How to use the cube and box volume calculator
- Under Shape pick Cube if every edge is the same length, or Box (cuboid) if the sides differ.
- Choose the Unit of length. Inches are selected to start. Use one unit for every side.
- For a cube, type the Edge length (s). For a box, type the Length (L), Width (W) and Height (H), the three edges that meet at one corner, in any order.
- Read the Volume, the same volume in cubic feet, cubic yards, liters, US gallons and cubic meters, then the surface area and the diagonals.
The formulas
- Cube: V = s³, surface area = 6s², space diagonal = s√3, face diagonal = s√2.
- Box (rectangular prism): V = L × W × H, surface area = 2(LW + WH + LH), space diagonal = √(L² + W² + H²).
- Conversions: 1 cubic foot = 1,728 cubic inches, 1 cubic yard = 27 cubic feet, and 1 US gallon = 231 cubic inches = 3.785411784 liters (NIST SP 811, Appendix B.8).
These match the MathWorld cube entry and its cuboid entry.
Worked example
The calculator opens on Cube with s = 5 inches. V = 5³ = 125 in³, which is 0.072338 cubic feet, 0.00267918 cubic yards, 2.0484 liters or 0.541126 US gallons. The surface area is 6 × 25 = 150 in², the space diagonal is 8.6603 in and the face diagonal is 7.0711 in. In Box (cuboid) mode the starting 10 × 6 × 4 box gives 240 in³, a surface area of 248 in² and a space diagonal of 12.3288 in.
Limits and edge cases
- To find how much a box holds, use its inside measurements, so subtract the wall thickness from each side.
- Every number must be greater than 0 and at most 1,000,000,000,000. Thousands commas are fine; use a period for decimals. Results show up to 4 decimals.
- For soil, mulch or gravel, the Cubic yards row is the number suppliers sell by. For a poured slab, the concrete calculator adds waste and bag counts.
- Round shapes are on the cylinder volume calculator and the sphere volume calculator. Flat footprints are on the rectangle area calculator, and the volume converter covers units that are not listed.
Cube and box volume FAQ
How do I find the volume of a box in cubic feet?
Convert each side to feet and multiply, or multiply in inches and divide by 1,728, because a cubic foot is 12 × 12 × 12 inches. A box 12 by 10 by 8 inches has 12 × 10 × 8 = 960 cubic inches, and 960 ÷ 1,728 = 0.555556 cubic feet.
What is the difference between a cube and a rectangular prism?
A cube is a rectangular prism whose edges are all the same length. A box, also called a cuboid or rectangular prism, can have three different edges. The box formula L × W × H becomes s³ when all three equal s.
How do I find the edge of a cube from its volume?
Take the cube root: s = ∛V. A cube of 125 cubic inches has an edge of 5 inches. For other volumes use the x^(1/3) key on a scientific calculator, for example 100^(1/3) = 4.6416.
How many cubic yards is a cube or box?
Divide the volume in cubic feet by 27, because a cubic yard is 3 × 3 × 3 feet. A cube 3 feet on each side is 27 cubic feet, exactly 1 cubic yard. Pick Feet, enter 3, and the Cubic yards row shows 1.
How do I find the longest straight line that fits inside a box?
That is the space diagonal, √(L² + W² + H²). For a 10 by 6 by 4 box it is √152 = 12.3288. For a cube it is s × √3, so the starting 5-inch cube has a space diagonal of 8.6603 inches.
Sources: Wolfram MathWorld, Cube; Wolfram MathWorld, Cuboid; NIST Special Publication 811, Appendix B.8.