Volume Calculator – Rectangular Prism, Cylinder, Sphere & Cone

What is a volume calculator?

A volume calculator computes how much 3D space a solid shape takes up. Pick the shape, enter the required dimensions in any common unit, and the calculator runs the right formula and returns the volume in cubic units. This calculator covers the six shapes you meet most often in geometry class and in everyday measurement: rectangular prism, cube, cylinder, sphere, cone, and pyramid.

How the volume calculator works

Pick a shape, enter the dimensions, and the calculator:

• Applies the volume formula for the chosen shape.
• Reports the volume in the cubic unit that matches your input (in³, ft³, yd³, cm³, or m³).
• Converts the result to the other cubic units that differ from it, using the exact factors below.
• Shows the formula, substitutes your numbers into it, and walks through the arithmetic one step at a time.

To read about the formulas themselves rather than run one, see the volume formula guide.

Volume formulas for common shapes

• Rectangular prism: V = L × W × H
• Cube: V = s³
• Cylinder: V = π × r² × h
• Sphere: V = (4/3) × π × r³
• Cone: V = (1/3) × π × r² × h
• Pyramid (rectangular base): V = (1/3) × base length × base width × h

All formulas multiply three dimensions, so the result is always in cubic units. The radius r in the cylinder, sphere, and cone formulas is half the diameter of the circular base or sphere.

Cubic unit conversions

• 1 cubic foot = 1,728 cubic inches (exact)
• 1 cubic yard = 27 cubic feet (exact)
• 1 cubic meter = 1,000,000 cubic centimeters (exact)
• 1 cubic foot = 0.028316846592 cubic meters (exact)
• 1 cubic meter ≈ 35.3147 cubic feet

The first four are exact rather than rounded because the inch, foot, and yard are themselves defined exactly in metres: 1 inch = 0.0254 m, 1 foot = 0.3048 m, and 1 yard = 0.9144 m. Cubing those definitions gives cubic factors that are exact as well. The calculator converts every result through metres using them, which removes the error that a truncated conversion constant used to introduce. The arithmetic itself still runs in double-precision floating point, and displayed figures are rounded to six significant digits for presentation.

Assumptions and limitations

• Every shape is treated as a perfect, solid geometric figure. Real objects have wall thickness, seams, rounded corners, and manufacturing tolerance that this math does not model.
• The cone and pyramid diagrams show a right solid, with the apex directly above the centre of the base, and h is the perpendicular height from the base plane to the apex. The formula is not limited to that case: an oblique cone or pyramid with the same base area and the same perpendicular height has the same volume. What changes is the slant height, which is longer than h and is never the value to enter here.
• The pyramid mode assumes a rectangular base. For any other base shape, compute the base area separately and use V = (1/3) × base area × h.
• All dimensions must share one unit. The calculator does not mix units within a single calculation.
• Results are computed in double-precision floating point and displayed to six significant digits. No intermediate value is rounded before the final multiplication, so the only rounding is for presentation. Floating point still carries its usual tiny representation error, which is far below the precision shown.
• Volume is not capacity. A container’s internal capacity uses its inside dimensions, not its outside ones.

Volume vs other project calculators

The volume calculator is the right tool for general 3D shape volume in any unit. For specific project workflows, dedicated calculators add the extras you actually need when ordering materials:

• The cubic feet calculator focuses on box-shaped volumes (storage, shipping, refrigerators) in cubic feet first.
• The cubic yard calculator focuses on landscaping and concrete volumes in cubic yards, with weight estimates.
• The concrete calculator adds the number of bags or yards of mixed concrete you need for slabs, footings, and columns.
• The gravel calculator converts cubic yards of gravel into tons for delivery.
• The square footage calculator covers 2D area (floors, walls, yards), not 3D volume.

Use the volume calculator on this page for the pure math of any 3D shape; use the project calculators when you also need bags, tons, or area-specific output.

Worked examples

• Box 10 × 8 × 6 ft: V = 10 × 8 × 6 = 480 cubic feet.
• Cube with side 5 ft: V = 5³ = 125 cubic feet.
• Cylinder r = 5 ft, h = 10 ft: V = π × 25 × 10 ≈ 785.40 cubic feet.
• Sphere r = 5 in: V = (4/3) × π × 125 ≈ 523.60 cubic inches.
• Cone r = 5 ft, h = 10 ft: V = (1/3) × π × 25 × 10 ≈ 261.80 cubic feet.
• Pyramid 6 × 4 × 9 ft: V = (1/3) × 6 × 4 × 9 = 72 cubic feet.

Common mistakes

• Using diameter where the formula calls for radius. The cylinder, sphere, and cone formulas use radius, which is half the diameter.
• Forgetting the 1/3 factor on cones and pyramids. A cone or pyramid holds exactly one third of the cylinder or prism with the same base and height.
• Mixing units within a single calculation. All dimensions must use the same unit before multiplying.
• Confusing area with volume. Area is 2D and uses square units; volume is 3D and uses cubic units.
• Treating diameter as the base width for a pyramid. The pyramid formula uses base length and base width, not radius.

Related tools

• Volume formula guide for the formulas, worked examples, and why cones and pyramids carry a one-third factor.
• Surface area formula guide for the outside-area formulas that pair with these solids.
• Surface area calculator for the outside surface of the same 3D shapes.
• Volume converter for converting between mL, L, fl oz, cup, gallon, ft³, m³, and more.
• Cubic feet calculator for box volume in cubic feet first.
• Cubic yard calculator for landscaping and concrete volumes.
• Square footage calculator for floor and wall area.
• Concrete calculator for slab, footing, and column estimates with bag counts.
• Gravel calculator for cubic yards and tons of gravel.
• Mulch calculator for cubic yards and bag-count estimates for mulch.
• All education calculators and all home calculators.

Sources

• Unit conversions: NIST Special Publication 811, Appendix B.9 lists inch → metre (2.54 E−02), foot → metre (3.048 E−01), and yard → metre (9.144 E−01) as exact conversion factors. Those three definitions generate every cubic factor this page uses.
• One-third factor for cones and pyramids: Euclid, Elements, Book XII, Proposition 10 (cone and cylinder) and the corollary to Proposition 7 (pyramid and prism).