Volume Calculator
Calculate volume for any 3D shape — rectangular boxes, cylinders, cones, spheres, and more. Get results in cubic feet, cubic yards, and gallons for construction and material ordering.
Enter your values above to see the results.
Tips & Notes
- ✓All dimensions must be in the same unit. If length is in metres, all other dimensions must also be in metres. volume is then in m³.
- ✓Volume unit is the cube of your input unit: metres → m³, feet → ft³, centimetres → cm³.
- ✓Radius is half the diameter. Entering the full diameter in the radius field makes the volume 8× too large.
- ✓For cylinders and cones, height must be the perpendicular height. not the slant length.
- ✓Surface area (unit²) and volume (unit³) are different measurements. do not confuse them.
- ✓For liquid containers, 1 litre = 1,000 cm³. Convert units to centimetres first for litre results.
Common Mistakes
- ✗Multiplying Length × Width × Depth with depth in inches rather than feet — a 4-inch slab entered as 4 rather than 0.333 produces a volume 12 times too large.
- ✗Confusing cubic yards with square yards — square yards measure area (flooring, sod), cubic yards measure volume (concrete, gravel). Ordering 10 cubic yards when you needed 10 square yards of material results in an enormous overorder.
- ✗Forgetting that water volume and concrete volume are different — a form that holds 10 cubic feet of water holds 10 cubic feet of concrete, but concrete weighs 2.4 times more. Structural forms must be designed for the weight of concrete, not just its volume.
- ✗Calculating the volume of a hollow cylinder (pipe) without subtracting the wall thickness — the interior volume of a 12-inch outer diameter pipe with 1-inch walls uses radius 5 inches (interior), not 6 inches (exterior).
- ✗Not converting between metric and imperial units when mixing measurement sources — a project with some measurements in feet and others in meters requires explicit conversion before multiplying.
Volume Calculator Overview
Volume is the measure of three-dimensional space enclosed within a boundary — the calculation that determines how much concrete, soil, water, gravel, or other material fills or occupies any given space. Every bulk material order in construction and landscaping ultimately reduces to a volume calculation, typically converted to cubic yards for ordering purposes. Understanding which formula applies to which shape, and how to convert between units, is essential for accurate material estimation.
Rectangular box volume:
Volume = Length × Width × Height
EX: Planter box 8 ft × 3 ft × 1.5 ft deep → Volume = 36 ft³ ÷ 27 = 1.33 yd³ of soil neededCylinder volume — pipes, tanks, post holes, sonotubes:
Volume = π × r² × Height | where r = diameter ÷ 2
EX: Round post hole 12 in diameter, 3 ft deep → r = 0.5 ft → Volume = 3.14159 × 0.25 × 3 = 2.36 ft³ → ÷27 = 0.087 yd³ per holeVolume formulas for common construction shapes:
| Shape | Formula | Variables | Common Use |
|---|---|---|---|
| Rectangular box | L × W × H | Length, Width, Height | Slabs, footings, beds, tanks |
| Cylinder | π × r² × H | Radius, Height | Post holes, columns, tanks |
| Cone | ⅓ × π × r² × H | Radius, Height | Gravel piles, stockpiles |
| Sphere | 4/3 × π × r³ | Radius | Tanks, domes |
| Triangular prism | ½ × b × h × L | Triangle base, height, Length | Triangular drainage channels |
| Trapezoidal prism | ½ × (a+b) × h × L | Two parallel sides, Height, Length | Irrigation channels, earthworks |
| Unit | Cubic Feet | Cubic Yards | Gallons | Liters |
|---|---|---|---|---|
| 1 cubic foot | 1 | 0.037 | 7.481 | 28.317 |
| 1 cubic yard | 27 | 1 | 201.97 | 764.6 |
| 1 gallon (US) | 0.134 | 0.00495 | 1 | 3.785 |
| 1 cubic meter | 35.315 | 1.308 | 264.2 | 1,000 |
Frequently Asked Questions
Divide cubic feet by 27. This is because one cubic yard = 3 ft × 3 ft × 3 ft = 27 cubic feet. Example: 81 cubic feet ÷ 27 = 3 cubic yards. To go the other direction, multiply cubic yards by 27: 3 yd³ × 27 = 81 ft³. This conversion is used constantly in concrete, gravel, and soil ordering — suppliers quote prices and minimums in cubic yards, while most people measure their projects in feet.
Standard single-axle dump truck: 5–6 cubic yards. Tandem-axle dump truck: 10–12 cubic yards. Tri-axle (most common for concrete and gravel): 13–15 cubic yards. Transfer dump trucks: up to 20+ cubic yards. For residential projects, most batch plants and aggregate suppliers deliver via tri-axle at 13–14 yards. If your project requires less than 5 yards, you may face a short-load fee or need to arrange pick-up rather than delivery.
Divide the shape into basic geometric components: rectangular boxes, cylinders, cones, or wedges. Calculate the volume of each component separately using the appropriate formula. Sum all component volumes for the total. For excavations with sloped walls: calculate the average cross-section area (midpoint method) and multiply by the length. For very complex shapes: use the prismatoid formula V = L/6 × (A₁ + 4Am + A₂) where A₁ and A₂ are end areas and Am is the middle cross-section area.
Volume = 4/3 × π × r³, where r is the radius. For a sphere with diameter 6 feet (r = 3 ft): Volume = 4/3 × 3.14159 × 27 = 113.1 ft³ = 4.19 yd³. A sphere 10 feet in diameter holds approximately 523.6 ft³ = 19.4 yd³. Sphere volume is used for water tank capacity, dome calculations, and stockpile estimation when material has been piled into a roughly spherical shape.
For a cylindrical tank: Volume = π × r² × height. For a 4-foot diameter, 5-foot tall tank: r = 2 ft, Volume = 3.14159 × 4 × 5 = 62.83 ft³ × 7.481 gal/ft³ = 470 gallons. For a rectangular tank: Length × Width × Height × 7.481 gallons/ft³. For an above-ground pool 18 feet in diameter, 4 feet deep: Volume = π × 81 × 4 = 1,017.9 ft³ × 7.481 = 7,615 gallons. Water weighs 8.34 lbs per gallon, so this pool contains approximately 63,500 lbs (31.7 tons) of water.
Volume = ⅓ × π × r² × height. A cone is exactly one-third the volume of a cylinder with the same base and height. For a cone-shaped gravel pile 8 feet in diameter and 4 feet tall: r = 4 ft, Volume = ⅓ × 3.14159 × 16 × 4 = 67.0 ft³ = 2.48 yd³. This formula is useful for estimating the volume of material in a stockpile, which often approximates a cone or a partial sphere, for inventory and ordering purposes.