Use this engineering calculation for a transparent preliminary estimate or independent arithmetic check when geometry, materials, loads, operating conditions, and units are defined consistently.

Friction Angle Degrees (°)

Required number input.

Unit Weight Newtons Per Cubic Meter (N/m³)

Required number input.

Depth Meters (m)

Required number input.

Rankine passive lateral earth pressure at depth z for level cohesionless backfill: Kpγz, Kp=(1+sinφ)/(1−sinφ). The tool evaluates the supplied inputs together and returns the named outputs below; it does not infer omitted operating conditions or change the units shown.^[1]

Pressure Pascals (Pa)

The resulting pressure pascals returned as a number.

• Soil pressure, bearing, permeability, and consolidation results depend on stratigraphy, drainage, stress history, groundwater, sampling, laboratory method, anisotropy, construction sequence, and failure mechanism. Site investigation and code-specific factors are essential.
• Use finite inputs in the displayed units and preserve more precision than the final presentation requires. Independently verify safety-critical, financial, compliance, or production decisions.

Check assumptions against drawings, measurements, current material data, and the applicable design code. Apply required load combinations and safety factors, then obtain qualified review and testing for consequential designs.

• Soil Active Pressure

  Rankine active lateral earth pressure at depth z for level cohesionless backfill: Kaγz, Ka=(1−sinφ)/(1+sinφ).

• Soil At Rest Pressure

  Jaky at-rest lateral earth pressure K0γz for normally consolidated cohesionless soil, K0=1−sinφ.

• Horizontal Curve Radius

  Minimum ideal level-curve radius for specified speed and combined superelevation plus lateral friction: R=v²/[g(e+f)].