How do I calculate cubic yards from dimensions?

Multiply length x width x depth in feet, then divide by 27 to convert cubic feet to cubic yards. For example, a 10' x 10' area that is 4" (0.333') deep: 10 x 10 x 0.333 = 33.3 cubic feet / 27 = 1.23 cubic yards. If your measurements are in inches, divide the cubic inches result by 46,656 (the number of cubic inches in a cubic yard).

How do I convert cubic feet to cubic yards?

Divide cubic feet by 27 to get cubic yards. One cubic yard is a cube measuring 3' x 3' x 3', which equals 27 cubic feet. For example, 81 cubic feet / 27 = 3 cubic yards. This is the standard conversion used when ordering concrete, gravel, topsoil, and mulch.

What is the volume formula for a cylinder?

The volume of a cylinder is pi x radius squared x height, or pi x (diameter / 2)^2 x height. For a 12" diameter Sonotube that is 4' (48") deep: pi x 6^2 x 48 = 5,429 cubic inches = 3.14 cubic feet = 0.116 cubic yards. This formula applies to all cylindrical shapes including pipes, columns, and round tanks.

How do I calculate the volume of a cone?

The volume of a cone is one-third of a cylinder with the same base and height: 1/3 x pi x (diameter / 2)^2 x height. A cone holds exactly 33.3% of what a cylinder of the same dimensions holds. This is useful for estimating material piles (gravel, sand) and hopper volumes.

What is the difference between area and volume?

Area measures a flat (2D) surface in square units (sq ft, sq m), while volume measures 3D space in cubic units (cu ft, cu yd, cu m). Area tells you how much paint, carpet, or roofing material you need. Volume tells you how much concrete, fill dirt, or water fits in a space. A 10' x 10' floor has 100 sq ft of area; a 10' x 10' x 1' box has 100 cu ft of volume.

How do I calculate surface area for a box?

The surface area of a box (rectangular prism) is 2 x (length x width + length x height + width x height). This gives you the total area of all six faces. For a 10' x 8' x 4" slab, the surface area includes the top, bottom, and all four edges. Surface area is essential for calculating coatings, waterproofing, and insulation wrap.

How many cubic yards in a truckload?

A standard concrete truck holds 8 to 10 cubic yards. A dump truck typically carries 10 to 14 cubic yards of loose material (gravel, sand, topsoil) depending on the truck size and material weight. Most ready-mix plants have a 1 cubic yard minimum delivery, and many charge a short-load fee for orders under 3 to 5 yards.

Volume & Area Calculator — Construction Shapes

How to Use the Volume Calculator

How to Calculate Volume for Construction Projects

Volume calculations are fundamental to every construction project. Whether you are estimating material for a concrete pour, sizing a water tank, calculating fill dirt for grading, or figuring out how much insulation to blow into an attic, you need to convert real-world shapes into cubic measurements. This calculator handles the seven most common construction shapes and converts results into cubic inches, cubic feet, cubic yards, and cubic meters automatically.

The key to accurate volume estimation is choosing the right geometric shape to approximate your project. A driveway is a slab (rectangular prism). A Sonotube pier is a cylinder. A pile of gravel is roughly a cone. A gable attic space is a triangular prism. Most real-world construction shapes can be broken down into combinations of these basic forms.

Slab / Box (Rectangular Prism)

The rectangular prism is the most common shape in construction. Slabs, walls, footings, beams, and pads are all rectangular prisms. The formula is simply Length × Width × Height (Depth). For example, a 10' × 12' patio slab poured 4" thick has a volume of 120" × 144" × 4" = 69,120 cubic inches, which converts to 40 cubic feet or 1.48 cubic yards.

When calculating slabs, be careful to use consistent units. If you enter length and width in feet and depth in inches, this calculator handles the conversion automatically. The surface area result tells you the total exterior area of all six faces, which is useful for estimating paint, sealer, or waterproofing membrane.

Cylinder / Column

Cylinders are used for Sonotubes, round columns, water tanks, pipes, and well casings. The formula is π × (diameter / 2)² × height. A 12" diameter Sonotube poured 4' deep contains about 3.14 cubic feet of concrete. The surface area includes both circular end caps and the curved lateral face, which is useful for calculating form tube material or paint coverage on round columns.

Cone

Cones appear in construction as material piles (gravel, sand, topsoil), hopper bottoms, and decorative elements. The volume of a cone is exactly one-third of a cylinder with the same base and height: 1/3 × π × (diameter / 2)² × height. This means a conical pile of gravel holds only 33% as much material as a cylinder with the same diameter and height — a critical distinction when estimating delivery quantities.

Gable / Triangular Prism

Triangular prisms model gable ends, A-frame structures, ridge beams, and wedge-shaped excavations. The formula is 1/2 × base × height × length. A gable attic with a 24' wide base, 8' peak height, and 40' length contains approximately 35.6 cubic yards of space — important for insulation volume, ventilation calculations, or storage planning.

Sphere

Spheres appear less frequently in construction but are used for bollards, decorative elements, tank calculations, and underground storage vessels. The formula is 4/3 × π × (diameter / 2)³. A key property of spheres is that volume scales with the cube of the diameter — doubling the diameter increases the volume by a factor of eight.

Trapezoid Prism

Trapezoidal prisms model ditches, channel sections, retaining wall backfill, tapered foundations, and road cross-sections. The formula is 1/2 × (top width + bottom width) × height × length. When the top and bottom widths are equal, the formula reduces to a standard rectangular prism. Trapezoidal cross-sections are common in drainage and grading work where sides slope at a specified ratio.

Triangle (2D Area)

Sometimes you just need the area of a triangle, not a volume. Gable wall sheathing, diagonal cuts, and triangular footprints are all calculated with 1/2 × base × height. This calculator returns the area in square inches, square feet, and square meters. For triangular sections that have depth (making them prisms), use the Gable shape instead.

Pro Tips for Accurate Volume Estimation

Always add a waste factor to your calculated volume. For concrete, use 10% for standard pours and 15% for irregular shapes. For loose fill materials (gravel, sand), add 5–10% for settling and compaction.
When a project combines multiple shapes, calculate each shape separately and add the volumes together. A concrete stoop, for example, might be a slab (the platform) plus a trapezoidal prism (the ramp) plus cylinders (the pier footings).
Remember that 1 cubic yard equals 27 cubic feet. One cubic yard of concrete weighs about 4,000 pounds. One cubic yard of gravel weighs about 2,800 pounds depending on moisture content and material type.
Surface area is important for coating calculations. One gallon of paint covers approximately 350–400 square feet on a smooth surface. Concrete sealer coverage varies from 100–300 square feet per gallon depending on porosity.

Free Volume & Area Calculator — Construction Shapes