Retaining Wall Calculator
Check a cantilever concrete retaining wall: enter the height of soil it holds back, the stem and footing, and the soil, and see whether it overturns, slides or overloads the soil, and the bars the stem needs. Pro adds the footing bars and a PDF report.
The wall works, using 91% of what it can take (limited by sliding).
The wall in section, to scale: the soil pressure behind it, the stem and footing, and where the bars go.
Stability
| OverturningSafety factor 4.45, at least 1.5 | 34% |
| SlidingSafety factor 1.65, at least 1.5: 0.35 × 2,745 lb + 225 lb in front against 720 lb | 91% |
| Soil bearing920 psf under the toe, 1,500 psf allowed | 61% |
| The resultant in the middle third3 in off center, 8 in allowed (a sixth of the footing) | 40% |
Active soil pressure coefficient 0.333 (Rankine, friction angle 30°), the same as 40 pcf of fluid pressure: 720 lb per ft of wall. The wall, the footing and the soil over it weigh 2,745 lb per ft.
Stem
#4 at 13 in vertical bars on the backfill side, 1.5 in clear of the face, hooked into the footing, and #4 horizontal bars at 12 in.
| Stem bending16 kip-in per ft (factored) at the base | 26% |
| Stem shear0.80 kips per ft (factored); the stem takes 3.33 | 24% |
| The stem bars' hooks in the footingA standard hook needs 9.0 in; the footing has 9 in above the 3 in bottom cover | 100% |
Footing bars Pro
The toe and heel bars, their bending and shear checks, the bars along the footing, and a PDF report of the whole wall with every calculation.
- Keep water from building up behind the wall: gravel backfill against the stem and a drain at the footing, or weep holes. This calculator assumes drained soil.
Safety factor 1.5 against overturning and sliding (IBC 1807.2.3); passive pressure 150 pcf on the front of the footing, leaving out the top 1 ft. 3,000 psi concrete and grade 60 bars to ACI 318-19, with the soil pressure factored by 1.6.
Retaining wall footing sizes by height
The least concrete that works for each height of level backfill with no surcharge, in soil weighing 120 pcf with a 30° friction angle, 0.35 sliding friction, 150 pcf passive pressure and 1,500 psf allowable bearing, with the footing 1′ below the ground in front and 3,000 psi concrete. Sliding sets the width of most of these walls; firmer soil or a deeper footing makes them narrower.
| Retained height | Stem | Stem bars | Footing | Width | Toe | Heel |
|---|---|---|---|---|---|---|
| 2′ | 8 in | #4 at 13 in | 12 in | 2′ 3″ | 0′ 9″ | 0′ 10″ |
| 3′ | 8 in | #4 at 13 in | 12 in | 3′ | 1′ | 1′ 4″ |
| 4′ | 8 in | #4 at 13 in | 12 in | 4′ | 1′ 3″ | 2′ 1″ |
| 5′ | 8 in | #4 at 13 in | 12 in | 5′ 3″ | 1′ 9″ | 2′ 10″ |
| 6′ | 8 in | #4 at 13 in | 12 in | 6′ 3″ | 2′ | 3′ 7″ |
| 7′ | 8 in | #4 at 11 in | 12 in | 7′ 6″ | 2′ 6″ | 4′ 4″ |
| 8′ | 8 in | #4 at 8 in | 12 in | 8′ 6″ | 2′ 9″ | 5′ 1″ |
| 9′ | 10 in | #4 at 8 in | 12 in | 9′ 9″ | 3′ 3″ | 5′ 8″ |
| 10′ | 8 in | #5 at 6 in | 16 in | 10′ 9″ | 3′ 6″ | 6′ 7″ |
Stem bars are vertical, on the backfill side, hooked into the footing. Check your own wall above; soils vary more than these walls do.
