# Active Earth Pressure (Rankine) Calculate the Rankine active earth pressure on a smooth vertical wall backfilled with cohesionless soil. K_a = tan²(45°−φ/2). Optional uniform surcharge q. Returns the base pressure p₀, the total force P, and the resultant height. > Canonical page: https://elysiatools.com/en/tools/active-earth-pressure - **Category:** Math & Numbers - **Keywords:** active earth pressure, Rankine, K_a = tan²(45-φ/2), retaining wall, lateral earth pressure, cohesionless soil, geotechnical, civil engineering ## Overview Calculate the Rankine active earth pressure on a smooth vertical retaining wall backfilled with cohesionless soil. This calculator computes the active earth pressure coefficient (Ka), base pressure, total lateral force, and the height of the resultant force, with optional support for uniform surcharge loads. ## Inputs - **Friction Angle φ (°)** (number): e.g. 30 - **Wall Height H (m)** (number): e.g. 5 - **Soil Unit Weight γ (kN/m³)** (number): e.g. 18 - **Surcharge q (kPa, optional)** (number): Optional uniform surcharge on the backfill surface. - **Decimal Places** (number) ## When to use - Designing smooth, vertical retaining walls backfilled with dry, cohesionless soil. - Estimating lateral earth pressures and resultant force locations for preliminary geotechnical design. - Evaluating the impact of uniform surcharge loads on the lateral pressure distribution of a retaining structure. ## How it works - Input the soil friction angle (φ) in degrees, the wall height (H) in meters, and the soil unit weight (γ) in kN/m³. - Optionally enter a uniform surcharge load (q) in kPa acting on the backfill surface. - The tool calculates the active earth pressure coefficient (Ka) using the formula Ka = tan²(45° − φ/2). - It computes the base pressure, total lateral force, and the height of the resultant force above the wall base. ## Use cases - Geotechnical engineers sizing gravity or cantilever retaining walls in granular soils. - Civil engineering students verifying homework calculations for lateral earth pressure distributions. - Structural designers calculating lateral load inputs for retaining wall stability checks against sliding and overturning. ## Frequently asked questions ### What is Rankine's active earth pressure theory? It is a method that assumes a plastic equilibrium state in a soil mass behind a smooth, vertical retaining wall to calculate lateral earth pressure. ### Can this calculator handle cohesive soils? No, this calculator is designed specifically for cohesionless (granular) soils where cohesion (c) is zero. ### How does a surcharge load affect the resultant height? A uniform surcharge adds a rectangular pressure distribution, which shifts the resultant force height upward compared to soil pressure alone. ### What units should I use for the inputs? Use degrees for the friction angle, meters for wall height, kN/m³ for soil unit weight, and kPa for surcharge. ### Does this tool account for wall friction or sloping backfills? 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