Lateral Earth Pressure Calculator (Rankine)

Compute Rankine active, at-rest, and passive earth pressure coefficients and the resulting lateral forces on a wall from backfill friction angle, unit weight, wall height, and an optional uniform surcharge.

Educational / preliminary estimating tool. Results use published correlations and idealized assumptions (homogeneous soil, no groundwater effects unless stated). They are not a substitute for a site-specific investigation and design by a licensed geotechnical engineer.

Wall & Backfill Parameters

Friction Angle φ

Backfill Unit Weight γ

pcf

Wall Height H

Surface Surcharge q

psf

Enter soil properties and wall height to compute lateral earth pressures.

The coefficients

K_a = tan²(45 − φ/2) · K₀ = 1 − sinφ · K_p = tan²(45 + φ/2)

Active pressure develops when the wall yields slightly away from the soil; at-rest applies to rigid, non-yielding walls (basement walls, braced boxes); passive is the resistance mobilized when a wall pushes into soil. The active resultant on a wall of height H is P_a = ½·K_a·γ·H², acting at H/3 above the base for triangular pressure — a uniform surcharge adds a rectangular block K_a·q·H acting at mid-height, and the calculator reports the combined resultant and its location.

Assumptions

Rankine theory assumes a level backfill, a vertical, frictionless wall face, and cohesionless soil — reasonable for granular backfill behind typical retaining structures. Sloped backfill, wall friction (Coulomb), or cohesive soils with tension cracks change the numbers. Hydrostatic pressure from a saturated backfill is not included and is exactly why wall drainage matters: water pressure can exceed the soil pressure itself.

Frequently Asked Questions

What is the difference between active, passive, and at-rest pressure?

Active is the minimum lateral pressure, mobilized when a wall moves slightly away from the soil. Passive is the maximum, mobilized pushing into soil. At-rest sits between them and applies to walls that cannot move, like braced basement walls.

Where does the earth pressure resultant act?

For triangular (self-weight) pressure, at one-third of the wall height above the base. Adding a uniform surcharge shifts the combined resultant upward; the calculator reports the exact height.

Should I design a basement wall for active or at-rest pressure?

At-rest — a braced basement wall cannot yield enough to reach the active state, so designing for the lower active pressure would be unconservative.