Enter the active earth pressure coefficient (Ka) and any two of the other values into the calculator to determine the active lateral earth pressure (horizontal stress) at a depth.

Active Soil Pressure Calculator

Unit system
Metric
Imperial
Input type
Kₐ
Friction angle φ
kN/m³
m

Active Soil Pressure Formula

The following formula is used to calculate the active lateral earth pressure (horizontal stress) at a depth h for a given soil unit weight and active earth pressure coefficient (Ka). 

P_a = K_a * γ * h

Variables:

  • Pa is the active lateral earth pressure (horizontal stress) at depth h
  • Ka is the active earth pressure coefficient (dimensionless)
  • γ is the soil unit weight (in kN/m³)
  • h is the depth below the ground surface (in meters)

To calculate the active lateral earth pressure at depth, multiply the active earth pressure coefficient by the soil unit weight and the depth. (If you set Ka = 1, this reduces to vertical overburden stress σv = γh.)

What is Active Soil Pressure?

Active soil pressure (often called active lateral earth pressure) is the lateral pressure exerted by a soil mass on a retaining structure when the wall moves away from the soil enough for the soil to reach an “active” stress state. In the simplest dry, cohesionless case with level backfill, the horizontal stress increases approximately linearly with depth and is commonly estimated with an active earth pressure coefficient Ka. In real designs, surcharge loads, groundwater (pore water pressure), and cohesion can add or modify pressure, so Ka alone may not capture all conditions.

How to Calculate Active Soil Pressure?

The following steps outline how to calculate the Active Soil Pressure.

  1. Determine the active earth pressure coefficient (Ka) for your conditions (commonly from a method such as Rankine or Coulomb).
  2. Determine the soil unit weight (γ).
  3. Determine the depth of interest (h).
  4. Calculate the active lateral earth pressure at that depth using the formula Pa = Ka * γ * h.
  5. After inserting the values and calculating the result, check your answer with the calculator above.

Example Problem : 

Use the following variables as an example problem to test your knowledge.

Active earth pressure coefficient (Ka) = 0.333 (example value)

Soil unit weight (γ) = 18 kN/m³

Depth of soil (h) = 5 m