What is the formula used for the passive earth pressure coefficient?

The calculator uses Rankine's formula: K_p = tan²(45° + φ/2), where φ is the soil friction angle.

Can I include a surcharge load in the calculation?

Yes, you can input an optional uniform surcharge (q) in kPa, which will be added to the lateral pressure distribution.

Does this calculator account for wall friction?

No, Rankine's theory assumes a smooth vertical wall with no friction. The calculated K_p represents an upper bound, and designers typically apply a reduction factor.

What types of soil is this calculator suitable for?

It is designed for cohesionless soils (such as sand or gravel) where cohesion is zero.

What outputs does the calculator provide?

It outputs the passive earth pressure coefficient (K_p), the base pressure (p₀), the total lateral force (P), and the height of the resultant force.

Elysia Tools

Navigation

Math & Numbers

Passive Earth Pressure (Rankine)

Calculate the Rankine passive earth pressure on a smooth vertical wall backfilled with cohesionless soil. K_p = tan²(45°+φ/2). Optional uniform surcharge q. Returns the base pressure p₀, the total force P, and the resultant height. Note: theoretical K_p is an upper bound; designers often apply a reduction factor for wall friction.

Execution

Run this tool

Fill in the form, run the tool, and review the result in one place.

Prepared example runs

Click an example to fill the form automatically. File inputs still need an upload.

1 examples

φ=30°, H=2 m, γ=18 kN/m³ → K_p=3.0000, P=108 kN/m

K_p = tan²(45+15)° = tan²60° = 3.0000. p₀ = K_p·γ·H = 3·18·2 = 108 kPa. P_soil = ½·K_p·γ·H² = ½·3·18·4 = 108 kN/m. Resultant at H/3 = 0.667 m.

{"result":"Rankine passive pressure, φ=30°, H=2 m, γ=18 kN/m³. K_p = tan²(45+15)° = 3.0000. Base pressure p₀ = K_p·γ·H = 108.00 kPa. Total force P = ½·K_p·γ·H² = 108.00 kN/m. Resultant at H/3 = 0.6667 m above the base. Note: theoretical K_p is an upper bound — apply a reduction factor in design.","metadata":{"input":{"phi":30,"H":2,"gamma":18},"result":{"coefficient":3,"basePressure":108,"basePressureUnit":"kPa","totalForce":108,"totalForceUnit":"kN/m","resultantHeight":0.6667,"resultantHeightUnit":"m"}}}

Inputs

Set the required fields, then run the tool.

5 options

SettingsAdjust formats, ranges, numbers, and modes.5

Friction Angle φ (°)numberRequiredWall Height H (m)numberRequiredSoil Unit Weight γ (kN/m³)numberRequiredSurcharge q (kPa, optional)numberOptionalOptional uniform surcharge on the backfill surface.Decimal PlacesnumberOptional

Result

Ready for a run

Run the tool to preview files, text, structured data, or streamed output here.

Samples

Passive Earth Pressure (Rankine)

Run this tool

Prepared example runs

Inputs

Result

Examples that match this tool

Continue with connected tools and hubs

Prepared example runs

Inputs

Result

Learn when to use this tool, what it supports, and how real users apply it.

Key facts

Overview

When to use

How it works

Use cases

Examples

1. Standard Cohesionless Backfill Calculation

2. Retaining Wall with Surcharge Load

FAQ

Android Image Processing Java Samples

Android Image Processing Kotlin Samples

Web Image Processing Python Samples

Web Image Processing Rust Samples

Active Earth Pressure (Rankine)

RLC Admittance Calculator (Y = G + jB)

Antilog Calculator

Arithmetic Sequence Calculator