How the calculator checks a retaining wall
A cantilever retaining wall is a concrete stem standing on a footing. The footing's toe sticks out in front and its heel runs back under the soil, so the soil's own weight on the heel helps hold the wall up. Per foot of wall:
- Soil pressure: Rankine's active pressure for the soil's friction angle and the backfill slope (or the equivalent fluid pressure from a soils report), on a vertical plane through the end of the heel, from the bottom of the footing to the ground. A surcharge adds a uniform pressure over the same height.
- Overturning: the weight of the stem, footing and soil over it, turning the wall back about the toe, must be at least 1.5 times the soil pressure turning it over (IBC 1807.2.3).
- Sliding: friction under the footing plus the passive pressure of the soil in front of it and of a key, if there is one, leaving out the top 1 ft, must be at least 1.5 times the push.
- Bearing: the soil pressure at the toe or heel, from where the weight and the push meet the bottom of the footing, must be no more than the allowable. That point must stay in the middle third of the footing, so the whole footing presses on the soil.
- Water: below the water level the soil weighs 62.4 pcf less but the water pushes with its full weight, and water under the footing pushes up, from its full height at the heel to nothing at the toe.
- Earthquakes: with SDS entered, the soil pushes harder, by 3/8 kh γ H² at 0.6 H (Seed and Whitman, kh = SDS / 2.5), and the wall and the soil on its heel shake with kh times their weight. Overturning and sliding then need a safety factor of 1.1. The stem and footing take the earthquake's part at 1.0 and the soil and water at 1.6.
- Stem: bending and shear at its base, with the soil pressure times 1.6 (ASCE 7 2.3.1), to the American Concrete Institute's ACI 318-19: vertical bars on the backfill side, spaced to keep cracks narrow, at least 0.0018 of the stem, and long enough to hook into the footing (or the key below it). Hooks are full length unless you choose to cut them by the steel needed over the steel provided (ACI 25.4.10.1).
- Block stems: concrete block with every cell grouted, by TMS 402-16 strength design: bars in the cells nearest the soil, bending with a 0.80 f′m stress block, no more steel than lets the bars yield well before the block crushes, shear 2.25 An √f′m, and dowels hooked into the concrete footing and lapped with the stem bars. The footing is concrete either way.
- Toe and heel (Pro): each bends as a cantilever off the stem. The toe is pushed up by the soil, the heel down by the soil and any surcharge on it. A key bends as a cantilever down from the footing under the passive pressure on it.
Not checked: walls braced at the top (see the basement wall calculator), settlement, and the slope of the ground as a whole. A wall over 4 ft from the bottom of the footing to the top, or one holding up a surcharge like a driveway, needs a building permit (IBC 105.2), and often an engineer's stamp.
Retaining wall questions
How wide should a retaining wall footing be?
Usually from half to the full height of the wall, measured from the bottom of the footing to the top of the soil. Loose or wet soil, sloped backfill and a surcharge all push it wider. About a third of the width goes in front of the stem and the rest behind it, where the soil on the heel helps hold the wall up.
What soil values do I use without a soils report?
IBC Table 1806.2 gives presumptive values: 1,500 psf bearing and 100 pcf passive pressure for clay and silt, 2,000 psf and 150 pcf for sand, 3,000 psf and 200 pcf for sandy gravel. Sliding friction is 0.25 for sand and 0.35 for gravel; clay resists sliding with 130 psf of cohesion instead, which this calculator doesn't count, so use 0.25 or less on clay. A friction angle of 30° and 120 pcf soil are typical for clean sand and gravel backfill.
Why does my wall slide?
Sliding sets the width of most walls. Widen the heel to put more soil on the footing, set the footing deeper so more soil sits in front of it, or add a key: a short wall of concrete under the stem that digs into the soil, so the soil in front of it pushes back. Keys are common once sliding sets the width, usually 12 in wide and 12 to 24 in deep. The calculator suggests one when it makes the footing at least a foot narrower.
Does the wall need drainage?
Yes. Water behind a wall can double the pressure on it. Put free-draining gravel against the back of the stem with a perforated drain along the footing, or weep holes through the stem, so the soil stays drained. If water can rise behind the wall anyway, enter its level and the calculator counts it.