Footing Concrete Calculation: Box and Trapezoidal Footing Volume in m³ and cft

An isolated footing 1.8 m long and 1.5 m wide, with a 300 mm rectangular base and a 300 mm sloped top, holds about 1.19 m³ (42.1 cft) of concrete. The 100 mm PCC bed under it adds another 0.34 m³ (12 cft).

Footing concrete calculation is a sum of simple shapes. A box footing is one block: length × width × depth. A trapezoidal footing, the sloped kind seen under most house columns, is a block with a sloping frustum on top, and the slope is where most quantities go wrong. This guide gives the formula for each part, works one footing in metres and one in feet, and shows the shortcut that overstates the slope by about a sixth.

There are no rupee figures on this page. Rates change every season; the volume of a footing does not.

What is the formula for footing concrete calculation?

Footing concrete = the rectangular base + the sloped or stepped part above it, worked out for one footing and multiplied by the number of identical footings. The PCC bed under the footing is a separate item and is added after.

• Box footing: V = L × B × D, where L and B are the plan sizes and D is the depth.
• Trapezoidal footing: V = (L × B × D1) + the frustum of depth D2 on top, worked out with the prismoidal formula in the next section.
• Stepped footing: add up each step as its own box.
• PCC bed: V = (L + 2 × offset) × (B + 2 × offset) × bed thickness.

Keep every dimension in metres for an answer in cubic metres (m³), or in feet for cubic feet (cft). One cubic metre is 35.31 cft.

Reading the figure

• 1: the column. Its concrete is not part of the footing.
• 2: the sloped part, a frustum of depth D2. Its top is the column size plus a small offset on every side.
• 3: the rectangular base of depth D1, the full plan size of the footing.
• 4: the PCC bed, wider than the footing on every side.

The line between 1 and 2 matters. IS 1200 (Part 2), the Indian Standard for measuring concrete work, says in clause 4.2.2.1 that columns are measured from the top of the column base. So the footing stops at the top of its slope and the column starts there. Count the stub inside the footing once, in the footing, and begin the column quantity above it.

How do you calculate the volume of a trapezoidal footing?

Use the prismoidal formula for the sloped part:

V = D2 ÷ 6 × (A1 + 4 × Am + A2)

A1 is the area at the bottom of the slope (L × B). A2 is the area at the top (the column size plus the offset, both ways). Am is the area halfway up, found by averaging the lengths and the widths separately and multiplying them. It is the formula for any solid with two flat, parallel rectangular faces joined by straight sides, so it is exact for a sloped footing.

Many site notebooks use a second version: V = D2 ÷ 3 × (A1 + A2 + √(A1 × A2)). That one is exact only when the top and bottom have the same shape, a square on a square for example. For an ordinary footing the two agree within a fraction of a per cent. On a long footing with a square top, say 3.0 × 1.2 m under a 450 × 450 mm top, the square-root version comes out about 2% low.

The shortcut to avoid is the plain average: D2 × (A1 + A2) ÷ 2. The area of a sloped footing shrinks fast as the slope rises, so the true average sits well below the midpoint of the two end areas, and this shortcut always overstates. In the worked footing below it gives 0.45 m³ for a slope that holds 0.38 m³, about 16% too much.

Worked example: one isolated footing in m³ and cft

Take a column 450 × 300 mm on a footing 1.8 × 1.5 m. The base is 300 mm deep, the slope rises another 300 mm, and the top of the slope stands 75 mm out from the column on each side. So the top is 0.60 × 0.45 m. The PCC bed is 100 mm thick and 100 mm wider than the footing on every side. These are illustration sizes; the real ones come from your structural drawing.

Two checks are worth doing on any drawing. The edge of this footing is 300 mm thick, and IS 456 clause 34.1.2 asks for at least 150 mm at the edge of a footing on soil, so the slope cannot run down to nothing. And a plain box of the same plan, 600 mm deep all through, would hold 1.62 m³. The slope saves about 0.43 m³ on every footing, which is why designers use it.

IS 1200 (Part 2) clause 2.4.3 works cubic contents to the nearest 0.01 m³, so 1.1925 is written 1.19 in a bill of quantities.

How thick is the PCC bed under a footing?

Most house drawings in India show a PCC bed 75 to 100 mm thick, projecting 100 to 150 mm beyond the footing on each side. That is drawing practice; neither IS 456 nor IS 1080 fixes a bed thickness. The bed gives a clean, level surface to set the steel and cover blocks on, so the bottom bars do not sit on mud.

The bed is plain concrete, usually 1:4:8 or 1:3:6, and it is billed on its own line because its mix and its rate differ from the footing above. The PCC vs RCC guide explains which mix goes where in a house.

Do not confuse the bed with a plain concrete footing. A footing with no steel at all is a different design, and IS 1080 clause 4.8 limits it: the load may spread no wider than 1 vertical to 1 horizontal through cement concrete, and the edge must be at least 150 mm thick. If the footing is too shallow for that spread, it has to be reinforced.

Doing the same sum in feet

Plenty of house sites measure in feet, so here is a footing worked entirely in feet. Footing 6 ft × 5 ft, base 1 ft deep, slope 1 ft high, column 18 × 12 in, offset 3 in each side. The top of the slope is therefore 2 ft × 1.5 ft.

• Base = 6 × 5 × 1 = 30 cft.
• A1 = 6 × 5 = 30 sq ft. A2 = 2 × 1.5 = 3 sq ft.
• Am = ((6 + 2) ÷ 2) × ((5 + 1.5) ÷ 2) = 4 × 3.25 = 13 sq ft.
• Slope = 1 ÷ 6 × (30 + 4 × 13 + 3) = 85 ÷ 6 = 14.2 cft.

