Retaining Wall Calculator — Active Earth Pressure (Rankine)
Estimate the lateral soil pressure and total force acting on a retaining wall: enter the wall height, soil properties, and any surcharge load to get the Rankine active pressure coefficient, force distribution, and resultant height.
m
kN/m³
°
kPa
Total active earth pressure force per metre of wall length
- 1
Rankine Ka
(1 − 0.5) ÷ (1 + 0.5) = 0.3333Active earth pressure coefficient derived from the soil friction angle. - 2
Soil force (triangular)
½ × 0.3333 × 18 × 3² = 27 kN/m - 3
Surcharge force (uniform)
0.3333 × 10 × 3 = 10 kN/m - 4
Total lateral force
27 + 10 = 37
How does this calculator work?
Rankine active earth pressure: Ka = (1−sinφ)/(1+sinφ). Total lateral force = ½·Ka·γ·H² (soil) + Ka·q·H (surcharge) in kN per metre of wall. The resultant acts at roughly H/3 from the base for soil alone. For a 3 m wall with γ = 18 kN/m³, φ = 30°, and q = 10 kPa, total force ≈ 54 kN/m.
Formula
How this is calculated
A retaining wall holds back soil that would otherwise spread under gravity. The soil exerts a horizontal (lateral) pressure on the wall — the active earth pressure — which the wall must resist. Rankine's theory (1857) gives the simplest widely-used formula for cohesionless (granular) soils without wall friction: the active pressure coefficient Ka = (1 − sinφ) / (1 + sinφ), where φ is the soil's internal friction angle.
The horizontal pressure increases with depth: at depth z, σ_a(z) = Ka × γ × z, where γ is the soil unit weight. This triangular pressure distribution gives a total lateral force (per metre of wall length) of Pa = ½ × Ka × γ × H². If there is a uniform surcharge q on the soil surface (vehicles, storage, a slab), it adds a uniform pressure Ka × q at all depths, giving an additional force of Ka × q × H. The total resultant acts at a height that reflects the combined triangular and rectangular distributions.
Important limitations: Rankine's theory assumes cohesionless horizontal backfill, no wall friction, and fully active conditions (enough wall movement to mobilise the failure wedge — typically 0.1–0.5% of wall height). For clay soils (cohesive), sloped backfill, seismic loading, or tall walls, more advanced methods (Coulomb, log-spiral, finite element) are needed. Soil parameters γ and φ are estimates — always obtain site-specific geotechnical data for any real structural design.
Frequently asked questions
Typical values (2025 estimates): loose sand 25–30°, medium dense sand 30–35°, dense sand/gravel 35–40°, well-graded gravel 35–45°. The default 30° is a conservative estimate for common granular backfill. For design, use values from a soil investigation report for your specific site.
Active pressure occurs when the wall moves away from the soil, allowing it to expand — this is the lower-bound loading a wall must resist. Passive pressure occurs when the wall is pushed into the soil (e.g., the toe of a gravity wall), which is much larger (Kp = 1/Ka for Rankine). Passive resistance is what prevents overturning and sliding.
This calculator gives a preliminary lateral load estimate for educational and scoping purposes. Structural design of retaining walls — checking bearing capacity, sliding, overturning, and wall element strength — requires a licensed geotechnical and structural engineer, especially for walls over 1.2 m high or near structures.
Also known as
TG we-Calculate Editorial Team. (2026). Retaining Wall Calculator — Active Earth Pressure (Rankine) [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/retaining-wall-calculator
TG we-Calculate Editorial Team. "Retaining Wall Calculator — Active Earth Pressure (Rankine)." TG we-Calculate. 2026. https://we-calculate.com/calculator/retaining-wall-calculator.
TG we-Calculate Editorial Team, "Retaining Wall Calculator — Active Earth Pressure (Rankine)," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/retaining-wall-calculator
@misc{wecalculate_retaining_wall_calculator, title = {Retaining Wall Calculator — Active Earth Pressure (Rankine)}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/retaining-wall-calculator}}, year = {2026}, note = {TG we-Calculate} }
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