Math
Cube Calculator
A cube is fixed by its edge, so the cube calculator only needs one measurement.
Give it the edge, a face diagonal, the space diagonal, the surface area, or the volume, and it returns everything else, keeping the diagonals exact (edge 3 gives face diagonal 3√2 and space diagonal 3√3) and converting the volume to liters when you pick a real unit.
Surface area is in square units, volume in cubic units, the rest are lengths.
Pick the unit your measurements use. Area is reported in square units and volume in cubic units.
Try an example
Result
Volume
—
- Edge
- —
- Surface area
- —
- Face diagonal
- —
- Space diagonal
- —
- One face
- —
- Inscribed / circumscribed sphere radius
- —
More details (1 more)
- Capacity
- —
Student quick launch
Grade planning, algebra checks, and formulas students reach for most.
Study path
Use this calculator with
Follow these when you want the formula behind the answer, a short lesson, or nearby tools in the same topic.
What the cube calculator solves
A cube is fixed by its edge, so the cube calculator only needs one measurement. Give it the edge, a face diagonal, the space diagonal, the surface area, or the volume, and it returns everything else, keeping the diagonals exact (edge 3 gives face diagonal 3√2 and space diagonal 3√3) and converting the volume to liters when you pick a real unit.
Formula
How to use it
- Choose the cube measurement you know and enter it.
- Pick a unit; surface area and volume get square and cubic labels, and volume converts to liters.
- Read the edge, volume, surface area, both diagonals, and the sphere radii.
How to read the answer
The face diagonal crosses one square face (s√2); the space diagonal runs corner to opposite corner through the middle (s√3). The inscribed sphere touches all six faces (radius s/2) and the circumscribed sphere passes through all eight corners (radius s√3/2).
Common mistakes and edge cases
- Confusing the face diagonal with the space diagonal — the space diagonal is longer (√3 vs √2 times the edge).
- Finding the edge from surface area without dividing by 6 first: s = sqrt(SA/6).
- Using the square root instead of the cube root when going from volume to edge.
- Zero or negative measurements cannot form a cube.
Worked examples
Edge 3
Volume
27
Volume 1000 cm³ (a liter)
Volume
1,000
Surface area 150 in²
Volume
125
Face diagonal 5√2 ≈ 7.0711
Volume
125
Space diagonal 5√3 ≈ 8.6603
Volume
125
Decimal edge 2.5 m
Volume
15.625
Negative volume (impossible)
Volume
Error
Frequently asked questions
What is the volume of a cube?+
Edge cubed: V = s³. A cube with 3 cm edges holds 27 cm³. Going backward, the edge is the cube root of the volume.
What is the surface area of a cube?+
Six identical square faces: SA = 6s². Edge 5 gives 6 × 25 = 150 square units.
How long is the diagonal of a cube?+
The space diagonal (corner to opposite corner) is s√3 ≈ 1.732s. The diagonal of one face is s√2 ≈ 1.414s.
How do I find the edge from the volume?+
Take the cube root: s = ∛V. Volume 1000 gives edge 10; volume 50 gives about 3.684.
What sphere fits inside a cube?+
The inscribed sphere has diameter equal to the edge, so its radius is s/2. The sphere through the corners has radius s√3/2.
How many liters is a cube?+
Convert the volume: 1 L = 1000 cm³, so a 10 cm cube is exactly 1 liter. The calculator does this when you choose a real unit.
About this calculator
- Written by
- mathcheck editorial team
- Last reviewed
- September 4, 2026
Method
- Uses the values entered by the user and stable formulas documented on the page.
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Last updated: September 4, 2026