Retaining Wall Calculation: Formula and Example

A retaining wall calculation estimates the lateral force of soil against a wall and checks whether the wall can resist sliding, overturning, and bearing pressure. Enter the wall height, soil unit weight, friction angle, and base dimensions to get a preliminary estimate of the active earth force and basic stability ratios; a real design also needs site-specific soil, water, loading, and code information.

Formula

For a vertical wall retaining level, cohesionless soil, the simplified Rankine active pressure coefficient is K_a = (1 − sin φ) / (1 + sin φ). The total active force per metre of wall is P_a = ½ γ H²K_a. Here, φ is the soil friction angle in degrees, γ is soil unit weight in kN/m³, and H is retained height in metres. The force acts about H/3 above the base for the triangular pressure distribution assumed by this model.

The calculator’s other outputs are screening ratios, not a complete stability design. Its simplified sliding ratio divides an assumed friction resistance, B tan 30°, by the soil force per metre; its overturning ratio compares a simplified base-weight moment with the soil-force moment. B is base width in metres. The resistance assumptions are deliberately generic and cannot represent an actual wall’s weight, heel and toe geometry, foundation friction, surcharge, or reinforcement. A ratio above 1 means only that this simplified resistance exceeds the calculated demand; it does not establish safety or compliance.

Worked Example

Using the calculator’s default values—H = 2 m, γ = 18 kN/m³, φ = 30°, and B = 1.2 m:

1. Calculate the coefficient: K_a = (1 − sin 30°) / (1 + sin 30°) = 0.5 / 1.5 = 0.3333.
2. Calculate the active force: P_a = ½ × 18 × 2² × 0.3333 = 12.00 kN/m.
3. Calculate the simplified sliding ratio: [1.2 × tan 30°] / [½ × 2 × 0.3333] = 0.6928 / 0.3333 = 2.08.
4. Calculate the simplified overturning ratio: [1.2² × 18] / [2² × 0.3333] = 25.92 / 1.3332 = 19.44.

The headline answer is 12.00 kN of horizontal active force per metre of wall. The unusually high simplified overturning ratio illustrates why this output must not be treated as an engineering verdict: it uses a rough assumed resisting weight and omits important geometry and loads.

What the Calculation Represents

Soil pressure generally increases with depth. In the idealized case used here, pressure is zero at the top and reaches γHK_a at the base, creating a triangular distribution. The resultant is the area of that triangle, ½γH²K_a. Doubling wall height therefore makes the estimated force four times as large, while doubling unit weight doubles it.

“Active” pressure applies when the wall can move or deflect enough for the retained soil to reach its active state. A rigid wall that cannot yield may experience greater, at-rest pressure. Compaction, nearby buildings, vehicles, stored materials, sloping ground, and earthquake effects can also change the loading. The formula assumes none of these additional effects.

Inputs, Units, and Use

• Height: measure the retained vertical soil height, not the sloping length of the wall. The default and formula use metres.
• Unit weight: use soil weight per unit volume, in kN/m³. A value must come from suitable geotechnical information; soil type alone does not determine it precisely.
• Friction angle: enter degrees, not radians. The calculator uses a trigonometric function in degrees.
• Base width: the simplified screening outputs use metres. Actual checks require the wall’s full cross-section and foundation dimensions.

The answer is force per metre of wall length. For example, 12 kN/m over a straight 5 m wall corresponds to 60 kN total only if the same conditions apply uniformly along its length. In US customary units, force is often reported in pounds per foot (lb/ft), height and width in feet, and soil unit weight in pounds per cubic foot (lb/ft³). Keep a consistent system throughout; 1 kN/m is approximately 68.5 lb/ft, and 1 kN/m³ is approximately 6.37 lb/ft³.

Checks a Real Wall Needs

A practical retaining-wall design considers more than the soil-force estimate. Depending on the wall and site, checks include sliding, overturning, bearing pressure and settlement, structural bending and shear, global slope stability, and drainage. Water behind the wall can create substantial hydrostatic pressure; relieving it requires a designed drainage path and maintenance, not merely an assumption that the soil drains freely.

Designers also account for surcharges and boundary conditions. A uniformly distributed surcharge on level ground can add lateral pressure; a nearby footing or concentrated load may need a different analysis. Sloping backfill, layered soils, cohesive soils, wall friction, and restricted movement may invalidate the simple Rankine expression. The appropriate earth-pressure model depends on geometry and soil behavior.

Common Misconceptions and Limits

• The ratio is not a factor of safety for a finished wall. The calculator’s resistance estimates are not based on the actual wall mass, base friction, soil strength, or design criteria.
• Drainage does not erase the need to consider water. A blocked outlet, groundwater, or poor drainage can impose water pressure in addition to earth pressure.
• More wall thickness is not automatically enough. Foundation conditions, reinforcement, wall type, and loads influence performance.
• Rounding can hide important differences. Use unrounded inputs in design calculations and apply the relevant engineering factors and load combinations.

This tool is for understanding the basic relationship between soil height, soil properties, and lateral force. It is not a construction drawing, a permit determination, or a substitute for a qualified professional’s site-specific design. Seek engineering review for tall or heavily loaded walls, unstable or sloping sites, nearby structures, groundwater, or any wall whose failure could injure people or damage property.

Frequently Asked Questions

How do you calculate pressure on a retaining wall?
For the simplified active case, calculate K_a = (1 − sin φ)/(1 + sin φ), then calculate total force per metre as ½γH²K_a. The pressure at the base is γHK_a.

Where does the soil force act on the wall?
For the triangular pressure distribution assumed here, the resultant acts H/3 above the base. Different load patterns, water, or soil conditions change the pressure diagram and the point of application.

Does this calculation include water pressure?
No. It estimates soil pressure only. Water behind a wall can add hydrostatic pressure, so groundwater and drainage must be assessed separately.

Is a sliding ratio above 1 safe?
Not necessarily. The calculator uses a generic friction assumption and omits actual wall weight, foundation properties, design load combinations, and applicable criteria. Its ratio is only a preliminary illustration.

Can I use this for a sloped backfill or a wall beside a driveway?
Not without additional analysis. Slopes and nearby traffic or structures add or alter loads, so the level-backfill, no-surcharge assumptions do not apply.

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in h | Wall height | m | 2 | 0
in g | Soil unit weight | kN/m3 | 18 | 0
in p | Soil friction angle | deg | 30 | 0
in b | Base width | m | 1.2 | 0
out force | Active soil force per metre of wall | kN/m | 0.5 * g * h^2 * (1 - sind(p)) / (1 + sind(p)) | 2
out slide | Sliding resistance ratio (simplified) | - | b * tand(30) / (0.5 * h * (1 - sind(p)) / (1 + sind(p))) | 2
out overturn | Overturning resistance ratio (simplified) | - | b^2 * 18 / (h^2 * (1 - sind(p)) / (1 + sind(p))) | 2