A cube is the simplest three-dimensional solid: six identical square faces, twelve equal edges, and eight corners. Despite that simplicity, its volume comes up constantly in everyday life — sizing a shipping box, working out how much storage a cubical freezer offers, ordering concrete for a cubical form, or checking how many cubic feet of sand a cubical sandbox holds. This cube volume calculator takes a single edge length and returns the volume, the area of one face, the total surface area, and the space diagonal across the inside of the cube.
Type any edge length into the box and every figure below updates instantly. Because a cube has no separate width, depth, or height — they are all the same number — you only have to measure one edge.
How to Use
- Measure the edge length of the cube. Pick up a ruler or tape and measure one side; every edge of a true cube is identical, so a single measurement is enough.
- Enter that number in the Edge Length (Side) field. Use the same units everywhere — if you measure in centimeters, your result is in cubic centimeters; if you measure in feet, your result is in cubic feet.
- Set Decimal Places to control rounding on every output (use 0 for whole numbers, 2 for everyday use).
- Set Fill Percentage to the share of the cube that is occupied — 100 for a full empty-to-the-brim cube, 50 for a cube half-full of water or cargo. The Filled Volume result applies this percentage to the total volume.
- Read the Volume — the highlighted result. This is how much interior space the cube holds, in cubic units.
- Check Total Surface Area if you are painting, wrapping, or sheet-material estimating: it tells you the combined area of all six faces.
- Use the Space Diagonal when you need to know the longest straight line you can fit inside the cube — for example, the longest rod that will slide into a cubical shipping carton.
The rule that ties it all together is V = s³: you take the edge length, multiply it by itself twice, and the cube of that number is the volume.
The Cube Formulas
For a cube whose edge length is s:
- Volume: V = s × s × s = s³
- Area of one face: A = s²
- Total surface area: SA = 6 × s² (six square faces)
- Space diagonal: d = s × √3
The √3 comes from the Pythagorean theorem applied twice. First the diagonal of one square face is s√2, then that diagonal, the edge, and the space diagonal form a new right triangle: d² = (s√2)² + s² = 2s² + s² = 3s², so d = s√3 ≈ s × 1.732.
Worked example on a cube with edge 5: the volume is 5 × 5 × 5 = 125 cubic units, each face is 5 × 5 = 25 square units, the total surface area is 6 × 25 = 150 square units, and the space diagonal is 5 × 1.732 ≈ 8.66 units.
Real-World Uses
Knowing the cube's volume turns abstract geometry into practical decisions. A cubical moving box that measures 24 inches on each edge holds 24³ = 13,824 cubic inches, or 8 cubic feet. If a courier charges by the cubic foot at roughly $0.60 per ft³, that box costs about $4.80 to ship — so comparing box sizes directly compares shipping cost. In the kitchen, a cubical storage container that is 20 cm on each edge holds exactly 8 liters, because 1 liter is 1,000 cm³.
The surface area is just as useful. A cubical planter box 1 meter on a side has 6 m² of exterior to paint. A cube that is half filled with water reaches 50% of its height, but because the cross-section stays square, it holds exactly (½)³ = 12.5% of its total volume — a reminder that volume scales with the cube, not the edge length.
Examples
Example 1 — A standard moving box. A cubical shipping carton is 24 in (2 ft) on each edge. Its volume is 2³ = 8 cubic feet. At a typical courier rate of $0.60 per cubic foot, filling it costs roughly $4.80 before weight. Its space diagonal is 2 × 1.732 ≈ 3.46 ft, so the longest rigid object you can lay diagonally inside is about 3 ft 5 in.
Example 2 — A cubical storage tank. A tank built as a cube with a 100 cm edge holds 100³ = 1,000,000 cm³ = 1,000 liters (one cubic meter) of water. If the tank is filled to 75% of its height, it holds (0.75)³ ≈ 42% of its total capacity, not 75% — because volume scales with the cube, not the edge length. Setting Fill Percentage to 42 on this cube gives a Filled Volume of about 420 liters, which is the number to use for pump or drain sizing.
Example 3 — Scaling up. Doubling the edge does not double the volume — it multiplies it by 2³ = 8. A cube of side 2 holds 8 units³ while a cube of side 1 holds 1 unit³. Going from side 5 to side 10 grows the volume from 125 to 1,000, an 8× jump, even though the edge only doubled. This cubic scaling is the single most important thing to remember when estimating materials or shipping cost.
FAQ
What is the formula for the volume of a cube?
The volume of a cube is V = s³, where s is the length of any edge. Multiply the edge length by itself, then by itself again: s × s × s. For an edge of 5, the volume is 5 × 5 × 5 = 125 cubic units.
How do I find the surface area of a cube?
A cube has six identical square faces, each of area s². The total surface area is SA = 6 × s². For edge 5, each face is 25 square units, so the total is 6 × 25 = 150 square units.
What is the space diagonal of a cube?
The space diagonal is the longest straight line inside the cube, running from one corner to the opposite corner through the interior. It equals s × √3 ≈ s × 1.732. For edge 5 it is about 8.66. This is not the same as the diagonal of a single face, which is s × √2.
Can I use this for a rectangular box that is not a cube?
No. A rectangular box with different length, width, and height uses V = l × w × h. This calculator assumes l = w = h = s. If your box has unequal dimensions, use a rectangular-prism or generic volume calculator instead.
How do I convert cubic inches to cubic feet?
There are 12 inches in a foot, so one cubic foot is 12³ = 1,728 cubic inches. Divide your cubic-inch volume by 1,728 to get cubic feet. For example, a 24-inch cube holds 13,824 ÷ 1,728 = 8 cubic feet.
Why does doubling the edge multiply the volume by 8?
Volume scales with the cube of the linear dimension. If the edge doubles to 2s, the new volume is (2s)³ = 8s³, eight times the original. The surface area only grows by a factor of 4 (because it scales with s²), which is why larger cubes hold proportionally more volume per unit of surface area.
What units should I use?
Any consistent unit works. Measure the edge in centimeters and you get cubic centimeters; measure in feet and you get cubic feet; measure in meters and you get cubic meters. Just keep the same unit for the edge, and the volume and surface area will be in the corresponding cubic and square units.
Disclaimer
This cube volume calculator is provided for informational purposes only and does not constitute engineering, architecture, or trade advice. Results are based on the standard geometry formulas V = s³, SA = 6s² and d = s√3 applied to the edge length you enter. Always double-check critical measurements and confirm quantities with a qualified professional before ordering materials or constructing anything.