Footing Concrete Volume Calculation (Rectangular, Sloped and PCC Bed)

Short answer: an isolated sloped footing is calculated in two parts. The bottom rectangular block = L × B × D. The sloped (trapezoidal) top part = h/6 × (A₁ + A₂ + 4A_m), where A₁ is the bottom area, A₂ the top area and A_m the area at mid-height. Add the PCC bed (usually 75–150 mm thick, projecting beyond the footing) as a separate item.

In the worked example below, a 2.4 m × 1.8 m sloped footing works out to 1.64 m³ of RCC plus 0.57 m³ of PCC.

Parts of an isolated footing

• PCC bed (lean concrete): M7.5 (1:4:8) or M10 (1:3:6), commonly 100 mm thick, projecting about 100–150 mm beyond the footing on all sides. It gives a clean, level base for reinforcement and shuttering.
• Rectangular block: the constant-depth bottom portion of the footing (the "edge depth").
• Sloped portion: a frustum-like shape rising from the full base to a small flat top just bigger than the column, usually with an offset of about 50–75 mm around the column for placing column shuttering.
• Column stub: from the top of footing to plinth, measured with columns, not with the footing.

IS 456 requires the thickness at the edge of a footing on soil to be not less than 150 mm. For a plain rectangular (block) footing, there is no sloped part, and the volume is simply L × B × D. A stepped footing is the sum of its blocks. For the choice between isolated, combined, raft and pile foundations see types of foundations.

Formulas

Here L × B is the base, a × b the top of the slope, and h₂ the height of the sloped part (total depth minus edge depth). Note that A_m is the area of the section at mid-height, not the average of A₁ and A₂.

Worked example: one sloped isolated footing

Data: column 400 mm × 300 mm; base L × B = 2.4 m × 1.8 m; edge depth h₁ = 250 mm; total depth at column face = 550 mm; offset around column at top = 75 mm; PCC 100 mm thick with 150 mm projection; concrete M20 for footing, 1:4:8 for PCC.

Step 1: Rectangular block

V₁ = 2.4 × 1.8 × 0.25 = 1.080 m³

Step 2: Dimensions of the sloped part

• Top of slope: a = 0.40 + 2 × 0.075 = 0.55 m; b = 0.30 + 2 × 0.075 = 0.45 m
• Height of slope h₂ = 0.55 − 0.25 = 0.30 m
• A₁ = 2.4 × 1.8 = 4.320 m²
• A₂ = 0.55 × 0.45 = 0.2475 m²
• A_m = ((2.4 + 0.55)/2) × ((1.8 + 0.45)/2) = 1.475 × 1.125 = 1.6594 m²

Step 3: Prismoidal formula

V₂ = 0.30/6 × (4.320 + 0.2475 + 4 × 1.6594) = 0.05 × (4.320 + 0.2475 + 6.6375) = 0.05 × 11.205 = 0.560 m³

Check with the frustum formula: 0.30/3 × (4.320 + 0.2475 + √(4.320 × 0.2475)) = 0.1 × (4.5675 + 1.0340) = 0.560 m³. The two agree to within 0.02% here.

Step 4: Total RCC in one footing

V = 1.080 + 0.560 = 1.640 m³

Step 5: PCC bed

V₃ = (2.4 + 2 × 0.15) × (1.8 + 2 × 0.15) × 0.10 = 2.7 × 2.1 × 0.10 = 0.567 m³

Step 6: For 12 identical footings

Step 7: Materials (dry volume factor 1.54, no wastage added)

• M20 (1:1.5:3) for 19.68 m³: dry volume 30.31 m³ → cement 158.7 bags, sand 8.27 m³, aggregate 16.53 m³
• 1:4:8 PCC for 6.80 m³: dry volume 10.48 m³ → cement 23.2 bags, sand 3.22 m³, aggregate (40 mm) 6.45 m³

Add 2–3% wastage before ordering, so roughly 163 bags for the footings and 24 bags for the PCC. The material figures use the standard dry-volume method (cement = dry volume × 1/sum of ratio × 1440 kg/m³), and the RCC estimator will do the whole set of footings for you.

The common error: averaging the two areas

Many people take the sloped part as h₂ × (A₁ + A₂)/2. For our footing that gives 0.30 × (4.320 + 0.2475)/2 = 0.685 m³ instead of 0.560 m³, an overestimate of about 22% on the sloped part. The end-area average only works when the sides are parallel; for a footing that tapers to a small top, it always overestimates.

Earthwork and shuttering go with it

Excavation is normally taken to the PCC size plus working space, to the bottom of the PCC; see how to calculate earthwork quantity. Shuttering is needed for the vertical sides of the rectangular block (perimeter × edge depth = 2 × (2.4 + 1.8) × 0.25 = 2.1 m² per footing). The sloped faces are usually finished by hand without top shuttering if the slope is gentle; very steep slopes need top formwork.

Site tips

• Confirm the footing size from the structural drawing; sizes depend on load and safe bearing capacity, not on thumb rules.
• Check the slope can be held. As a practical guide (not a code rule), slopes flatter than about 1 vertical : 2 horizontal can be finished by hand, while steeper ones need top formwork. In our example the steepest face is on the short side: 0.30 m rise over (1.8 − 0.45)/2 = 0.675 m, about 1 : 2.25, so it can be hand-finished.
• Measure PCC and RCC separately; they are different items with different rates in the BOQ.
• Keep the edge depth at least 150 mm and maintain clear cover to the bottom bars as per the drawing.
• Do not include the column stub in the footing volume; take it with columns from top of footing.