) formula to clays or including wall friction/backfill slope — those cases need the full Coulomb or code passive theory, not this simplified Rankine estimate.

Frequently asked questions

What is the difference between active and passive earth pressure?

Active pressure is what the retained soil pushes onto a wall as it tends to move away from the soil (coefficient Ka = tan²(45 − phi/2), always less than 1). Passive pressure is the resistance the soil provides when the wall is pushed into the soil (coefficient Kp = tan²(45 + phi/2), always greater than 1). Passive pressure is much larger, which is why the embedded toe of a wall or a footing edge can resist sliding.

Why can't I use the full passive thrust in my design?

Passive resistance is only fully mobilised after the wall moves a significant amount into the soil — far more movement than active pressure needs. Because that movement may be unacceptable in service, geotechnical standards apply a large factor of safety or a mobilisation factor, so only a fraction of the calculated Pp is relied upon. Always follow the relevant code and confirm with a geotechnical engineer.

Does this include the water table or wall friction?

No. This is the simplified Rankine case: dry, cohesionless soil, a smooth vertical wall, a level backfill and no wall friction. A water table adds hydrostatic pressure and reduces the effective soil weight, and wall friction increases Kp. For those effects use the full Coulomb theory or the passive provisions of your design code.

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