What this calculator does
Earth pressure decides how much steel goes into a basement wall or a retaining structure. This calculator returns both the active coefficient (for a wall that can move) and the at-rest coefficient (for a wall that cannot), with the resulting thrust and the height at which it acts.
How to use it
- Enter the soil unit weight and friction angle from the investigation.
- Enter the retained height and any uniform surcharge.
- Use the active coefficient when the wall is free to deflect; use the at-rest coefficient for a propped basement wall.
- The resultant height tells you where to place the tie-back or reinforcement.
Governing formula
Ka = (1−sin φ)/(1+sin φ) ; K₀ = 1 − sin φ ; Pa = ½γH²Ka + qKaH Where:
-
Ka= Active earth pressure coefficient [–] -
K₀= At-rest coefficient (Jaky) [–] -
q= Uniform surcharge [kPa]
Derived Equations:
z̄ = (γKaH³/6 + qKaH²/2) / Pa Worked example — 3 m of soil at 18 kN/m³ with φ = 30°
The figures below were produced by running this page's own engine with the example inputs (Soil unit weight (kN/m³), Friction angle (°), Retained height (m), Uniform surcharge (kPa)). If the calculator returns something different for the same numbers, that is a bug, not a rounding difference.
| Active coefficient Ka | 0.33 – |
|---|---|
| At-rest coefficient K₀ | 0.5 – |
| Active pressure at the base | 21.33 kPa |
| At-rest pressure at the base | 32 kPa |
| Active resultant | 37 kN/m |
| Height of the resultant above the base | 1.14 m |
| Assessment | Active resultant 37.0 kN/m acting at 1.14 m above the base (Coulomb sediment-free, vertical wall, dry backfill). |
- At 30° the active coefficient is 1/3 and the at-rest coefficient is 0.5.
- The triangular soil thrust is 0.5 × 18 × 9 × 1/3 = 27 kN/m, plus 10 kN/m from the surcharge.
- A propped wall cannot deflect, so design it for K₀ = 0.5, which is 50 % more thrust.
Assumptions & limitations
Engineering calculation. Rankine active and at-rest horizontal earth pressure with a surcharge. No wall friction, compaction stresses or seismic coefficients.
- Rankine assumes a smooth vertical wall and horizontal backfill; sloping backfill or wall friction changes the coefficients (use Coulomb).
- Compaction-induced "locked-in" stress and seismic loading are not included.
- Groundwater is assumed absent; water pressure adds to the total horizontal thrust below the water table.
This tool supports professional engineering work; it does not replace a sealed design. Confirm every result against the applicable standard and a licensed engineer before it is built.
References & standards
- BS EN 1997-1 — earth pressures on retaining structures.
- GECP 7 — design of embedded retaining walls.
- Rankine (1857) — stability of loose and cohesive earth.