Find volume from side length
If a = 4 cm, then V = 4³ = 64 cm³. The surface area is S = 6 × 4² = 96 cm².
Cube Calculator: Volume, Surface Area, and Diagonal
Diagram & Inputs
Tip: Enter any one value. If you provide multiple values, the calculator checks whether they describe the same cube.
Results
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How the Cube Calculator Works
A cube is a regular hexahedron with all edges the same length a. From that single measure you can compute surface area, volume, face area, lateral area, total edge length, face diagonal, and space diagonal.
Each input has its own unit. Side length, face diagonal, and space diagonal use length units; surface area uses squared units; volume uses cubic or liquid capacity units. The calculator converts everything internally before deriving the results in your selected output unit.
- From S:
a = √(S/6) - From V:
a = ³√V - From face diagonal f:
a = f/√2 - From d:
a = d/√3
Common volume conversions include liters, milliliters, cubic inches, cubic feet, and US gallons. If you enter multiple rounded values, a small mismatch can trigger a warning even when the values are practically close.
Cube Formulas
| Known value | Formula for edge a | Derived results |
|---|---|---|
Side length a |
a |
S = 6a², V = a³, f = a√2, d = a√3 |
Volume V |
a = ³√V |
S = 6a², face area = a², total edge length = 12a |
Surface area S |
a = √(S/6) |
V = a³, lateral area = 4a², diagonals f = a√2, d = a√3 |
Face diagonal f |
a = f/√2 |
S = 6a², V = a³, space diagonal d = a√3 |
Space diagonal d |
a = d/√3 |
S = 6a², V = a³, face diagonal f = a√2 |
Additional measurements: base or face area = a², lateral area = 4a², total edge length = 12a, and surface-area-to-volume ratio = S/V = 6/a.
Common pitfalls: mixing units between inputs, entering negative values, or rounding too early. If you see an inconsistency warning, double-check your unit labels.
Accuracy Note
Formulas used: S = 6a², V = a³, f = a√2, d = a√3, a = √(S/6), a = ³√V, a = f/√2, and a = d/√3.
Calculations run in your browser. Last reviewed: June 9, 2026. Source note: formulas follow standard Euclidean geometry for a cube.
Worked Examples
Find side length from volume
If V = 125 cm³, then a = ³√125 = 5 cm. The face diagonal is 5√2 = 7.07 cm.
Find side length from surface area
If S = 150 in², then a = √(150/6) = √25 = 5 in. The volume is 125 in³.
Find diagonals from side length
If a = 10 m, the face diagonal is 10√2 = 14.14 m and the space diagonal is 10√3 = 17.32 m.
Cube-shaped container
A cube container with side 20 cm holds 20³ = 8000 cm³, which is 8 L.
Cube Calculator: FAQs
How do you find the volume of a cube?
Cube volume is V = a³, where a is the side length. Enter the side length and the calculator cubes it in the selected unit.
How do you find the surface area of a cube?
Cube surface area is S = 6a² because a cube has six congruent square faces, each with area a².
How do you find side length from volume?
Use a = ³√V. The calculator converts the volume input to a consistent cubic unit, takes the cube root, then reports all measurements.
How do you find side length from surface area?
Use a = √(S/6). Divide the surface area by 6 to get one face area, then take the square root.
What is the difference between face diagonal and space diagonal?
The face diagonal crosses one square face and equals a√2. The space diagonal runs corner to corner through the cube interior and equals a√3.
Why do cube units become squared or cubed?
Surface area measures two-dimensional faces, so its units are squared. Volume measures three-dimensional space, so its units are cubed.
Does the calculator support rounded values?
Yes. You can set decimal places. If multiple rounded inputs do not exactly agree, the calculator may show a consistency warning while still giving useful derived results.
Does the calculator keep my data private?
Yes. Computation is entirely client-side; nothing is uploaded.