How do you size a cantilever retaining wall footing?

A common starting point is a base width B of about 0.5H to 0.7H, footing thickness about 0.1H (12 in minimum), toe about B/3, and a stem 12 in thick at the base for walls up to roughly 10 ft. Then check overturning (FoS ≥ 2.0), sliding (FoS ≥ 1.5), resultant within the middle third, and peak bearing against the allowable. Lengthening the heel is the most efficient fix for overturning and sliding, because it adds soil weight at a long lever arm.

What load factor applies to earth pressure in ACI 318?

ACI 318-19 §5.3.8 includes lateral earth pressure H with a load factor of 1.6 where it adds to the load effect. This calculator designs the stem for 1.6 × (soil + surcharge) lateral load, and the heel and toe for 1.2 × concrete and soil weight plus 1.6 × surcharge and lateral earth pressure, with the factored bearing pressure recomputed for that combination.

Where does the stem steel go and how much is the minimum?

Main vertical stem steel goes on the backfill (tension) face; heel steel goes in the top of the footing; toe steel goes in the bottom. Minimum flexural steel follows the one-way slab rule of ACI 318-19 Table 7.6.1.1 (0.0018·Ag for Grade 60), and maximum spacing is the lesser of 3h and 18 in (§7.7.2.3). Horizontal temperature and shrinkage steel and development/splice lengths must still be detailed.

Why is the surcharge over the heel ignored for overturning and sliding?

A live surcharge can be present on the backfill (pushing the wall) without being present over the heel (holding the wall down). Standard practice counts it as a driving force but not as a stabilizing force for overturning and sliding, and includes it for peak bearing pressure, where its weight increases the demand.

Is this calculator enough to build a retaining wall?

No. It is a preliminary sizing tool. A final design needs site-specific soil parameters, drainage design, global stability, settlement, sloping or broken backfill, water and seismic loads, reinforcement detailing (development, splices, temperature steel), and review and sealing by a licensed engineer. Most jurisdictions require an engineered design and a permit for walls over about 4 ft or walls carrying a surcharge.

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Cantilever Retaining Wall Design Calculator

Preliminary design of a reinforced concrete cantilever retaining wall: Rankine active pressure with uniform surcharge, factors of safety against overturning and sliding, resultant eccentricity, and bearing pressure — then ACI 318-19 flexure for the stem, heel and toe with a trial bar size and spacing, and one-way shear checks. Level backfill, vertical back face of stem.

Units

Stem height above footing, H_sft

Footing thickness, t_fft

Toe length (front of stem to toe)ft

Heel length (back of stem to heel)ft

Stem thickness at topin

Stem thickness at basein

Soil cover over toeft

Backfill unit weight, γpcf

Backfill friction angle, φdegrees

Uniform surcharge, qpsf

Foundation soil friction angle, φ_f (μ = tan φ_f)degrees

Passive resistance at toe

Allowable bearing pressure, q_allow (0 = skip check)psf

Concrete unit weight, γ_cpcf

Concrete strength, f′_cpsi

Rebar yield strength, f_ypsi

Clear cover, stem backfill facein

Clear cover, footing (cast against earth)in

Trial bar size

Active coefficient, K_a——

Lateral force, P_a (soil + surcharge)—lb/ft

Stabilizing weight, ΣV—lb/ft

FoS overturning (≥ 2.0)——

FoS sliding (≥ 1.5)——

Eccentricity, e (limit B/6)—ft

Bearing, q_max / q_min—psf

Stem: M_u at base—kip-ft/ft

Stem: A_s required (backfill face)—in²/ft

Stem: trial vertical bars——

Heel: M_u / A_s (top steel)—in²/ft

Heel: trial bars——

Toe: M_u / A_s (bottom steel)—in²/ft

Toe: trial bars——

One-way shear, V_u/φV_c (stem · heel · toe)—≤ 1.0

Summary——

Moments are in kip-ft per ft of wall (kN·m/m in SI). Bar sizes are US inch-pound bars in both unit systems. Trial spacing is rounded down to the inch and capped at the lesser of 3h and 18 in; it is a starting point, not a detail. Horizontal temperature/shrinkage steel, development and lap lengths, the stem-to-footing dowel splice, and a shear key (if sliding governs) are not designed here.

$$ \Sigma V = W_{stem} + W_{footing} + W_{soil,heel} + W_{soil,toe}, \qquad e = \frac{B}{2} - \frac{M_r - M_o}{\Sigma V},\qquad q_{max,min} = \frac{\Sigma V}{B}\left(1 \pm \frac{6e}{B}\right) $$

$$ R_n = \frac{M_u}{\phi b d^2},\qquad \rho = \frac{0.85 f'_c}{f_y}\left(1 - \sqrt{1 - \frac{2R_n}{0.85 f'_c}}\right),\qquad A_s = \max(\rho b d,\ A_{s,min}) $$

$$ V_c = 8\lambda_s\lambda\,\rho_w^{1/3}\sqrt{f'_c}\,b d \le 5\lambda\sqrt{f'_c}\,b d,\qquad \lambda_s = \sqrt{\frac{2}{1+d/10}} \le 1 $$

H = H_s + t_f (pressure acts on the vertical plane through the heel) · M_o = P_a,soil·H/3 + P_a,q·H/2 · b = 12 in · d = thickness − cover − d_b/2 · φ = 0.90 flexure, 0.75 shear · A_s,min per ACI 318-19 Table 7.6.1.1 · V_c per Table 22.5.5.1(c), members without shear reinforcement. Surcharge over the heel is excluded from the overturning and sliding resistance and included for bearing.

