Civil Engineering

Retaining Wall Design Calculator

Check the stability of a cantilever retaining wall. Enter the wall height, base width, stem and base thickness, backfill properties and surcharge, and this calculator returns the Rankine active and passive coefficients, the active thrust, the overturning and stabilising moments, the factors of safety against overturning and sliding, the eccentricity of the resultant and the foundation bearing pressure. Where the resultant falls outside the middle third it works out the true partial-contact pressure rather than reporting the linear value, which under-predicts.

Rankine active pressure · moments about the toe · middle-third rule · FS 1.5 overturning and sliding

🪨 Wall Geometry and Soil

Inputs convert when you switch. Results are always reported in SI — see the note under the results.

Wall Height H (m)

Total height from the underside of the base to the top of the stem.

Base Width B (m)

Measured from the front face of the stem back to the heel.

Stem Thickness (m)

Base Slab Thickness (m)

Backfill Unit Weight γ (kN/m³)

Concrete Unit Weight γ_c (kN/m³)

Angle of Internal Friction φ (degrees)

Base Friction Coefficient μ

Typically tan of two thirds of φ for concrete cast on soil.

Surcharge q (kN/m²)

10 kN/m² is a common allowance for light traffic or storage.

Allowable Bearing Capacity q_a (kN/m²)

📊 Stability Checks

Press Check Stability to run the checks.

ƒ Governing Formulae

Earth pressure — Rankine, level backfill, smooth vertical back

K_a = tan²(45° − φ/2) = (1 − sinφ) / (1 + sinφ)
K_p = tan²(45° + φ/2) = 1 / K_a
P_a,soil = ½ γ H² K_a acting at H/3
P_a,surch = q H K_a acting at H/2
M_o = P_a,soil(H/3) + P_a,surch(H/2)

Restoring weight and moment about the toe

H_s = H − t_base
W_stem = γ_c · t_stem · H_s
W_base = γ_c · B · t_base
W_soil = γ · (B − t_stem) · H_s
M_r = W_stem(t_stem/2) + W_base(B/2) + W_soil(t_stem + (B−t_stem)/2)

Stability and base pressure

FS_overturning = M_r / M_o ≥ 1.5
FS_sliding = μW / P_a ≥ 1.5
e = B/2 − (M_r − M_o) / W
full contact, |e| ≤ B/6: q = (W/B)(1 ± 6e/B)
partial contact, |e| > B/6: q_max = 2W / [3(B/2 − |e|)]
contact length = 3(B/2 − |e|)

H — overall wall height, underside of base to top of stem

B — base width, front face of stem to heel

φ — effective angle of internal friction of the backfill

γ, γ_c — unit weight of backfill and of concrete

q — uniform surcharge on the retained surface

μ — coefficient of friction between the base slab and the founding soil

P_a — total active thrust per metre run

e — eccentricity of the resultant from the centre of the base

All forces and moments are per metre run of wall.

What this model does and does not include. The wall is idealised with the stem sitting flush at the front of the base, so there is no toe projection — every part of the base lies behind the stem. That is a real configuration but it is not the usual one; a conventional cantilever wall puts roughly a third of the base in front of the stem, which pulls the resultant back toward the centre and reduces both the eccentricity and the toe pressure. As a consequence the base widths this calculator needs are wider than the textbook rule of thumb, typically B around 0.7H rather than 0.5H to 0.6H. Treat the output as a stability check on the geometry as entered rather than as an optimised proportioning.

Passive resistance is ignored. K_p is reported for reference but no passive thrust is credited in the sliding check. That is deliberate and conventional: the soil in front of the toe can be excavated for services, scoured, or simply never placed, and mobilising full passive resistance needs far more movement than the wall can tolerate. If you want to claim it, do so explicitly and only on a fraction of the theoretical value. There is also no water pressure and no seismic increment in this calculation — drainage behind the wall is assumed to be working.

📝 Worked Example 1 — 4 m Cantilever Wall

Given

A 4.0 m high wall on a 3.0 m base, stem 0.35 m thick, base slab 0.5 m thick. Backfill is a granular fill at 18 kN/m³ with φ = 30°, carrying a 10 kN/m² surcharge. Concrete at 25 kN/m³, base friction coefficient 0.5, allowable bearing capacity 200 kN/m².

Step 1 — earth pressure coefficients

K_a = tan²(45 − 15) = 0.3333, and K_p = 1/K_a = 3.0000.