Total: about 44.2 cft, or 1.25 m³, for one footing. A 4 in PCC bed with 4 in projection all round is 6.67 × 5.67 × 0.333 = 12.6 cft. To turn cft into m³, divide by 35.31.

How much cement, sand and aggregate does a footing need?

Multiply the wet volume by 1.54 to get the loose dry material, then split it by the mix. The building material calculation guide explains the 1.54 factor and why one 50 kg bag counts as 0.0347 m³.

First decide the grade, because a footing is not mild exposure. IS 456 Table 3 puts concrete “in contact or buried under non-aggressive soil” in the moderate class, and Table 5 then asks reinforced concrete for at least M25, 300 kg of cement per m³ and a water-cement ratio no higher than 0.50. IS 456 clause 9.3 allows nominal mixes only up to M20, so an M25 footing needs a designed mix with its own cement figure. The code floor still lets you check an order: 1.19 m³ × 300 kg is about 358 kg, a little over 7 bags.

Some small house drawings still call for M20 nominal mix in the footings. If yours does, ask the engineer about it. For a drawing that does specify 1 : 1.5 : 3, the worked footing takes:

Order whole bags and add the site allowance from the guide to wastage of materials in construction.

For a whole house the concrete is large enough to plan the mixing properly. Compare concrete mixer models and prices before the excavation is finished.

How much concrete goes into common footing sizes?

This table is for checking a contractor’s figure, not for design. Every row is a square footing under a 300 × 300 mm column, with the top of the slope 75 mm out from the column on each side (450 × 450 mm) and a 100 mm PCC bed projecting 100 mm all round. The depths are typical of house drawings; yours may differ.

Multiply by the number of footings of each type on the drawing. A house with nine footings like the worked example needs about 10.7 m³ (379 cft) of footing concrete and 3.1 m³ of PCC, which is several mixer loads, not one.

Why does my footing quantity not match the contractor’s?

When two careful people get different footing totals, it is usually one of these.

• The slope was averaged. D2 × (A1 + A2) ÷ 2 overstates the sloped part, by about 0.06 m³ on a 1.5 m footing and 0.29 m³ on a 2.4 m one in the table above. Across a house it adds up to a few bags.
• The column stub was counted twice. The concrete inside the footing belongs to the footing. The column starts at the top of the slope (IS 1200 Part 2, clause 4.2.2.1).
• PCC was folded into the footing. They are different mixes on different lines. Add both before comparing totals.
• Steel was deducted. IS 1200 (Part 2) clause 4.1.8 makes no deduction for the volume taken by reinforcement, so neither should you.
• Over-excavation was poured as concrete. The measured quantity is the footing as drawn. Concrete that fills an over-dug pit is a site loss, not a measured item, and it is a good reason to check the pit before the pour.
• A stepped footing was treated as sloped. Steps are boxes. A 1.8 × 1.5 × 0.3 m base with a 1.2 × 0.9 × 0.3 m step holds 1.13 m³, close to the sloped version but worked differently.

Steel, shuttering and cover for the footing

Concrete is one line of the footing’s quantity sheet. The bottom mesh and the column starter bars are taken off bar by bar in a bar bending schedule. IS 456 clause 26.4.2.2 sets the minimum cover in footings at 50 mm, and the spacers that hold it are sized in the guide to cover block size for slab, beam, column and footing.

The formwork for a footing is only its vertical sides. A sloped top of up to 30° is normally finished by hand with a stiff mix, with no shutter on the slope. How those side areas are measured is covered in shuttering area calculation, which uses the same footing shapes as this page.

Digging and pouring the footings

Footing pits for a house are usually dug with a backhoe loader, then trimmed by hand to the drawing level. The JCB 3DX and the JCB 2DX are the backhoes Indian buyers ask about most, and the full range is under backhoe loaders.

At 10 to 15 m³ for a small house, footing concrete is often mixed on site. Self-loading mixers such as the Tarle SLM 2200 and the CONMAT CSLM 2800 load, mix and carry the concrete to the pit in one machine. Ask the dealer for the output per batch before you plan how many footings one load will fill. Where a designed M25 mix is needed, ready-mixed concrete from a plant is often the simpler route.

The footings in the cost of a house

Once each footing type is measured, the footings become one item of the substructure estimate, next to the PCC, the excavation and the plinth beam. The house construction cost calculator shows how those items build up a full estimate. The stair above uses the same method, in staircase concrete calculation, and more estimating guides sit under construction cost. When the pits are marked out, browse concrete mixers and talk to a dealer near your site.

Prices, specifications and features are indicative, vary by variant, location and date, and should always be confirmed with the official OEM or authorised dealer before any purchase decision. DesiMachines is not liable for decisions taken on the basis of information that may have changed after publication.

Code references: IS 456 : 2000 (plain and reinforced concrete, code of practice), clause 9.3 (nominal mix up to M20), Table 3 (concrete buried under non-aggressive soil is moderate exposure), Table 5 (M25, 300 kg/m³ and 0.50 for reinforced concrete in moderate exposure), clause 26.4.2.2 (50 mm cover in footings) and clause 34.1.2 (footing edge at least 150 mm on soil); IS 1200 (Part 2) : 1974 (method of measurement, concrete works, reaffirmed 2022), clauses 2.4.3, 4.1.8 and 4.2.2.1; IS 1080 : 1985 (shallow foundations in soils), clause 4.8. The worked examples are illustrations; your structural drawing decides the footing sizes, the grade and the final quantity.