Starting proportions

Typical first-trial proportions for a cantilever wall of total height H
Dimension	First trial	What to change if a check fails
Base width, B	0.5H – 0.7H	Lengthen the heel for overturning and sliding
Toe length	≈ B/3	Lengthen the toe to pull the resultant forward and cut peak bearing
Footing thickness	≈ 0.1H, 12 in minimum	Thicken if heel or toe shear fails
Stem at base	≈ 0.08H – 0.1H, 10–12 in minimum	Thicken if shear fails or steel is not tension-controlled
Stem at top	8–12 in	12 in makes placing concrete around two curtains of bars practical

Acceptance criteria used

Checks and limits in this calculator
Check	Limit	Basis
Overturning	FoS ≥ 2.0	Classical service-load practice (IBC §1807.2.3 sets 1.5 as the floor)
Sliding	FoS ≥ 1.5	IBC §1807.2.3; classical practice
Eccentricity	e ≤ B/6	Full base contact on soil
Bearing	q_max ≤ q_allow	Trapezoidal or triangular distribution
Flexure	φM_n ≥ M_u, ε_t ≥ 0.005	ACI 318-19 §21.2, §22.2
Minimum steel	0.0018A_g (Gr 60)	ACI 318-19 Table 7.6.1.1
Maximum spacing	min(3h, 18 in)	ACI 318-19 §7.7.2.3
One-way shear	V_u ≤ φV_c	ACI 318-19 Table 22.5.5.1(c), checked at the face of stem

Worked example

Example — 10-ft stem, 100 psf surcharge (the calculator defaults)

Given: H_s = 10 ft, t_f = 1.25 ft, toe 2.25 ft, heel 4.75 ft, stem 12 in top / 15 in base (B = 8.25 ft), 1 ft of soil over the toe; backfill γ = 120 pcf, φ = 32°; q = 100 psf; foundation φ_f = 28°, no passive; f′_c = 4,000 psi, f_y = 60,000 psi, #5 bars.

K_a = tan²(45 − 16) = 0.307 · H = 11.25 ft · P_a = ½(0.307)(120)(11.25²) + 0.307(100)(11.25) = 2,334 + 346 = 2,679 lb/ft

ΣV = 1,500 + 188 + 1,547 + 5,700 + 270 = 9,204 lb/ft · M_r = 45,125 ft-lb/ft · M_o = 2,334 × 3.75 + 346 × 5.625 = 10,694 ft-lb/ft · FoS_OT = 4.22 ✓ · FoS_SL = tan 28° × 9,204 / 2,679 = 1.83 ✓

For bearing, add the surcharge over the heel: ΣV = 9,679 lb/ft, e = 0.28 ft < B/6 = 1.38 ft ✓ · q_max = 1,412 psf, q_min = 935 psf

Stem: M_u = 1.6 × (1,844 × 10/3 + 307 × 10/2) = 12.29 kip-ft/ft, d = 15 − 2 − 0.31 = 12.69 in → ρbd = 0.22 in²/ft; A_s,min = 0.0018 × 12 × 15 = 0.32 in²/ft governs → #5 @ 11 in

Heel (factored 1.2D + 1.6(L+H), with the factored bearing pressure recomputed): M_u = 8.85 kip-ft/ft; toe M_u = 4.37 kip-ft/ft. Both are governed by minimum steel (#5 @ 11 in), and one-way shear runs at 0.49–0.56 of capacity. Everything passes with margin, so the next trial could shorten the heel or thin the stem.

What this calculator does not cover

Sloping or broken backfill, water pressure, seismic load. Each increases the lateral force, often a lot. A wall without working drainage (a free-draining zone plus weeps or a collector pipe) sees full hydrostatic pressure.
Global stability — a deep slip surface passing under the whole wall. Use a slope-stability program.
Settlement and tilt on compressible foundations.
Detailing: horizontal steel, development and splice lengths, the construction joint between stem and footing, shear keys, expansion and contraction joints.

References: ACI 318-19, Building Code Requirements for Structural Concrete, §5.3.8, §7.6.1.1, §7.7.2.3, §21.2, §22.2, Table 22.5.5.1. ICC, International Building Code, §1807.2 (retaining walls). Das, B.M., Principles of Foundation Engineering, retaining-wall chapters. Wight, J.K. & MacGregor, J.G., Reinforced Concrete: Mechanics and Design, cantilever retaining walls. Rankine, W.J.M. (1857), "On the Stability of Loose Earth," Phil. Trans. Royal Society 147.

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