Cube Volume Calculator
Two-way cube volume calculator: side length to volume (V = s³), or volume to side length with the cube root. Bonus outputs: surface area (6s²), space diagonal (s√3), conversions to liters, gallons and cubic feet, plus a labeled cube diagram.
Cube Volume Calculator
Volume
| Unit | Volume |
|---|
| Property | Formula | Value |
|---|---|---|
| Surface area | 6s² | |
| Space diagonal | s√3 |
Side length (cube root of volume)
| Property | Value |
|---|---|
| Surface area (6s²) | |
| Space diagonal (s√3) |
Worked Examples (Step by Step)
Example 1: side 5 cm
V = 5³ = 125 cm³ = 0.125 L. Surface area = 6 × 5² = 150 cm². Space diagonal = 5 × √3 = 8.6603 cm.
Example 2: side 2 m
V = 2³ = 8 m³ = 8000 L = 2113.3764 US gal. Surface area = 6 × 2² = 24 m². Space diagonal = 2 × √3 = 3.4641 m.
Example 3: side 10 in
V = 10³ = 1000 in³ = 16.3871 L = 4.3290 US gal. Surface area = 6 × 10² = 600 in². Space diagonal = 10 × √3 = 17.3205 in.
Example 4: volume 27 m³ (reverse)
s = ³√27 = 3 m. Surface area = 6 × 3² = 54 m². Space diagonal = 3 × √3 = 5.1962 m.
Cube Formulas Reference
| Property | Formula | Notes |
|---|---|---|
| Volume | V = s³ | Side length cubed |
| Side from volume | s = ³√V | Cube root of volume |
| Surface area | SA = 6s² | Six square faces |
| Space diagonal | d = s√3 | Corner to opposite corner through center |
| Face diagonal | f = s√2 | Diagonal of one square face |
Unit Conversion Factors Used
| Conversion | Factor |
|---|---|
| 1 m³ | 1000 L exactly |
| 1 m³ | 264.1721 US gal |
| 1 m³ | 219.9692 imperial gal |
| 1 m³ | 35.3147 ft³ |
| 1 m³ | 61023.7441 in³ |
| 1 US gal | 231 in³ exactly |
Cube Volume FAQs
What is the formula for the volume of a cube?
The volume of a cube is V = s cubed = s x s x s, where s is the side length. For example, a cube with side 5 cm has volume 5 x 5 x 5 = 125 cm3.
How do I find the side length of a cube from its volume?
Take the cube root of the volume: s = cube root of V. For example, a cube with volume 27 m3 has side length cube root of 27 = 3 m.
What is the surface area of a cube?
Surface area is SA = 6 x s squared, the area of one face (s squared) times six faces. A cube with side 5 cm has surface area 6 x 25 = 150 cm2.
What is the space diagonal of a cube?
The space diagonal is d = s x square root of 3, running from one corner of the cube to the opposite corner through the center. For a 2 m cube it is 2 x 1.7321 = 3.4641 m.
How many liters are in a cubic meter?
One cubic meter equals exactly 1000 liters. A cube with side 2 m has volume 8 m3, which is 8000 liters or 2113.3764 US gallons.
How do I convert cubic inches to gallons?
Divide cubic inches by 231 to get US gallons, because 1 US gallon is defined as exactly 231 in3. For example, 1000 in3 = 16.3871 liters = 4.3290 US gallons.
What is the difference between a cube and a rectangular box?
A cube is a box with all three edges equal, so V = s cubed. A general rectangular box has three different edges and V = length x width x height.
What are real-world uses of cube volume calculations?
Cube volume math is used for shipping boxes, water tank capacity, concrete and soil fill, packaging design, storage planning, and fish tank sizing.
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