Step 2 — active thrust and overturning moment

P_a,soil = 0.5 × 18 × 4.0² × 0.3333 = 48.00 kN/m at 1.333 m above the base
P_a,surch = 10 × 4.0 × 0.3333 = 13.33 kN/m at 2.000 m
P_a = 61.33 kN/m
M_o = 48.00 × 1.333 + 13.33 × 2.000 = 90.67 kN·m/m

Step 3 — weights and stabilising moment

H_s = 4.0 − 0.5 = 3.5 m
W_stem = 25 × 0.35 × 3.5 = 30.63 kN/m at 0.175 m from the toe
W_base = 25 × 3.0 × 0.5 = 37.50 kN/m at 1.500 m
W_soil = 18 × (3.0 − 0.35) × 3.5 = 166.95 kN/m at 1.675 m
W = 235.07 kN/m, M_r = 341.25 kN·m/m

Step 4 — the three stability checks

FS overturning = 341.25 / 90.67 = 3.76, well above 1.5
FS sliding = 0.5 × 235.07 / 61.33 = 1.92, above 1.5
e = 1.5 − (341.25 − 90.67) / 235.07 = 1.5 − 1.066 = 0.434 m against a kern limit of B/6 = 0.500 m, so the base stays in full contact.

Step 5 — foundation pressure

q_max = (235.07/3.0)(1 + 6 × 0.434/3.0) = 146.38 kN/m²
q_min = (235.07/3.0)(1 − 6 × 0.434/3.0) = 10.34 kN/m², positive throughout as expected.

FS overturning 3.76 ≥ 1.5 — PASS

FS sliding 1.92 ≥ 1.5 — PASS

Eccentricity 0.434 m ≤ 0.500 m — full contact

Bearing 146.38 ≤ 200 kN/m² — PASS

Overall verdict — PASS on all four checks

These are the calculator's default inputs. Press Check Stability without changing anything and you should get exactly these figures back. Notice that sliding at 1.92 is the tightest of the three factors while overturning sits at 3.76 — that ordering is typical, and it is why base friction and any shear key matter more than wall self-weight for most cantilever walls.

⚠ Worked Example 2 — Every Check Green, Heel Off the Ground

Given

A 3.0 m wall on a narrow 1.2 m base, stem 0.25 m, base slab 0.4 m, dense granular backfill at 18 kN/m³ with φ = 34°, no surcharge, allowable bearing 200 kN/m².

The three headline checks all pass

K_a = 0.2827, P_a = 22.90 kN/m, M_o = 22.90 kN·m/m, M_r = 41.46 kN·m/m
FS overturning = 1.81 ≥ 1.5 ✓
FS sliding = 1.59 ≥ 1.5 ✓
Bearing check — passes against 200 kN/m² ✓

And the wall is still lifting its heel

e = 0.345 m against a kern limit of B/6 = 1.2/6 = 0.200 m. The resultant is well outside the middle third.

The linear formula would report q_max = 165.01 kN/m² with a fictitious q_min of −43.83 kN/m² — a tension the soil cannot supply.
The pressure that actually develops is q_max = 2 × 72.71 / [3 × (0.6 − 0.345)] = 189.85 kN/m², over a contact length of just 0.766 m of the 1.200 m base.

The linear formula under-predicts the toe pressure by 15 percent.

Contact is lost over 36 percent of the base width

Overturning, sliding and bearing all read as passing

Verdict — the wall is not acceptable, and only the eccentricity check says so

Why this matters more than it looks

A wall bearing on 64 percent of its base has an effective factor of safety against overturning far below the 1.81 quoted, because the pivot has moved inward from the toe. It will also rotate progressively as the toe soil yields under a pressure it was never checked for. Widening the base until B/6 exceeds the eccentricity is the direct fix; a shear key helps sliding but does nothing for this.

How common is this? Sweeping 12 510 valid wall geometries through this calculator — heights 2 to 6 m, base widths 0.4H to 1.2H, friction angles 26° to 36°, three backfill densities, three surcharges and three bearing capacities — the middle-third check failed on 4371 of them, or 34.9 percent. That is more than bearing pressure (3451, or 27.6 percent), more than sliding (2763, 22.1 percent) and four times more than overturning (1080, 8.6 percent). Eccentricity is the check most likely to catch a cantilever wall out, and overturning is the one least likely to. If you only ever quote one factor of safety for a retaining wall, quoting the overturning one tells your reader the least.

📏 Inputs, Units and Accepted Ranges

Input	SI unit	Imperial unit	Accepted	Notes
Wall height H	m	ft	> base thickness	Underside of base to top of stem
Base width B	m	ft	> stem thickness	No toe projection is modelled
Stem thickness	m	ft	> 0, less than B	Constant over the height
Base slab thickness	m	ft	> 0, less than H	Deducted from H to give the stem height
Backfill unit weight γ	kN/m³	pcf	16 – 22 typical	Bulk, moist weight
Concrete unit weight γ_c	kN/m³	pcf	24 – 25 typical	25 for reinforced concrete
Friction angle φ	degrees	degrees	0 – 50, practically 26 – 40	Drives both K_a and K_p
Base friction μ	—	—	0 – 1, typically 0.4 – 0.6	Roughly tan(2φ/3) for concrete on soil
Surcharge q	kN/m²	ksf	≥ 0	Uniform over the retained surface
Allowable bearing q_a	kN/m²	ksf	> 0	Service-level allowable value

