🚧 Retaining Wall: Earth Pressure

Written and maintained by the PhDino author · Last reviewed 21 September 2026 · Checked against 2 independent reference calculations · how PhDino checks its numbers

Related standards: ACI 318

The lateral thrust a retained soil mass exerts on a wall, and the overturning moment it creates.

A retaining wall holds back soil that would otherwise slump to its natural angle of repose. That soil exerts lateral (sideways) pressure on the wall, which increases linearly with depth — the same way water pressure increases with depth in a dam. Rankine's theory gives the active earth pressure coefficient, which relates the vertical soil stress at any depth to the resulting horizontal pressure on the wall, assuming the wall is free to move slightly away from the soil (the "active" state).

That triangular pressure distribution resultant acts at one-third of the wall height from the base — which is why overturning moment (resultant force times its lever arm to the base) is central to checking whether the wall's footing is wide enough to resist tipping over.

Key formula

Ka = (1 − sinφ) / (1 + sinφ)
P = 0.5 × Ka × γ × H²
Overturning moment = P × H/3

Variables

φ

friction angle of the retained soil

γ

soil unit weight

H

wall height

How to use the Retaining Wall calculator

Use this to find the sideways force that retained soil puts on a wall, how large a turning moment that force creates about the base, and a starting base width. It is the loading half of a retaining wall design: what the wall has to resist before you can decide how big it must be.

It uses Rankine's active earth pressure for a level backfill and a wall free to move a little, which is the normal case for a cantilever or gravity wall. It does not check sliding, bearing or the strength of the wall itself, and it assumes the backfill is drained.

Wall Height (ft)

The height of the retained soil in feet, measured from the base of the wall to the top of the backfill. This is the most influential input because it appears squared in the force and cubed in the moment.

Soil Friction Angle (degrees)

The friction angle of the backfill in degrees: 28° to 34° for granular fill, less for clay. Use clean, free-draining granular backfill behind the wall wherever you can, so a well-defined friction angle applies.

Soil Unit Weight (pcf)

The unit weight of the backfill in lb/ft³. Compacted granular fill is about 110 to 130.

Worked example: a 6-foot wall in sand

A 6 ft cantilever wall retains level, free-draining sand with a friction angle of 32° and a unit weight of 120 lb/ft³. What does the soil push with, and what turning moment does it create?

Worked by hand:

1. Active pressure coefficient. K_a = (1 − sin φ) ÷ (1 + sin φ) = (1 − sin 32°) ÷ (1 + sin 32°) = 0.307.
2. Total thrust per foot of wall. P = ½ × K_a × γ × H² = 0.5 × 0.307 × 120 × 6² = 664 lb per foot of wall.
3. Where it acts. Pressure grows linearly with depth, so the resultant sits one third of the way up: 6 ÷ 3 = 2 ft above the base.
4. Overturning moment. M = P × H ÷ 3 = 664 × 2 = 1,327 ft-lb per foot of wall.
5. Starting base width. The H/2 rule of thumb gives 6 ÷ 2 = 3.0 ft.

The soil pushes with about 664 lb per foot of wall and tries to overturn it with about 1,327 ft-lb per foot. The wall's own weight and the soil resting on its heel must resist that moment with a safety factor commonly taken as at least 2, and resist sliding with a factor of at least 1.5. Make the wall 8 ft instead of 6 and the thrust rises to about 1,180 lb per foot, a jump of nearly 80 percent for a third more height.

Reading the result: why drainage and height dominate

Two things control a retaining wall more than anything else. The first is height: the thrust grows with the square of it and the overturning moment with the cube, so a modest increase in height is a large increase in demand. The second is water, which the drained, dry-soil assumption of this calculator leaves out.

Water behind a wall adds a hydrostatic thrust on top of the soil's. If the same 6 ft wall held saturated backfill, the water alone would push with 1,123 lb per foot, and together with the buoyant soil the total would be about 1,442 lb per foot, roughly 2.2 times the dry figure. Most retaining wall failures trace back to water that had nowhere to go.

• Provide drainage: free-draining gravel behind the wall, a perforated drain pipe at the base that daylights to a safe outlet, and weep holes where they suit the wall type.
• Surcharges add load that this calculator omits: a driveway, a slope rising behind the wall, a building or a parked vehicle within a wall height or two of the top.
• Many jurisdictions require a permit and an engineer's design for walls over about 4 ft, measured from the bottom of the footing to the top of the wall, or wherever the wall carries a surcharge. Check locally before building.
• Rankine's active pressure assumes the wall can yield slightly. A wall that cannot move, such as a basement wall braced by the floors, sees higher at-rest pressure.

Notes & limitations

• This is the active pressure case, which applies once a wall is free to deflect slightly. A wall that cannot move at all (rigid, braced) experiences at-rest pressure instead, which is higher; a wall being actively pushed into the soil experiences passive pressure, higher still.
• A complete retaining wall design also checks sliding and overall (global) stability, and sizes the footing width from the overturning/resisting moment balance — this calculator only computes the earth pressure loading side of that check.
• The base width the calculator prints is only the H/2 rule of thumb, a starting proportion (cantilever walls commonly land between roughly 0.4H and 0.7H). It is not derived from a stability check, and it does not use the soil bearing pressure.

Common mistakes

• Ignoring water. A wall designed for dry soil and backed by clay that holds water can see more than double the load.
• Treating the base-width output as a design. The H/2 rule of thumb is a starting proportion, not the result of a sliding, overturning and bearing check.
• Omitting a surcharge such as a driveway or a slope behind the wall, which can add as much load as the soil itself.
• Using the friction angle of the soil in place, not of the backfill. The pressure comes from the fill you put behind the wall, and clay backfill is much worse than the granular fill assumed here.
• Checking overturning only. A wall can also slide on its base or overload the soil under its toe, and each has its own factor of safety.
• Scaling a small wall up. Because the moment grows with the cube of the height, a design that works at 3 ft can be far too light at 6 ft.

Frequently asked questions

Papers worth reading

Compaction-induced earth pressures under K0-conditions Duncan, J. M. & Seed, R. B. (1986), Journal of Geotechnical Engineering (ASCE). Shows how compacting backfill against a wall can raise the lateral pressure it has to resist above the simple textbook value.