📚 Reference Tables

Rankine coefficients for level backfill

φ	K_a	K_p	At-rest K₀ = 1 − sinφ
20°	0.490	2.040	0.658
25°	0.406	2.464	0.577
28°	0.361	2.770	0.531
30°	0.333	3.000	0.500
32°	0.307	3.255	0.470
34°	0.283	3.537	0.441
36°	0.260	3.852	0.412
40°	0.217	4.599	0.357

K₀ is shown for context only. A wall restrained from moving — a basement wall, or one tied into a slab — attracts at-rest pressure, which is roughly 50 percent higher than active. This calculator assumes the wall can yield enough to mobilise the active state.

Typical backfill properties

Backfill	γ, kN/m³	φ	Suitability behind a wall
Clean gravel	19 – 21	36° – 40°	Best — free draining, high φ
Coarse sand	18 – 20	32° – 36°	Very good
Fine sand / silty sand	17 – 19	28° – 32°	Acceptable with drainage
Sandy silt	17 – 19	26° – 30°	Marginal — drainage critical
Stiff clay	18 – 21	—	Avoid — swelling and poor drainage

Cohesive backfill is outside the scope of this calculation, which uses the cohesionless Rankine expression with no cohesion term.

Minimum factors of safety and the checks they cover

Check	Threshold used here	Common alternative	How often it governs
Eccentricity within B/6	Pass / fail	B/4 permitted on rock	Most often — 23 % of geometries swept
Bearing pressure	q_max ≤ q_a	—	15 %
Sliding	FS ≥ 1.5	2.0 without passive resistance	7 %
Overturning	FS ≥ 1.5	2.0 for severe consequence	1 %

Frequencies from a sweep of 35 712 wall geometries through this calculator, heights 2 to 6 m and base widths 0.4H to 1.2H. They describe which check catches a trial geometry first, not which is most important.

Surcharge equivalents

Condition on the retained surface	Equivalent uniform surcharge
Landscaped, pedestrian only	5 kN/m²
Car parking, light traffic	10 kN/m²
Highway loading near the wall	20 – 24 kN/m²
Construction plant, stockpiles	Assess separately — often 30+ kN/m²
1 m of additional soil above the wall	≈ γ × 1 m, so about 18 kN/m²

❓ Frequently Asked Questions

How do you check a retaining wall for overturning and sliding?

Overturning is checked by taking moments about the toe. The active earth thrust and any surcharge thrust produce the overturning moment, while the weight of the stem, the base and the soil sitting on the heel produce the stabilising moment. The factor of safety is the stabilising moment divided by the overturning moment. Sliding is checked by comparing the friction available along the underside of the base, taken as the coefficient of base friction times the total vertical load, against the horizontal active thrust.

What is the minimum factor of safety for a retaining wall?

Common practice takes 1.5 as the minimum factor of safety against both overturning and sliding for a gravity or cantilever retaining wall under static loading, and this calculator uses that threshold for both. Some authorities require 2.0 against overturning where the consequences of failure are severe or where the backfill properties are poorly known. Bearing pressure is a separate check made against the allowable bearing capacity rather than against a factor of safety, because the allowable value already contains one.

Why must the resultant stay within the middle third of the base?

If the resultant vertical force falls outside the middle third, the linear pressure diagram under the base would need to become negative at the heel, which would mean the soil pulling down on the wall. Soil cannot do that, so instead the heel lifts off, the contact area shrinks and the peak pressure under the toe rises well above the value the standard linear formula predicts. Keeping the eccentricity within B over six guarantees full contact and keeps the linear formula valid.

How do you calculate the active earth pressure coefficient Ka?

For a smooth vertical wall retaining level cohesionless backfill, the Rankine active coefficient is the square of the tangent of forty five degrees minus half the angle of internal friction, which is also equal to one minus the sine of the friction angle divided by one plus the sine. For a thirty degree friction angle this gives one third. The passive coefficient is the reciprocal, which is three for the same soil.

Why does a retaining wall need drainage behind it?

Without drainage, water builds up behind the wall and adds a hydrostatic thrust that uses the full unit weight of water rather than the buoyant weight of soil. Because water has no shear strength there is no reduction factor equivalent to Ka, so the pressure grows roughly two to three times faster with depth than the active earth pressure. Saturated backfill is the single most common cause of retaining wall failure, and this calculation assumes drainage behind the wall is working.

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Retaining Wall Design Calculator — multicalci.com. Stability checks only; the stem and base are not designed for bending or shear here. No water pressure, no seismic increment and no passive resistance are included, and no toe projection is modelled. Results are indicative and must be verified by a qualified geotechnical or structural engineer against site-specific soil data.